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Test

2026-07-19T13:49:45Z

Baixie01000a7：撤销Baixie01000a7（讨论）的修订版本3472

此页面为测试页面。任何人都可以随意修改此页面以便测试。

我死的好惨呀！我是时间过得真慢QQ，我的聚集地和大群都被踢出去了，其他群也不要了，没有任何一个要我了，还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来

孩子们这并不好像，谁叫你还我命来的😂

=== 编写技巧 ===

* 行内代码块：<syntaxhighlight lang="text"><code>xxx</code></syntaxhighlight>效果是这样：<code>xxx</code>。
* 在列表里换行：使用 <syntaxhighlight lang="text"> </syntaxhighlight>效果是这样： 第一行； 第二行。
* 在列表里嵌套列表：无序列表使用<syntaxhighlight lang="text">
<ul> <li>123</li> <li>456</li> </ul>
</syntaxhighlight>效果是这样：<ul><li>123</li><li>456</li></ul>有序列表使用<syntaxhighlight lang="text">
<ol> <li>123</li> <li>456</li> </ol>
</syntaxhighlight>效果是这样：
<ol><li>123</li><li>456</li></ol>于是可以<ul> <li>awa<ul> <li>114514<ul> <li>3.1415926<ul> <li>123</li> <li>456</li> </ul></li> <li>789</li> </ul></li> <li>2.71828</li> </ul></li> <li>qwerty</li> </ul>
<ol> <li>awa<ol> <li>114514<ol> <li>3.1415926<ol> <li>123</li> <li>456</li> </ol></li> <li>789</li> </ol></li> <li>2.71828</li> </ol></li> <li>qwerty</li> </ol>
* 分界线：使用 <code>----</code>。效果是这样：

----

这句话有7个字

<math>\varnothing,\emptyset</math>，
$\varnothing,\emptyset$
LaTeX公式<code>\varnothing,\emptyset</code>用不同渲染方式的结果

<math display="block">\begin{aligned}
f(x)\;&=(a+b+1)/2-x\\
&=(a+2x-1-a+f(2x-1-a)+1)/2-x\\
&=f(2x-1-a)/2\\
&=f(2x-1-(x-1+f(x-1)))/2\\
&=f(x-f(x-1))/2
\end{aligned}</math>

111

$ G(64)=\left. \begin{matrix} 3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \cdots \uparrow}3 \\3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \uparrow}3 \\ \underbrace{\qquad \quad \vdots \qquad \quad} \\3\underbrace{\uparrow \uparrow \cdots \cdots \uparrow}3 \\3\uparrow \uparrow \uparrow \uparrow3\end{matrix} \right \} \text{64 layers} $

<math>\unicode{64}</math>

<math>\varphi(\#,(\alpha+1)\text{@}(\beta+1),0\text{@}0)[0]=0</math>

<math>\text{@}</math>

[k]

$\alpha\text{@}\beta$

其实还可以有个更简单的做法，\alpha{@}\beta = $\alpha{@}\beta$

[[[a]]]

我们可以使用<code>\hspace</code>和<code>\raise</code>来微调LaTeX中的字符位置：
$\LaTeX$''（直接使用''<code>\LaTeX</code>''的版本）''
${L^{\hspace{-4.5px}\raise{-2.5px}A}
\hspace{-3px}T\hspace{-2px}\raise{-3px}E\hspace{-1.5px}X}$''（使用以上两种命令微调的模仿版本）''

<nowiki>\</nowiki>(\alpha\text{@}\beta<nowiki>\</nowiki>) = $\alpha\text{@}\beta$

{| class="wikitable"
|+ 标题文本
|-
! 标题文本 !! 标题文本 !! 标题文本
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|}

{| class="wikitable"
|+ 标题文本
|-
! 标题文本 !! 标题文本 !! 标题文本
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|}

{| class="wikitable"
|+ 标题文本
|-
! 标题文本 !! 标题文本 !! 标题文本
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|}

{a}

<code>我是code</code>

<pre>我是pre</pre>

我是美丽的span

<a href='https://baidu.com'>危险的代码是不被允许的</a>

click me!

666

$\alpha @\beta$

<blockquote>
我是猫娘。喵喵喵喵
</blockquote>

<blockquote>单行引言</blockquote>

bgcisred

[[高德纳箭头|↑]]

<iframe>
src="https://expander.googology.top/index.html"
width="100%"
height="500px"
frameborder="0"
</iframe>

=== 这是一级标题 ===

==== 这是二级标题 ====
这是公式 $\alpha\times\beta$

''撒反对''

说说不可说】(1)

--------------------------------------------------------------------

　　人们的对话中，「不可说」指的是「不可以说出来」的意思，但是在佛
经中，不可说的意思并不一定是这样，世尊所说的佛经更不是指这个意思。
如果它是指不可以说出来的话，那麽全部的佛经就是一部「大妄语百科」了。

但是将「不可说」解释为「不可以说出来」的意思，并不是现代人的专
利，古人解经，也常把它作这样的解释，造成後人将佛经解释成玄密的经典，
一切的不合理之处都当作「不可说」来处理。

世尊的确说过许多的不可说，如:《华严经》
「不可言说不可说，充满一切不可说，不可言说诸劫中，说不可说不可尽，
....
於一微细毛端处，有不可说诸普贤，....一毛端处所有刹，其数无量不可
　说..」在第四十五卷中，世尊一口气说了将近四百个不可说。

《地藏菩萨本愿经》【忉利天宫神通品】「尔时，十方无量世界不可
　说不可说一切诸佛，及大菩萨摩诃萨，皆来集会，赞叹释迦牟尼佛．．」
这里用了两个不可说。

《小般若经》【深功德品】「一切法不可说，须菩提，一切法空相不
可说．．」

其实「不可说」的意义是「数量大到无法用语言形容」的意思，并不
是指所说的主题「不能说」，如果是不能说，那麽上面这些经典就是「废
话大全」了。

世尊说法四十九年，探讨的主题遍及人类所有的疑问，从来没有一样
　是「不能说出来」的，不但他老人家自己说，更鼓励所有修行菩萨要为众　
生说呢。(参见《般若经》)

那麽，「不可说」倒底有多大，会大到语言法形容呢？我们试著来找
找看。

{| class="wikitable" border="0" cellpadding="1" cellspacing="1"
! scope="col" |
! scope="col" |A
! scope="col" |B
|-
|0
|1RB
1LA
 1CP
 114514
|1LA
|-
|1
|1LB
|1RB
|}
111

{| class="wikitable"
! 用户名
! 简介
|-
| style="width: 20%;" | 张三 || style="width: 80%; word-wrap: break-word;" | 这是一个非常长的简介文本，会自动换行以适应列宽。
|}

表格？

{| class="wikitable" style="width: 300px; overflow: hidden; text-overflow: ellipsis"
! 用户名
! 简介
|-
| 张三
| 这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。
|}

<blockquote>这里是一个孤立页面我不知道它为什么还在这里

就当作是gggwiki的一个彩蛋吧（</blockquote>

[https://2023largenumber.fandom.com/zh/wiki/%F0%9F%98%B0#articleComments/ 果糕]
果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！

<div id="guogao1">将以下代码放入控制台并回车，有“小惊喜”：</div><nowiki>(()=>{document.getElementById("guogao1").appendChild((()=>{let a = document.createElement("div");a.innerHTML = `<div class="fixed-btn"><a onclick="let b=document.createElement('div');b.innerHTML=\`<div id='guogao' style='transition: transform .5s ease-out;position: absolute;top:45%;left:50%;z-index: 9999999;transform: scale(1);cursor: pointer;-webkit-user-select: none;-moz-user-select: none;-ms-user-select: none;user-select: none;' onclick='this.remove()'>${decodeURI('%F0%9F%98%B0')}</div>\`;document.body.appendChild(b);setTimeout(() => {document.getElementById('guogao').style.transform='scale(45)'}, 50)" class="new" title="${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}">${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}</a></div>`;return a})());return (()=>{console.clear();return decodeURI('%E7%A5%9E%E7%A7%98%E6%8C%89%E9%92%AE%E5%87%BA%E7%8E%B0%EF%BC%81')})()})()

</nowiki>
[[分类:入门]]

Test

2026-07-19T13:15:31Z

Baixie01000a7：

此页面为测试页面。任何人都可以随意修改此页面以便测试。

=== 编写技巧 ===

* 行内代码块：<syntaxhighlight lang="text"><code>xxx</code></syntaxhighlight>效果是这样：<code>xxx</code>。
* 在列表里换行：使用 <syntaxhighlight lang="text"> </syntaxhighlight>效果是这样： 第一行； 第二行。
* 在列表里嵌套列表：无序列表使用<syntaxhighlight lang="text">
<ul> <li>123</li> <li>456</li> </ul>
</syntaxhighlight>效果是这样：<ul><li>123</li><li>456</li></ul>有序列表使用<syntaxhighlight lang="text">
<ol> <li>123</li> <li>456</li> </ol>
</syntaxhighlight>效果是这样：
<ol><li>123</li><li>456</li></ol>于是可以<ul> <li>awa<ul> <li>114514<ul> <li>3.1415926<ul> <li>123</li> <li>456</li> </ul></li> <li>789</li> </ul></li> <li>2.71828</li> </ul></li> <li>qwerty</li> </ul>
<ol> <li>awa<ol> <li>114514<ol> <li>3.1415926<ol> <li>123</li> <li>456</li> </ol></li> <li>789</li> </ol></li> <li>2.71828</li> </ol></li> <li>qwerty</li> </ol>
* 分界线：使用 <code>----</code>。效果是这样：

----

这句话有7个字

<math>\varnothing,\emptyset</math>，
$\varnothing,\emptyset$
LaTeX公式<code>\varnothing,\emptyset</code>用不同渲染方式的结果

<math display="block">\begin{aligned}
f(x)\;&=(a+b+1)/2-x\\
&=(a+2x-1-a+f(2x-1-a)+1)/2-x\\
&=f(2x-1-a)/2\\
&=f(2x-1-(x-1+f(x-1)))/2\\
&=f(x-f(x-1))/2
\end{aligned}</math>

111

$ G(64)=\left. \begin{matrix} 3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \cdots \uparrow}3 \\3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \uparrow}3 \\ \underbrace{\qquad \quad \vdots \qquad \quad} \\3\underbrace{\uparrow \uparrow \cdots \cdots \uparrow}3 \\3\uparrow \uparrow \uparrow \uparrow3\end{matrix} \right \} \text{64 layers} $

<math>\unicode{64}</math>

<math>\varphi(\#,(\alpha+1)\text{@}(\beta+1),0\text{@}0)[0]=0</math>

<math>\text{@}</math>

[k]

$\alpha\text{@}\beta$

[[[a]]]

我们可以使用<code>\hspace</code>和<code>\raise</code>来微调LaTeX中的字符位置：
$\LaTeX$''（直接使用''<code>\LaTeX</code>''的版本）''
${L^{\hspace{-4.5px}\raise{-2.5px}A}
\hspace{-3px}T\hspace{-2px}\raise{-3px}E\hspace{-1.5px}X}$''（使用以上两种命令微调的模仿版本）''

<nowiki>\</nowiki>(\alpha\text{@}\beta<nowiki>\</nowiki>) = $\alpha\text{@}\beta$

{| class="wikitable"
|+ 标题文本
|-
! 标题文本 !! 标题文本 !! 标题文本
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|}

{| class="wikitable"
|+ 标题文本
|-
! 标题文本 !! 标题文本 !! 标题文本
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|}

{| class="wikitable"
|+ 标题文本
|-
! 标题文本 !! 标题文本 !! 标题文本
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|}

{a}

<code>我是code</code>

<pre>我是pre</pre>

我是美丽的span

<a href='https://baidu.com'>危险的代码是不被允许的</a>

click me!

666

$\alpha @\beta$

<blockquote>
我是猫娘。喵喵喵喵
</blockquote>

<blockquote>单行引言</blockquote>

bgcisred

[[高德纳箭头|↑]]

<iframe>
src="https://expander.googology.top/index.html"
width="100%"
height="500px"
frameborder="0"
</iframe>

=== 这是一级标题 ===

==== 这是二级标题 ====
这是公式 $\alpha\times\beta$

''撒反对''

说说不可说】(1)

--------------------------------------------------------------------

　　人们的对话中，「不可说」指的是「不可以说出来」的意思，但是在佛
经中，不可说的意思并不一定是这样，世尊所说的佛经更不是指这个意思。
如果它是指不可以说出来的话，那麽全部的佛经就是一部「大妄语百科」了。

但是将「不可说」解释为「不可以说出来」的意思，并不是现代人的专
利，古人解经，也常把它作这样的解释，造成後人将佛经解释成玄密的经典，
一切的不合理之处都当作「不可说」来处理。

世尊的确说过许多的不可说，如:《华严经》
「不可言说不可说，充满一切不可说，不可言说诸劫中，说不可说不可尽，
....
於一微细毛端处，有不可说诸普贤，....一毛端处所有刹，其数无量不可
　说..」在第四十五卷中，世尊一口气说了将近四百个不可说。

《地藏菩萨本愿经》【忉利天宫神通品】「尔时，十方无量世界不可
　说不可说一切诸佛，及大菩萨摩诃萨，皆来集会，赞叹释迦牟尼佛．．」
这里用了两个不可说。

《小般若经》【深功德品】「一切法不可说，须菩提，一切法空相不
可说．．」

其实「不可说」的意义是「数量大到无法用语言形容」的意思，并不
是指所说的主题「不能说」，如果是不能说，那麽上面这些经典就是「废
话大全」了。

世尊说法四十九年，探讨的主题遍及人类所有的疑问，从来没有一样
　是「不能说出来」的，不但他老人家自己说，更鼓励所有修行菩萨要为众　
生说呢。(参见《般若经》)

那麽，「不可说」倒底有多大，会大到语言法形容呢？我们试著来找
找看。

{| class="wikitable" border="0" cellpadding="1" cellspacing="1"
! scope="col" |
! scope="col" |A
! scope="col" |B
|-
|0
|1RB
1LA
 1CP
 114514
|1LA
|-
|1
|1LB
|1RB
|}
111

{| class="wikitable"
! 用户名
! 简介
|-
| style="width: 20%;" | 张三 || style="width: 80%; word-wrap: break-word;" | 这是一个非常长的简介文本，会自动换行以适应列宽。
|}

表格？

{| class="wikitable" style="width: 300px; overflow: hidden; text-overflow: ellipsis"
! 用户名
! 简介
|-
| 张三
| 这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。
|}

<blockquote>这里是一个孤立页面我不知道它为什么还在这里

就当作是gggwiki的一个彩蛋吧（</blockquote>

[https://2023largenumber.fandom.com/zh/wiki/%F0%9F%98%B0#articleComments/ 果糕]
果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！果糕糕糕！
果糕糕糕！

<div id="guogao1">将以下代码放入控制台并回车，有“小惊喜”：</div><nowiki>(()=>{document.getElementById("guogao1").appendChild((()=>{let a = document.createElement("div");a.innerHTML = `<div class="fixed-btn"><a onclick="let b=document.createElement('div');b.innerHTML=\`<div id='guogao' style='transition: transform .5s ease-out;position: absolute;top:45%;left:50%;z-index: 9999999;transform: scale(1);cursor: pointer;-webkit-user-select: none;-moz-user-select: none;-ms-user-select: none;user-select: none;' onclick='this.remove()'>${decodeURI('%F0%9F%98%B0')}</div>\`;document.body.appendChild(b);setTimeout(() => {document.getElementById('guogao').style.transform='scale(45)'}, 50)" class="new" title="${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}">${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}</a></div>`;return a})());return (()=>{console.clear();return decodeURI('%E7%A5%9E%E7%A7%98%E6%8C%89%E9%92%AE%E5%87%BA%E7%8E%B0%EF%BC%81')})()})()

</nowiki>
[[分类:入门]]

Test

2026-07-19T13:14:45Z

Baixie01000a7：

此页面为测试页面。任何人都可以随意修改此页面以便测试。

我死的好惨呀！我是时间过得真慢QQ，我的聚集地和大群都被踢出去了，其他群也不要了，没有任何一个要我了，还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来

孩子们这并不好像，谁叫你还我命来的😂

=== 编写技巧 ===

* 行内代码块：<syntaxhighlight lang="text"><code>xxx</code></syntaxhighlight>效果是这样：<code>xxx</code>。
* 在列表里换行：使用 <syntaxhighlight lang="text"> </syntaxhighlight>效果是这样： 第一行； 第二行。
* 在列表里嵌套列表：无序列表使用<syntaxhighlight lang="text">
<ul> <li>123</li> <li>456</li> </ul>
</syntaxhighlight>效果是这样：<ul><li>123</li><li>456</li></ul>有序列表使用<syntaxhighlight lang="text">
<ol> <li>123</li> <li>456</li> </ol>
</syntaxhighlight>效果是这样：
<ol><li>123</li><li>456</li></ol>于是可以<ul> <li>awa<ul> <li>114514<ul> <li>3.1415926<ul> <li>123</li> <li>456</li> </ul></li> <li>789</li> </ul></li> <li>2.71828</li> </ul></li> <li>qwerty</li> </ul>
<ol> <li>awa<ol> <li>114514<ol> <li>3.1415926<ol> <li>123</li> <li>456</li> </ol></li> <li>789</li> </ol></li> <li>2.71828</li> </ol></li> <li>qwerty</li> </ol>
* 分界线：使用 <code>----</code>。效果是这样：

----

这句话有7个字

<math>\varnothing,\emptyset</math>，
$\varnothing,\emptyset$
LaTeX公式<code>\varnothing,\emptyset</code>用不同渲染方式的结果

<math display="block">\begin{aligned}
f(x)\;&=(a+b+1)/2-x\\
&=(a+2x-1-a+f(2x-1-a)+1)/2-x\\
&=f(2x-1-a)/2\\
&=f(2x-1-(x-1+f(x-1)))/2\\
&=f(x-f(x-1))/2
\end{aligned}</math>

111

$ G(64)=\left. \begin{matrix} 3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \cdots \uparrow}3 \\3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \uparrow}3 \\ \underbrace{\qquad \quad \vdots \qquad \quad} \\3\underbrace{\uparrow \uparrow \cdots \cdots \uparrow}3 \\3\uparrow \uparrow \uparrow \uparrow3\end{matrix} \right \} \text{64 layers} $

<math>\unicode{64}</math>

<math>\varphi(\#,(\alpha+1)\text{@}(\beta+1),0\text{@}0)[0]=0</math>

<math>\text{@}</math>

[k]

$\alpha\text{@}\beta$

[[[a]]]

我们可以使用<code>\hspace</code>和<code>\raise</code>来微调LaTeX中的字符位置：
$\LaTeX$''（直接使用''<code>\LaTeX</code>''的版本）''
${L^{\hspace{-4.5px}\raise{-2.5px}A}
\hspace{-3px}T\hspace{-2px}\raise{-3px}E\hspace{-1.5px}X}$''（使用以上两种命令微调的模仿版本）''

<nowiki>\</nowiki>(\alpha\text{@}\beta<nowiki>\</nowiki>) = $\alpha\text{@}\beta$

{| class="wikitable"
|+ 标题文本
|-
! 标题文本 !! 标题文本 !! 标题文本
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|}

{| class="wikitable"
|+ 标题文本
|-
! 标题文本 !! 标题文本 !! 标题文本
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|}

{| class="wikitable"
|+ 标题文本
|-
! 标题文本 !! 标题文本 !! 标题文本
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|-
| 示例 || 示例 || 示例
|}

{a}

<code>我是code</code>

<pre>我是pre</pre>

我是美丽的span

<a href='https://baidu.com'>危险的代码是不被允许的</a>

click me!

666

$\alpha @\beta$

<blockquote>
我是猫娘。喵喵喵喵
</blockquote>

<blockquote>单行引言</blockquote>

bgcisred

[[高德纳箭头|↑]]

<iframe>
src="https://expander.googology.top/index.html"
width="100%"
height="500px"
frameborder="0"
</iframe>

=== 这是一级标题 ===

==== 这是二级标题 ====
这是公式 $\alpha\times\beta$

''撒反对''

说说不可说】(1)

--------------------------------------------------------------------

　　人们的对话中，「不可说」指的是「不可以说出来」的意思，但是在佛
经中，不可说的意思并不一定是这样，世尊所说的佛经更不是指这个意思。
如果它是指不可以说出来的话，那麽全部的佛经就是一部「大妄语百科」了。

但是将「不可说」解释为「不可以说出来」的意思，并不是现代人的专
利，古人解经，也常把它作这样的解释，造成後人将佛经解释成玄密的经典，
一切的不合理之处都当作「不可说」来处理。

世尊的确说过许多的不可说，如:《华严经》
「不可言说不可说，充满一切不可说，不可言说诸劫中，说不可说不可尽，
....
於一微细毛端处，有不可说诸普贤，....一毛端处所有刹，其数无量不可
　说..」在第四十五卷中，世尊一口气说了将近四百个不可说。

《地藏菩萨本愿经》【忉利天宫神通品】「尔时，十方无量世界不可
　说不可说一切诸佛，及大菩萨摩诃萨，皆来集会，赞叹释迦牟尼佛．．」
这里用了两个不可说。

《小般若经》【深功德品】「一切法不可说，须菩提，一切法空相不
可说．．」

其实「不可说」的意义是「数量大到无法用语言形容」的意思，并不
是指所说的主题「不能说」，如果是不能说，那麽上面这些经典就是「废
话大全」了。

世尊说法四十九年，探讨的主题遍及人类所有的疑问，从来没有一样
　是「不能说出来」的，不但他老人家自己说，更鼓励所有修行菩萨要为众　
生说呢。(参见《般若经》)

那麽，「不可说」倒底有多大，会大到语言法形容呢？我们试著来找
找看。

{| class="wikitable" border="0" cellpadding="1" cellspacing="1"
! scope="col" |
! scope="col" |A
! scope="col" |B
|-
|0
|1RB
1LA
 1CP
 114514
|1LA
|-
|1
|1LB
|1RB
|}
111

{| class="wikitable"
! 用户名
! 简介
|-
| style="width: 20%;" | 张三 || style="width: 80%; word-wrap: break-word;" | 这是一个非常长的简介文本，会自动换行以适应列宽。
|}

表格？

{| class="wikitable" style="width: 300px; overflow: hidden; text-overflow: ellipsis"
! 用户名
! 简介
|-
| 张三
| 这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。
|}

<blockquote>这里是一个孤立页面我不知道它为什么还在这里

就当作是gggwiki的一个彩蛋吧（</blockquote>

[https://2023largenumber.fandom.com/zh/wiki/%F0%9F%98%B0#articleComments/ 果糕]
果糕糕糕！
果糕糕糕！果糕糕糕！
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<div id="guogao1">将以下代码放入控制台并回车，有“小惊喜”：</div><nowiki>(()=>{document.getElementById("guogao1").appendChild((()=>{let a = document.createElement("div");a.innerHTML = `<div class="fixed-btn"><a onclick="let b=document.createElement('div');b.innerHTML=\`<div id='guogao' style='transition: transform .5s ease-out;position: absolute;top:45%;left:50%;z-index: 9999999;transform: scale(1);cursor: pointer;-webkit-user-select: none;-moz-user-select: none;-ms-user-select: none;user-select: none;' onclick='this.remove()'>${decodeURI('%F0%9F%98%B0')}</div>\`;document.body.appendChild(b);setTimeout(() => {document.getElementById('guogao').style.transform='scale(45)'}, 50)" class="new" title="${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}">${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}</a></div>`;return a})());return (()=>{console.clear();return decodeURI('%E7%A5%9E%E7%A7%98%E6%8C%89%E9%92%AE%E5%87%BA%E7%8E%B0%EF%BC%81')})()})()

</nowiki>
[[分类:入门]]

Googology

2026-07-11T05:59:48Z

Baixie01000a7：/* 历史 */

'''Googology'''，又名'''大数数学'''，是一门专门研究大[[序数#有限序数|自然数]]的学科。<ref>曹知秋. 大数理论. (EB/OL), Vol.1, pp.27-36. https://github.com/ZhiqiuCao/Googology</ref>

== 词源 ==
该术语是由 André Joyce（安德烈·乔伊斯）根据 Michael Halm（迈克尔·哈尔姆）的虚构故事创造的，由 [[古戈尔|googol]]（这是一个经典的大数）+ -logos（希腊语后缀，意思是“学习”）组合而成。Joyce 的 googology 包含根据文字游戏和异想天开的推断设计一个数字名称系统，虽然目前的大数学家已经不在热衷于命名大数。

'''googologist（大数“学家”）'''，现在一般指大数数学爱好者。

== 历史 ==
主词条：[[大数简史]]

从最早的原始计数法到进制计数法，古人发展的大数已经足够日常生活使用了。近几百年来发展的指数函数以及科学计数法，乃至指数塔的推广，也已经足够除了极少数数学分支以外的科学研究使用了。但是直到 20 世纪，大数数学的萌芽才逐渐开始出现。

较早的大数数学研究都是非常零散的。Sudan 于 1927 年提出了 [[Sudan 函数]]，Ackermann 在 1928 年定义了 [[阿克曼函数|Ackermann 函数]]，这两个函数是非原始递归函数，具有较高增长率。早在 1944 年，Goodstein 就在研究序数的过程中就提出了 [[Goodstein函数|Goodstein 序列]]，它的强度远远超过了当时（以及之后几十年）的所有大数记号，只不过这一结果当时在大数领域中并未得到人们的足够重视。Goodstein 在 1947 年正式提出了超运算的概念。Knuth于 1976 年定义了描述超运算的 [[高德纳箭头|Knuth 箭头]]记号，这一记号一直沿用至今。Graham 在1971 年为了解决超立方体染色的问题，提出了 [[葛立恒数#葛立恒函数|Graham 函数]]，而后 Gardner 在 1977 年以它为基础定义了一个更容易理解，同时也更加强大的 [[葛立恒数|Graham 数]]，从而使得大数问题被人们所知。Conway 于 1996 年提出了 [[链式箭头记号|Conway 链]]，这可以视为 Knuth 箭头的一个强大的推广。

而早在 19 世纪 70 年代，Cantor 就开始系统性地研究无穷的性质，并导致了数学史上璀璨的明珠<del>——</del>集合论的诞生。他提出了[[序数]]的概念，并且定义了诸如 ω, ε 等序数。在1908 年，Veblen 提出了 [[Veblen 函数]]，它能够利用序数[[不动点]]系统性地刻画更大的序数。与此同时，Zermelo 提出了集合论公理化系统，后经过 Fraenkel 以及 Skolem 改进，形成了完整的 [[ZFC公理体系|ZFC]] 集合论体系。1950 年，Bachmann 首次提出了[[序数坍缩函数|序数折叠函数]]，而更加现代的序数折叠函数是 Buchholz 于 1986 年提出的。1995 年，Rathjen 利用反射序数提出了更加强大的序数折叠函数，后续的工作又将其强度进一步提高到了很高的层次。

集合论独立地发展了很长的时间，直到 1970 年，在 Wainer 提出最早的 Wainer 层次之后，它才与大数数学建立起来联系。它给出了一种将大序数映射为大数的方式，因此能够利用集合论中的成果来系统性地构造大数。Ketonen 与 Solovay 在 1981 年提出了[[增长层级#快速增长层级|快速增长层次]]的现代版本，并一直沿用至今。但是长期以来，这一结果也并未得到大数领域的重视。大数记号和大（递归）序数记号的真正联系要等到 2014 年以后才得以实现。

进入 21 世纪之后，大数的发展开始变得更加迅速了。在 2001-2004 年，Bowers 首先提出了 [[BEAF|Bowers 数阵]]（Bowers’ Exploding Array Function，BEAF），这是人们首次为了创造一个大数本身（而并非去为了解决其他问题）而创造的大数记号。这一记号在大数历史上具有重要的意义，一些研究者也将这一工作视为大数数学开始独立的起点。此时开始出现了一些零散的大数数学研究者，他们并非是职业的数学家，而是业余的数学爱好者。这一时期的记号主要为 Saibian 于 2005-2008 提出的 [[超E记号|E#]] 记号，以及 Bird 于 2010-2013 年提出的 [[BAN|Bird 数阵]]（Bird’s Array Notation，BAN）。后来数阵记号又得到了较为充分的发展，例如[[美元记号]]等。2016 年提出的[[SAN|强数阵记号]] (Strong Array Notation, SAN) 是数阵型记号的顶峰，它所提出的下降（[[Dropping]]）模式在之后的几年中一直是大数数学研究的最前沿模式。

在 2014 年左右，序数记号开始被引入到大数领域的研究之中。人们发现实际上序数记号与大数记号是统一的，大数记号的核心结构实际上就对应于一个序数，而序数记号套上一层简单的壳子就得到了有限的大数记号。序数记号和大数记号的统一无疑是大数数学有史以来最深刻的发现。至此人们的研究中心逐渐由大数记号转移到了大序数记号上，大数领域也真正迎来了迅速的发展。在这一阶段，递归序数记号的代表是 2015 年提出的 [[TON|Taranovsky 序数记号]]，它远远超过了当时人们所能够理解的强度。HypCos 的《大数入门》恰好成书于这段时间，它反映了大数领域的这场深刻的变革。

与此同时，关于非递归分析的研究也逐渐变得越来越深入，大量[[序数#非递归序数|非递归序数]]的结果被引入到大数数学中。人们意识到通过将越来越强大的非递归序数引入到序数折叠函数之中的方法，可以得到越来越强的递归序数。研究者们从序数分析和证明论中吸收了大量相关的结果，发展了诸如[[反射序数]]、[[稳定序数]]等非递归序数的折叠理论。2014 年的[[方括号稳定]]揭示了 [[Σ1稳定序数|Σ1 稳定序数]]的复杂行为，2018 年的 [[UNOCF]] 则是将反射序数系统性地放入序数折叠函数中的尝试。2020 年提出的[[投影序数|投影]]记号是一个强大的非递归记号。由于非递归分析对于数理逻辑的要求非常高，因此关于非递归分析的研究进展相对缓慢，相关的前沿成果也并不十分为研究者所理解。

在非递归分析发展的同时，人们也在寻求着更加强大的递归记号模式。由 Bashicu 于2014 年提出，并于 2018 年完善的 [[BMS|Bashicu 矩阵]] 是大数数学中划时代的工作。它开启了 [[Beklemishev's Worm|Worm]] 型记号的全新范式，至今仍然有着非常深远的影响。BMS 的强度远远超过了此前记号的极限，但是人们早期对此并没有十分充分的认识。只有当对 BMS 记号的分析变得越来越深入之后，它的强大之处才逐渐显现出来。在 BMS 提出后的相当长一段时间内，对其强度的分析是当时最为重要的工作之一，而这一分析过程也极大地催生了大数界相关数学工具的发展。但由于 BMS 的复杂性，这一项工作直到2025年才被完成，通过很晚近的[[向上投影]]。同时由于 BMS 的强大性和系统性，它现在已经成为了分析其他记号的标准。

2020 年 Yukito 提出的 [[Y序列]] 则是 Worm 型记号的又一座高峰。BMS 与 [[0-Y]] 序列是等价的，而通常所说的 Y 序列指的是 1-Y 序列，在这之上还有更加强大的 [[ω-Y|ω−Y]] 序列。相比于 BMS 的平凡扩展来说，Y 序列彻底超越了 BMS 的强度，达到了前所未有的境地。在 Y 序列之中蕴含的复杂结构也仍然有待于人们进行进一步的探索。

尽管人们一直在试图提出强于 Y 系列的新记号，但是这些记号都没有严谨的证据表明其具有超过 Y 系列记号的预期强度。且这些记号在各自方面相对于传统的广义 Y 系列记号一脉都还只是刚刚有一定的基础，其各自的体系仍然没有完善。在 Y 系列记号的内部，定义任意的 α − Y 乃至更加强大的 Ω − Y 的尝试一直也没有停止。尽管 CIF’s Ω-Y 已经遭遇了失败，但是一些其他的记号仍然在探索序列型记号的进一步推广。目前在这一方向上的代表为由 HypCos 于 2024 年提出的山脉记号（[[Mountain Notation]]，MN）、以及由 Aarex 于 2023 年提出，并且由 HypCos 和 ProjectCF 改进的[[MMS|变异矩阵系统]]（Mutant Matrix System，MMS），由 318'4 提出的[[FOS|基本列序数系统]]（Fundemental Ordinal Sequence，FOS）等。

除了在 Y 序列记号内部进行扩展之外，也存在着一些超出 Y 序列记号体系的尝试。近年来挖掘记号之中的[[传递]]结构已经成为了递归构造的前沿问题，除此之外，由 Asheep233 提出的[[对角化理论]]正在试图找寻 googology 构造记号的一般规律。除此之外，由 Yahtzee 于 2022 年提出，并由夏夜星空改进的 [[Fake Fake Fake Zeta]]（fffz）记号为我们揭示了更加强大的 Stellar 模式的冰山一角，它将有希望为我们揭示递归序数的更深刻结构。近期关于[[构造理论]]的研究为我们揭示了记号强度的部分来源，并将有可能指导我们创造出更加强大的记号。

以上我们讨论的都是可以被明显构造出来的递归记号，这是大数研究者最为关心的部分。然而在此之外，确实存在着一些更加强大的记号。在证明论的研究之中，自然地涌现出了一批非常强大的序数，称为[[证明论序数]]（Proof Theory Ordinal，PTO）。证明论序数是与公理系统相关联的，一个公理系统的强度越高，它的证明论序数就越大。长期以来，序数分析领域的专业数学家对证明论序数进行了深入的研究，得到许多重要的结果。我们猜想 <math>\mathrm{PTO}(\mathrm{Z}_{2})</math> 就达到了 BMS 极限的层次，<math>\mathrm{PTO}(\mathrm{Z}_{\omega})</math> 可能已经远远超越了目前所有递归记号的极限，而 <math>\mathrm{PTO}(\mathrm{ZFC})</math> 则更加遥不可及。1992 年，Laver 提出了 [[Laver Table|Laver 表]]。2001 年，Loader 提出了 [[Loader 数]]，这是一个增长率为 <math>\mathrm{PTO}(\mathrm{Z}_{\omega})</math>的记号。此外 Friedman 还提出了[[有限树序列]]、[[贪心团序列]]等，它们的增长率上界都已经达到较强系统的证明论序数的层次。

在一切递归函数之上的是非递归函数，它们的增长速度超越了一切的递归记号。1961年，Rado 在研究计算理论的时候定义了 [[忙碌海狸函数|Busy Beaver]]。它是基于 Turing 机的性质构建的，是一个重要的非递归函数。2013 年，Goucher 提出了 [[Ξ函数]]，这是一个增长率更高的非递归函数。而基于更加强大的超计算模型，我们可以构建一些增长率更高的不可计算函数。在所有这些记号之上的是 Rayo 于 2007 年提出的 [[Rayo函数|Rayo 数]]，它利用了一阶逻辑的不可描述性质，远远超越了之前的所有记号。

== 意义 ==
研究大数有什么意义？事实上，大数数学的发展就是人们对数这一概念的认识不断加深的过程。

我们回想一下原始社会中的文明，他们的数学水平几乎为零，仅仅是对数有着模糊的概念。若他们的语言中可能会有 10 个表示数字的单词，那么这种计数法所能表达的极限大概为 10。在这个数字范围之内的数是能够为原始人所把握的，而这也差不多是他们所能够直观地把握的极限。

语言确实会影响人的思维。如果一个东西是不能够被我们说出来的，那么它在我们的头脑中也同样是几乎是无法设想的。对于原始人来说，他们或许知道这个世界上确实存在着更大的数，但是他们对这些数的大小已经没有了具体的感知。对于那些更大的数，例如部落中的人口数量、森林里树木的数量、采摘回的果子的数量等等，他们只能够模糊地知道这些数非常巨大，但却无法知道这些数具体有多大。

随着文明的发展，更大的计数法被创造了出来，人们也能够理解一些更大的概念。或者说，正是对处理更大数字的迫切需要，催生了人们对于更优秀的计数法的发展。为了统计诸如城镇所拥有的耕地面积、交战军队所要携带的物资这样的数，更大的计数法被创造了出来。对于古希腊和古罗马来说，它们的计数系统可以表示几万到几十万的数字。后来随着进制计数法的逐渐普及，计数法的能力达到了数亿的量级，这已经足够古人理解生活中的所有大数了。

科学的发展要求人们认识和处理更大的数字，在这种情况下，传统的计数法日益显得捉襟见肘，阻碍了人们的思维。随着指数计数法的发展，人们逐渐解决了这一问题。也正是由于有了更加强大的计数法，我们才能够理解那些大得无法设想的数字，并能够通过对这些数字的处理进一步地发展科学。最终我们的成就是辉煌的：自然界中所能够达到的任何数字都被限制在了五层[[高德纳箭头#幂塔|指数塔]]之内，我们已经一劳永逸地表示出了实际世界中的所有大数。

但是，这显然不是我们的终点。尽管我们原则上已经得到了所有的自然数，我们也可以用指数塔表示出任意大的数，但除非我们能够构造出更加强大的表示法，那么我们永远也不可能从直观上认识到那些更大的数的存在。这正如如果只有进制计数法，就永远无法设想指数塔层次的大数一样，一旦我们发展了更加强大的计数法，我们立刻会觉得指数塔层次的大数小得可怜，而更高层次的大数也只有在此时才能够直观地展现在我们的面前。大数记号的发展让我们对于自然数体系的结构有了更深刻的认识。

正如 Saibian 所说：

<div style="word-wrap: break-word;text-wrap: pretty;color: var(--color-subtle);font-style: italic;width:Fit-content;padding:1rem;border-left:solid #00000030 5px;background-color:var(--color-surface-2)">大数使[[序数#超限序数|无穷大]]显得更大的作用远远超过无穷大使大数显得更小的作用。<ref>Saibian, S. One to Infinity: A Guide to the Finite. ''(M/OL)'', (alpha 2.0.0.0.8). https://sites.google.com/site/largenumbers.</ref></div>

诚然，我们早就知道无穷大远远大于任何有限的数，但是我们恐怕对此始终没有直观的认识。只有当我们真正明显地构造出那些难以设想的大数之后，我们才会认识到无穷大究竟大到了何种程度，我们也才能够真正了解自然数体系之内所蕴含的丰富结构。事实上对于任何一个有限的数来说，不仅仅是有无限多的自然数比它更大，甚至“几乎所有”的自然数都会比它更大，无论这个数自身已经大到了何种程度。大数为我们理解无穷的性质提供了一个直观的参考。

在近几十年的研究中，人们逐渐意识到了大数领域与集合论的密切联系。对集合论的研究极大地促进了大数领域的发展，我们也相信大数领域可以对数理逻辑等领域的研究进行反哺。大数领域与其他的数学体系有着千丝万缕的联系，对大数的研究也有助于我们进一步地理解数学体系中的其他部分。

[[证明论序数|证明论]]与[[SCG函数 & SSCG函数|图论]]等领域中为我们提供了大量增长极快的问题，解决这些问题需要发展更加强大的大数表示法。但或许大数数学的真正魅力并不在于对于其他问题的解决，而恰恰在于'''发现更大的大数'''这件事本身。借助理性的力量，我们在大数的世界之中不断地前进，一次又一次地挑战已知的极限。我们正在试图用我们渺小的头脑，去追寻那些整个宇宙都承载不了的数字。这是人类智慧的一场别开生面的冒险，它已经吸引了许多的数学爱好者参与其中。

== 相关亚文化 ==
以下是一些 googology 相关的亚文化。

=== 挑战葛立恒数 ===
作为大数界的“守门员”，Graham数利用简单的迭代规则创造出了一个在现实世界之中大得难以置信的数。这样一个数字的大小引起了人们的好奇，人们认识到了通常的十进制计数法和指数计数法也存在着表示的极限，在它们之上还有着更加强大的数字。Graham 数（以及一些其他的同样巨大的数字）的知名度不断地提高，而这也吸引了网络上的博主对其进行进一步的解释和宣传。一时间，“写出一个比 Graham 数更大的数字”（即“挑战 Graham 数”）仿佛成为了一个时尚的智力小游戏，吸引着无数人前来参与。

参与数学游戏对人的智力总归是一种锻炼，但是大多数跟风的参与者对大数仅仅有高中水平的认识，因此其想象力仅仅停留在各种自然界中存在的大数（宇宙中的原子数量/一天中一次彩票的概率等），以及最多达到指数塔层次的运算方法和迭代规则。仅仅依靠这些显然是不可能达到葛立恒数的，绝大多数挑战者因此铩羽而归。当然，也有一些挑战者感受到了这一问题的有趣之处，从而愿意对于大数数学有一些更深入的了解。

=== 伪数学 ===
对于伪数学更恰当的称呼应该是“虚构大数学”，它致力于创造出一些仅存在于想象之中的、不存在的大数。这并不是一个数学分支，因为它所讨论的并不是数学对象。伪数学的爱好者会创造出一系列的符号和概念，以此来试图说明一些非常大的数（典型的如所谓各种“绝对无穷”等）。当然，这些结论并不是严肃的数学，而只是一场想象力的狂欢而已。伪数学通常是以视频的形式来表现的，这些视频中充斥着眼花缭乱的特效，以试图表现伪数学世界的狂暴与杂乱无章。伪数学的创作没有任何限制，如果有的话，那么唯一的一条限制就是“怎么都行”。除此之外，伪数学还与其他的社区（如数字方块）有一定的联系。

有关更多信息，请移步<nowiki/>https://fictional-googology.fandom.com

=== 论战 ===
论战指的是战力比较。不同文学或者娱乐作品之中刻画了许多具有超凡力量的角色，如何比较这些角色之间战斗力的强弱便成为了一个困难的问题。一般来说，要想对一系列角色的战斗力进行比较，可以首先根据其破坏力划分量级，量级高者战斗力占优势。而如果是在统一量级之中实力非常接近的角色，则是借助一个（或者一系列）中间角色 B，通过比较 A > B, B > C 来间接论证 A > C。由于论战问题天然地与大数以及大序数（超越无穷的排序）、大基数（不同层次的无穷大）的问题相关，因此在论战的过程中，这些概念逐渐地开始为人所知。在有限的层面上，可以简单地通过破坏力来划分量级。战力的论证过程一旦上升到无穷，就需要数学的语言来进行进一步的阐述，但是这一部分目前尚没有十分统一的标准。例如可以设想某角色能够毁灭一个无限大的宇宙（单体宇宙），一个角色可以毁灭无限个无限大的宇宙（多元宇宙），一个角色可以毁灭无限个无限大的宇宙，而这里的每个宇宙中又包含了无限个宇宙，这样下去直至无穷（无限盒子），以此类推。当然，人的思维不能够直观地刻画无限，因此即便一个设定上全知全能的角色，其实力也总是以有限的形式表现出来的，这受限于作者本人的想象力。

论战社群非常庞大，且分布极为分散。由于论战社群兴趣的广泛性，它与其他亚文化群体的关联也非常紧密，如二次元动漫、欧美奇幻作品、玄幻小说等。不同的论战群体之间关注的问题以及讨论的方式也完全不同，因此要对论战社群进行一个完整的概括并不是容易的，并且事实上也很难找到能够被整个论战社群所承认的共识。

除了论战之外，还有“自创”设定的做法，即以文字或者小说的形式描述那些尽可能强大的概念。

=== 增量游戏 ===
放置/增量游戏是一种独特的游戏类型，这种游戏通过大量的点击等操作，来获取随时间增长的资源。其经典的设计模式是设计一种或多种随时间增长的资源，然后在增长的过程中可以利用这些资源来升级，以进一步提高资源的增长速度。有些游戏比较侧重玩法，这类游戏被称为放置类游戏。比较经典放置类游戏的有饼干点击（Cookie Clicker）、点击泰坦（Tap Titans）以及进化（Theresmore）等。更加广义的放置类游戏还包含一部分养成类型的游戏，近年来火热的抽卡手游有相当一部分都是广义的放置类游戏。

而有些游戏则去掉了所有其余的部分，而只保留了一个数值增长的核心，这样的游戏称为增量游戏。增量游戏通常是以单纯的文字模式呈现的，例如反物质维度（Antimatter dimensions）、序数增量（Ordinal Markup）等。相比于注重玩法的放置类游戏来说，增量游戏与大数数学的关系要更加密切一些。增量游戏是一个小众的门类，增量游戏的数值设计是不容易的，因为不论何种层次的增长，在一个合适的计数法之下总会被压平成线性的。换句话说，在这一尺度下新的增长模式实际上和最基础的加一又没什么区别了。为了突破这一限制，就要在玩法中引入新的机制，而为了保证可玩性，这一机制加入的时间和强度都需要进行精心设计。一些优秀的增量游戏可以达到很大的数值。

== 讨论 ==
虽然上述亚文化中所有人的目标都是对那些强大得难以想象的概念的追求，但是由于所选择的道路不同，其讨论方式以及风格也完全不同。

仅以严格性论之，数理逻辑等领域的专业数学家最强，其次是严肃的大数数学研究者，他们尽可能严格地使用严格的概念（尽管对于目前的大数数学来说，还不总是能够真正做到这一点）。再其次是论战爱好者，他们不严格地使用那些数学上的概念，通常并不能够理解其含义，有时也自创数学概念。最后是伪数学爱好者，他们使用那些并没有明确定义的概念。
而若以圈子规模来看，那么论战爱好者的人数要远远多于其余的所有人（当然，并非所有的论战爱好者都关心大数和无限的相关问题）。

由此可见，这一时期大数数学已经在国内形成了一个独具特色的亚文化群体。大数数学吸引了大量的爱好者参与其中，逐渐演变成了一场盛况空前的网络狂欢。
客观上来说，这极大地拓展了大数数学的影响力，使其从一个冷僻的数学分支变成了为许多人所了解的有趣问题。同时由于大数数学问题的趣味性和低门槛的特征，许多没有经受过专业的数学训练的人也可以在这一问题上以自己的方式进行探索和研究。这些人将自己探索得到的结果（即便可能是非常弱的结果）发布在网络上，而这又会吸引更多的人加入到这一问题的研究之中。

但是另一方面，大量爱好者的涌入使得中文互联网上本就散乱的大数数学的知识变得更加鱼龙混杂。大量低质、无意义甚至错误的内容充斥着整个社区，使得真正志于深入了解这一问题的爱好者几乎寸步难行。

目前在互联网上，有关于大数数学的低劣内容已经多到了令人发指的程度。许多人对于大数数学的认识（比如 Graham 数或者是 TREE(3)）是一知半解，甚至是完全错误的。这些错误的观念经过宣传之后在网络上获得了很高的知名度，反而是正确的观念由于其难度超过了普通人的理解能力而完全无人理睬。
许多流传于互联网上的信息是毫无价值的。大量由完全不了解大数数学的人创造的结构混乱、强度孱弱、定义残缺，甚至根本不能够被称为“数学内容”的记号几乎淹没了一切有价值的信息。
这种低质量的记号不仅无益于大数数学的发展，反而会加深对于大数数学的刻板印象，认为只是小孩子过家家的比大小游戏。同时这样的记号蒙蔽了真正有意义的递归结构，对它们进行了解不仅仅是白白地浪费时间，还有损于数学的品味，令有志于从事大数数学研究的爱好者误入歧途。

即使是在那些正确的信息之中，绝大多数也已经严重过时了。目前网络上流行的大数记号仍然为 Knuth 箭头、Conway 链、E# 记号以及 Bowers 数阵。
以上的记号之中除了 Knuth 箭头以及 Bowers 数阵的一部分（单行线性数阵）仍然作为大数数学的基础之外，其余的记号早就已经被当前的大数数学界淘汰了。这些记号已有二十年左右的历史，它们仍然是大数数学刚刚出现的时候提出的，其结构仍然带有着那个时代的粗糙痕迹，其强度也十分有限。
少部分“较新”的资料会提到 Bird 数阵，而这一数阵已经是十年前的成果了。而真正的“现代”记号（例如 Bashicu 矩阵），仅仅能够在寥寥可数的几份资料中得以一见而已。

近二十年以来，大数数学取得了长足的发展，涌现出了一大批丰富而又深刻的结果。然而在互联网上，近十年的成果几乎是对外界完全“封闭”了起来。

大数数学社区之外的人难以凭借着自己的力量找到真正有意义的资料，这一点即使是对于有志于学习大数数学的严肃爱好者来说也是如此。
尽管目前大数数学的研究者已经编写了一些较为深入的资料，但是除非已经预先知道相应的关键词，否则这些资料并不容易找到。并且即使找到了这些资料的一部分，可能也会因为它们不够完整和难度较高而放弃。
而真正最前沿的进展，只能够在一些非公开的网络平台（例如 QQ 群或者 discord）上才能找得到。

互联网的发展伴随的不仅仅是知识的流通，还有严重得多的垃圾信息膨胀。在垃圾信息的海洋之中，大数数学只有最表面的一些东西能够为人所知。而更深层次的内容则随着没有意义的垃圾信息一起，被埋葬在了冰冷的海底。
大数数学的问题不仅仅在于知识的传播，还在于相关社区内爱好者不恰当的浮躁心态。在互联网上，许多人完全不能够理解大数数学的内容，而仅仅是通过大数数学里的概念来炫耀自己在互联网平台上的优越感。

令人遗憾的是，许多人到最后逐渐演变成了只会堆叠名词的“名词党”，或者是只沉溺于自己世界中的“民科”。在他们眼中，“大数”仿佛成为了某种时尚的网络单品，成为了一种炫耀自己身份的标志。
有些人受到了伪数学社区和论战社区的影响，误将这些社区的讨论作为真正的大数数学、乃至于整个数学学科本身。
有些人在与大数数学无关的地方不合时宜地发表令人生厌的言论，破坏其他社区的网络环境，这反过来又加剧了人们对于大数数学以及其他相关社区的刻板印象。

但不论如何，当热潮退去之后，[[Googology 社区|总会有真正的大数爱好者留下来，成为该方向上较为严肃的研究者]]。

在 test_alpha0 和夏夜星空的 QQ 群之中大约聚集了几百名爱好者，其中比较活跃的大数研究者大约有几十人，这些人或许占据了国内为数不多的研究者的绝大多数。（作为比较，Discord 大数频道聚集了全世界的大数研究者，其人数大约有一两千人，而其中活跃的研究者可能有几百人。）
他们确实在这个方向上不断地进行更加深入的研究，努力拓宽人类的知识边界。有一些研究者系统性地整理了大数数学的基本知识和一些最新的进展，用较为现代的视角重新审视着整个理论。

特别是在最近几年，国内大数研究者的热情空前高涨，新记号的提出层出不穷，理想的强度极限不断刷新。但是这些记号并未充分经过时间的考验，目前看来仍然有待进一步的完善。
不论如何，相比于前些年的惨淡景象来说，如今的大数界已经算得上是“欣欣向荣”了。

虽然近年来大数数学在国内已经得到了更多的重视，但是时至今日，大数数学仍然是一个极其专门和小众的领域，国内对于大数领域的研究仍然是比较有限的。
并且由于理论发展得越来越艰深，现在的大数数学前沿领域几乎已经超过了普通数学爱好者的能力极限了。
目前国内致力于该方向的研究者几乎都是业余的数学爱好者，人数也仍然较少，长期以来缺乏有能力做出实质性进展的新研究者的加入，与国际大数数学社区的交流仍然不够密切。

总体上来说，国内的大数领域仍然需要进一步的发展。

大数数学的未来是什么样的？目前看来还很难说。或许随着网络的进一步普及和信息化时代的进一步发展，大数数学会为越来越多的人所了解。

大数数学涉及到一些非常艰深的数学，在任何时代热爱数学的人都是极少数。但它毕竟是一个足够有趣的问题，尽管当今时代的人们已经变得越来越浮躁了，它也总会触动一部分人的心灵。

当一切繁杂的声音都逐渐消退之后，剩下的人将会真正地为大数数学的发展做出贡献。我们也期待数学界（特别是数理逻辑相关的领域）能够对大数数学给予更多的重视。

== 逸事 ==
主词条：[[Googology 梗百科|梗百科]]

外网的 discord 上的大数社区对 googology 有 goofology 这种半开玩笑的写法。

无独有偶，在国内大数社区也有类似的梗。

果糕，即😰使用 UTF-8 编码再用 GBK 解码会变成"馃槹"，谐音"果糕"。后来它在国内大数社区发展出了独特的亚文化。具体参见[https://2023largenumber.fandom.com/zh/wiki/%F0%9F%98%B0/ 此处]。而因为果糕和 googol 发音相似，因此 googology 有时被称为果糕逻辑。（一说是因为g(guo)g(gao)logy）

== 参考资料 ==

[[分类:重要概念]]
[[分类:入门]]

Rayo函数

2026-07-11T05:59:27Z

Baixie01000a7：/* 取值 */

Rayo函数，是目前被命名的增长速度最快速的函数之一。

== 定义 ==

=== 通俗定义 ===
在集合论中我们知道，每个自然数 n 都可以用一个集合来表示，而一个一阶逻辑语句的自由变元所能够取为的值同样能够构成一个集合。因此，如果这个一阶逻辑语句所描述的集合恰好对应于一个自然数，那么我们就用这个一阶逻辑语句成功地描述了一个自然数。

通俗地说，Rayo 函数 Rayo(n) 的定义为：不能够用包含字符数为 n 的[[一阶逻辑]]语句定义的最小的自然数。

Rayo数定义为<math>\text{Rayo}(10^{100})</math>

关于 Rayo 函数，有几点值得说明一下。首先，它不是用自然语言表述出的“不能用 n个字确定的最小自然数”。例如，我们可以考虑“不能用二十个字确定的最小自然数”，这句话确定了一个自然数。但是这句话本身又少于 20 个字，因此这个数也能够用小于 20 个字来确定。因此这句话产生了悖论，我们称之为 Perry 悖论。究其原因，这种悖论是由于自然语言的模糊性导致的。相比之下，Rayo 数的规则是明确的，因此不会产生这一问题。

另外，它也与“用 n 个字符所不能得到的最小自然数”不同。因为计算机程序总是递归的，而一阶逻辑不是递归的，它的描述能力要比计算机语言强得多。尽管初看起来，一阶逻辑的语言十分低效，但是一旦字符数量增加，我们就可以利用它定义一些非常高效的函数，它们的表示能力将大得惊人。

=== 正式定义 ===
令<math>[\phi]</math>和<math>[\psi]</math>为 Gödel 编码公式，s 和 t 为变量。定义<math>\text{Sat}([\phi], s)</math>如下:

<math>\forall R \{</math>
{
<math>\forall[\psi],t:R([\psi],t)\leftrightarrow([\psi]=''x_i\in x_j''\land t(x_i)\in t(x_j))</math>
<math>\lor([\psi]=''x_i=x_j''\land t(x_i)=t(x_j))</math>
<math>\lor([\psi]=''(\neg\theta)''\land\neg R([\theta],t))</math>
<math>\lor([\psi]=''(\theta\land\xi)''\land R([\theta],t)\land R([\xi],t))</math>
<math>\lor([\psi]='\exists x_i(\theta)''\land\exists t':R([\theta],t'))</math>
(where t′ is a copy of t with <math>x_i</math> changed)
<math>\} \Rightarrow R([\phi],s)</math>
}

我们称自然数 m 为 Rayo 可命名的，如果存在一个公式 <math>\phi(x_1)</math> 小于 n 个符号且<math>x_1</math>作为其唯一的自由变量满足以下性质：

# 存在一个变量赋值 s，赋值 x1 := m，使得<math>\text{Sat} ([\phi (x_1)] , s)</math>。
# 对于任何变量赋值 t，如果 <math>\text{Sat} ([\phi (x_1)] , t)</math>，则 t 必须有 <math>x_1 = m</math>。

Rayo(n) 是大于使用 n 个符号的 Rayo 可命名的所有数的最小数。

对 Rayo 函数定义的阐述如下：

# 原子公式“<math>x_a \in x_b</math>”表示第 a 变量是第 b 变量的元素。
# 原子公式<math>x_a=x_b</math>”表示第 a 变量等于第 b 变量。
# 公式 e 的公式“(<math>\neg e</math>) ”表示 e 的否定。
# 公式 e 和 f 的公式“(<math>e \land f</math>) ”表示 e 和 f 的合取（逻辑与）。
# 公式 e 的公式“<math>\exist x_a(e)</math>”意味着我们可以修改 a 变量的自由出现，即用 e 中所有集合的 V 类的另一个成员替换<math>x_a</math>使得公式 e 为真。

以上五条定义只是更加精确地给出了 ∈, =, ¬, ∧, ∃ 这五个逻辑的含义。这样我们就给出了用公式定义自然数的方法。若一个自然数是不能够以上述方式从长度为 n 的语句中定义的最小数，那么它就是 Rayo(n)。

== 取值 ==
我们有：

\begin{eqnarray*}0 & = & \{\} = (\neg\exists x_2(x_2 \in x_1)) \ \textrm{(10 symbols)} \\1 & = & \{\{\}\} = (\exists x_2(x_2 \in x_1) \land (\neg\exists x_3((x_3 \in x_1 \land \exists x_4(x_4 \in x_3))))) \ \textrm{(30 symbols)} \\2 & = & \{\{\},\{\{\}\}\} \\& = & (\exists x_2(\exists x_3((x_3 \in x_2 \land (x_2 \in x_1 \land x_3 \in x_1)))) \\& & \land (\neg \exists x_4(\exists x_2(\exists x_3((x_4 \in x_3 \land (x_3 \in x_2 \land x_2 \in x_1))))))) \ \textrm{(56 symbols)}\end{eqnarray*}

因此我们有：

<math>\begin{align}\text{Rayo}(0) &=& 0 \\\text{Rayo}(10) &\ge& 1 \\\text{Rayo}(30) &\ge& 2 \\\text{Rayo}(56) &\ge& 3 \\\end{align}</math>

这只是给出了下限，精确值是由Plain'N'Simple、Emk 和 Ytosk给出的<ref>Plain'N'Simple, [https://googology.fandom.com/wiki/User_blog:Plain%27N%27Simple/Proof_that_Rayo(n)_is_0_for_n_less_than_10 Proof that Rayo(n) is 0 for n less than 10], Googology Wiki user blog.</ref><ref>Emk, [https://googology.fandom.com/wiki/User_blog:Emk/Rayo(10)_is_exactly_1_(not_a_lower_bound) Rayo(10) is exactly 1 (not a lower bound)], Googology Wiki user blog.</ref><ref>Plain'N'Simple, [https://googology.fandom.com/wiki/User_blog:Plain%27N%27Simple/Proof_that_Rayo(n)_is_1_for_n_between_10_to_19 Proof that Rayo(n) is 1 for n between 10 and 19], Googology Wiki user blog.</ref><ref name="Yto">Ytosk, [https://googology.fandom.com/wiki/User_blog:Ytosk/Small_improvements_to_bounds_on_values_of_Rayo%27s_function Small improvements to bounds on values of Rayo's function], Googology Wiki user blog.</ref>

<math>\begin{align}\text{Rayo}(0) &=& 0 \\&\vdots& \\\text{Rayo}(9) &=& 0 \\\text{Rayo}(10) &=& 1 \\&\vdots& \\\text{Rayo}(29) &=& 1 \\\text{Rayo}(30) &\ge& 2 \\\end{align}</math>

除此之外，Ytosk还展示了<math>Rayo(88)\geq4</math>以及<math>Rayo(34+20n)>n</math>.<ref name="Yto"/>

从 2020 年 4 月开始，[[Googology]]爱好者关于如何使用Rayo字符串表示数字<math>65536=2\uparrow\uparrow 4</math>以及类似的，2的指数塔，做了大量的研究。Plain'N'Simple 是第一个完成这项任务的人，表明<math>\text{Rayo}(835+96n) > 2 \uparrow\uparrow n</math>.当然，这是早期成果，还有很多改进要做。最后，通过 Plain'N'Simple、P进大好きbot 和 Ytosk 的各种努力，表明<math>\text{Rayo}(260+20n) > 2\uparrow\uparrow n</math><ref name="Yto"/>，因此我们有：

<math>\begin{align}\text{Rayo}(320) &>& 16 \\\text{Rayo}(340) &>& 65536 \\\text{Rayo}(360) &>& 2^{65536} \\\text{Rayo}(380) &>& 2^{2^{65536}} \\ \end{align}</math>

Emk 已经证明<math>\text{Rayo}(7901)>\text{S}(2^{65536}-1)</math>,其中S(n)是[[忙碌海狸函数#疯狂青蛙函数 S(n)|疯狂青蛙函数]]<ref>Emk, [https://googology.fandom.com/wiki/User_blog:Emk/A_Rayo_name_larger_than_BB(10%5E100) A Rayo name larger than BB(10^100)], Googology Wiki user blog.</ref>。然而，由于他的博客文章使用过时的 Rayo 字符串，这个下限没有应有的那么强。目前我们有<math>\text{Rayo}(7339)>\text{S}(2^{65536}-1)</math>。

== 历史 ==
2007 年，Elga 与 Rayo 在麻省理工大学进行了一场别开生面的比赛[[Big Number Duel]]，其内容是尽可能地写出一个有限的自然数。比赛的规则是两人轮流写出一个更大的数，要求不能够使用原始语义词汇，例如不能说“比迄今为止人类命名的任何数字都大的最小数字”等；且后一个被提出的数字不能够容易地由前面的数字的构造方法容易地抵达，例如不能够在前一个数字上简单地 +1 来得到更大的数字。这场比赛的获胜者是 Rayo，他在这场比赛中提出的最大数字就是著名的 Rayo 数

据信Rayo和Elga的大数对决的灵感来自斯科特·亚伦森（Scott Aaronson）的文章[https://www.scottaaronson.com/writings/bignumbers.html 谁能说出更大的数字？]

== 讨论 ==
为了在集合论中定义一个自然数，我们需要明确基于哪些公理进行定义。Rayo数定义中的一个问题在于，Rayo并未阐明所使用的公理。在数学中，只要我们在ZFC集合论的框架下工作，通常会省略对公理的声明。按照这一传统，许多大数研究者认为Rayo数是在ZFC集合论中定义的，或者与公理选择无关，但这种观点是错误的。

至少，由于ZFC集合论无法在[[冯诺依曼宇宙|冯·诺伊曼宇宙]]中形式化真值谓词，除非我们将Rayo数的定义解释为可证性，否则它在ZFC集合论中是不良定义的。即使我们以这种方式解释其定义，所得到的大数也不会显著大于例如<math>\Sigma(10^{100})</math>（其中<math>\Sigma</math> 为[[忙碌海狸函数]]），因为递归可枚举理论中的可证性可以通过图灵机的停机信息判定。要显著超越忙碌海狸函数，我们必须放弃可证性，转而讨论特定模型中的真值——而该模型的存在性在ZFC集合论的一致性前提下是无法被证明的。

另一方面，FOST（一阶集合论语言）本质上只是一种形式语言，根据其定义与公理系统无关——但这并不意味着Rayo数的定义也与公理无关。FOST与公理的无关联性，或者忙碌海狸函数与Rayo数基于可证性解释之间的关系，可能是导致人们误认为"Rayo数与公理无关"的主要原因。

正如Rayo在其原始描述中所述，他使用二阶集合论来形式化原始语义词汇。因此，Rayo数实际上是基于某种未明确说明的二阶集合论公理系统定义的。在不可计算的大数研究中，明确公理系统至关重要，因为只有当两个不可计算大数采用相同的定义公理时，它们之间才能进行有意义的比较。幸运的是，存在多种二阶集合论公理系统可供选择来定义Rayo数。由此可以得出结论：'''对于那些关注公理明确性的研究者来说，Rayo函数是不良定义的'''。

2020年，Rayo新增了以下关于如何处理Rayo数的说明<ref>[https://web.mit.edu/arayo/www/bignums.html A. Rayo, "Big Number Duel", 2007]</ref><blockquote>"注：哲学家有时会采用集合论的实在论解释。在这种解释下，集合论表达式具有'标准'含义，能为语言中的每个句子确定明确的真值，而无需考虑这些真值是否可能被认知（例如参见Vann McGee的这篇文章）。在竞赛期间，Adam和我默认（二阶）集合论语言采用标准解释，这保证了最终条目对应确定的数。如果该语言基于某个公理系统进行解释，最终条目就会失效。这是因为每个（一致的）公理化系统都存在非同构模型，无法保证最终条目在不同模型中对应相同的数。"</blockquote>这意味着Rayo采用了一种哲学上的"解释"方式，将集合论公式与现实中"真值"相对应——这种做法在数学上是无法形式化的，且并未涉及具体公理系统的选择。这是大数研究在数学框架之外的一种合理探索方向。然而，最后一句中的辩解（关于为何要接受这种无法形式化的"真值"）更像是一种托词：虽然数值对模型的依赖性确实存在，但这与"无效性"并无逻辑关联。

在数学中，存在许多良定义但非绝对的概念（即依赖于模型），例如满足条件<math>(CH\rightarrow n=0)\land(\neg CH\rightarrow n=1)</math>的唯一自然数n。同样在大数领域，许多数值本身就具有模型依赖性，比如忙碌海狸函数的值。值得注意的是，在"大数对决"竞赛中，从未禁止过依赖模型的数值定义，甚至允许参与者不指定公理系统。

== 引证 ==
{{默认排序:相关问题}}
[[分类:记号]]

投影序数

2026-07-11T05:15:24Z

Baixie01000a7：/* 第一个 2-投影序数 */

投影序数（projection）是 test_alpha0 创造的非递归记号。投影序数是目前为止最方便的强大非递归序数表达方式，伴生的限制则是——它很有可能永远无法良定义（至少在比较小的序数处如此）。但即使如此，它可以作为非递归序数和递归记号的交接桥梁，并在国内大数社群广泛地被使用。

=== 定义 ===

==== 第一个 2-投影序数 ====
我们定义 1-投影序数（1-proj.）就是传统的非递归序数。

2-proj. 是一系列很大的非递归序数。它们被认为是 <math>a<_{\Sigma_1}Ord</math>。第 n 个<math>2\text{-proj.}</math>被写作 <math>a_n</math>。现在让我们把 <math>a</math> 放进 [[序数坍缩函数|OCF]] 里：

* <math>\psi_a(0)=\Omega</math>
* <math>\psi_a(X+1)=\psi_a(X)\times\omega</math>
* <math>\psi_a(X\sim a)=\beta\rightarrow\psi_a(X\sim\beta) \text{不动点}</math>，其中 ~ 是任意运算或者是任意递归函数

到这里，<math>\psi_a</math> 和 <math>\psi_{\Omega_2}</math> 还没有区别，区别在下面这一条：

如果 β 是非 2-proj. 的 1-proj.，则 <math>\psi_a(X\sim\beta)=\bigcup_{\gamma<\beta}\psi_a(X\sim\gamma)</math>，其中 ~ 是任意运算或者是任意递归函数

这条规则乍一看平平无奇，但是注意，a 的下一个 Ω 序数，即 <math>\Omega_{a+1}</math>，也是一个 1-proj.！这意味着，<math>\psi_a(\Omega_{a+1})\neq\psi_a(\psi_{\Omega_{a+1}}(\psi_{\Omega_{a+1}}(\psi_{\Omega_{a+1}}(\cdots))))</math>，而是等于 <math>\sup\{\psi_a(a),\psi_a(a^a),\psi_a(\varepsilon_{a+1}),\psi_a(\zeta_{a+1}),\psi_a(\Gamma_{a+1}),\psi_a(BO(a+1)),\cdots\}</math>。通俗的说，就是需要穷尽 a 的递归运算。投影序数能挣脱 <math>\Omega_2</math> 的藩篱，正是靠这个本事。但其问题也是出在这里。因为我们无法直接定义 <math>\Omega_{a+1}</math> 之下的所有递归运算，因此投影序数直接作为非递归记号依然是不良的。但是它作为放进 OCF 里的递归记号却是良的，因此放心使用。

==== 更多的 2-投影序数 ====
我们定义 <math>\psi_{a_n}</math> 如下：

* <math>\psi_a(0)=\Omega</math>
* <math>\psi_{a_{n+1}}(0)=\Omega_{a_n+1}</math>
* <math>\psi_{a_n}(X+1)=\psi_{a_n}(X)\times\omega</math>
* <math>\psi_{a_n}(X\sim a_m)=\psi_{a_n}(X\sim \beta\rightarrow\psi_{a_m}(X\sim\beta)\text{不动点})</math>，其中 ~ 是任意运算或者是任意递归函数，m>n
* 如果 β 是非 2-proj. 的 1-proj.，则<math>\psi_{a_n}(X\sim\beta)=\bigcup_{\gamma<\beta}\psi_{a_n}(X\sim\gamma)</math>,其中~是任意运算或者是任意递归函数

它们的作用可以理解为，当你在 <math>\psi_a</math> 内部需要用到 <math>\Omega_{a+2},I_{a+1},M_{a+1},\cdots</math> 这些东西的时候，需要 <math>\psi_{a_2}</math> 来表示它们。

==== n-投影序数 ====
定义 p_m 是 <math>m\text{th }n+1\text{-proj.}</math>，q 是 <math>\text{1st }n\text{-proj.}</math>，P_n 是 <math>n\text{-proj.}</math> 的集合：

<nowiki>$\begin{align}
&\psi_{p_1}(0) = q \tag{1}\\
&\psi_{p_{m + 1}}(0) =n-proj. ~aft~ p_m \tag{2}\\
&\psi_{p_m}(\#\sim X_{p_m + 1}) = \sup\{\psi_{p_m}(\#\sim t) \mid t < X_{p_m + 1}, X \in P_k, k \in \{1, \ldots, n\}\} \tag{3}\\
&\psi_{p_m}(t + 1) = \psi_{p_m}(t) \times \omega \tag{4}\\
&\psi_{p_m}(\#\sim p_m) = \beta \rightarrow \psi_{p_m}(\#\sim \beta) \quad \text{Fixed Point} \tag{5}
\end{align}$</nowiki>

以上规则便统一定义了 <math>n\text{-proj.}</math>。

通俗的说，<math>(n+1)\text{-proj.}</math> 之于 <math>n\text{-proj.}</math> 的关系就如同 <math>a_n</math> 之于 <math>\Omega_n</math>，高阶的投影序数可以对低阶的投影序数取并，从而造就极大地表示范围。

=== 扩展 ===
投影有许多强大的拓展，在这里介绍投影使用最为广泛的拓展：向上投影。这个拓展可以与[[BMS]]相抗衡。

==== 向上投影 ====
考虑一个很大的序数H，它可以折叠“投影点”：

<math>\psi_H(H)=\Omega</math>

<math>\psi_H(H\times2)=\Omega_2</math>

<math>\psi_H(H^2)=\alpha</math>

<math>\psi_H(H^2+H)=\Omega_{\alpha+1}</math>

<math>\psi_H(H^2\times2)=\alpha_2</math>

<math>\psi_H(H^3)=\beta</math>

<math>\psi_H(H^\omega)=\omega-\text{Projection}</math>

我们观察到，对于一个 <math>\psi_H(X\sim H)</math>，它可以“投影”<math>\psi_H(X\sim (H\times 2))</math> 之前的序数而不补层。比如说 <math>\psi_H(H^2)</math>（<math>\alpha</math>），可以“投影”<math>\psi_H(H^2\times2)</math>（<math>\alpha_2</math>）以前的序数，例如 <math>\psi_H(H\times(H+1))=\psi_H(H^2+H))</math>（<math>\Omega_{\alpha+1}</math>）。

下面我们考虑一个 (1,0)-Proj. <math>\psi_H(H^H)</math>，按照先前的规律，它可以“投影” <math>\psi_H(H^{H\times 2})</math>（(2,0)-Proj.）之前的序数而不补层。为了方便接下来的讲解，我们引入如下记号：

(a1,a2,...,an)-Proj.=<math>\psi_H(H^{H^{n-1}\times a_1+H^{n-2}\times a_2+\dots+H\times a_{n-1}+a_n})</math>，例如 (1,1,4,5,1,4)-Proj.=<math>\psi(H^{H^5+H^4+H^3\times4+H^2\times5+H+4})</math>

S=(1,0)-Proj.，σ 表示升 1 阶投影（如 σS=(1,1)-Proj.），θ 表示升 (1,0) 阶投影（如 θS=(2,0)-Proj.）

一开始，<math>\psi_S</math>函数与OCF表现得无异，有<math>\psi_S(S)=\varepsilon_0</math>，<math>\psi_S(S_\omega)=\text{BO}</math>。我们注意到<math>\psi_H(H^2)</math>投影<math>\psi_H(H\times(H+1))</math>，于是便可以让S投影<math>\psi_H(H^{H+1})</math>，也就是σS,因此，<math>\psi_S(\sigma S)=\Omega</math>。

接下来是Ω的递归运算：

<math>\psi_S(\sigma S+1)=\Omega\times\omega</math>

<math>\psi_S(\sigma S+\psi_S(\sigma S))=\Omega^2</math>

<math>\psi_S(\sigma S+\psi_S(\sigma S+\psi_S(\sigma S)))=\Omega^\Omega</math>

<math>\psi_S(\sigma S+S)=\varepsilon_{\Omega+1}</math>

这看起来并不强大，但是我们可以引入<math>S_2</math>让它变强。<math>\psi_{S_2}(\sigma S)</math>表示S递归运算的上确界，而S的递归运算又会被折叠为Ω的递归运算，因此<math>\psi_S(\sigma S+\psi_{S_2}(\sigma S))=\Omega_2</math>

于是，<math>\psi_S(\sigma S+\psi_{S_2}(\sigma S)\times2)=\Omega_3</math>

<math>\psi_S(\sigma S+\psi_{S_2}(\sigma S+1))=\Omega_\omega</math>

<math>\psi_S(\sigma S+\psi_{S_2}(\sigma S+S))=\rm{OFP}</math>

<math>\psi_S(\sigma S+\psi_{S_2}(\sigma S+\varepsilon_{S+1}))=\psi_I(\varepsilon_{I+1})</math>

<math>\psi_S(\sigma S+\psi_{S_2}(\sigma S+\psi_{S_2}(\sigma S)))=I</math>

<math>\psi_S(\sigma S+\psi_{S_2}(\sigma S+\psi_{S_2}(\sigma S)+1))=I_\omega</math>

<math>\psi_S(\sigma S+\psi_{S_2}(\sigma S+\psi_{S_2}(\sigma S)\times2))=I(1,0)</math>

<math>\psi_S(\sigma S+\psi_{S_2}(\sigma S+\psi_{S_2}(\sigma S+1)))=I(\omega,0)</math>

<math>\psi_S(\sigma S+\psi_{S_2}(\sigma S+\psi_{S_2}(\sigma S+S)+\psi_{S_2}(\sigma S)))=I(1,0,0)</math>

<math>\psi_S(\sigma S+\psi_{S_2}(\sigma S+\psi_{S_2}(\sigma S+\psi_{S_2}(\sigma S))))=M=\psi_\alpha(\Omega_{\alpha+1}^{\Omega_{\alpha+1}})</math>

<math>\psi_S(\sigma S+S_2)=\psi_\alpha(\varepsilon_{\Omega_{\alpha+1}+1})=\text{psd.}\Pi_\omega</math>

<math>\psi_S(\sigma S+\psi_{S_3}(\sigma S))=\psi_\alpha(\Omega_{\alpha+2})</math>

<math>\psi_S(\sigma S+\psi_{S_3}(\sigma S+1))=\psi_\alpha(\Omega_{\alpha+\omega})</math>

……

这样下去我们将会得到<math>\psi_S(\sigma S+S_\omega)=\psi_\alpha(\alpha_\omega)</math>，S只需稍微发力，便能击穿整个2-投影层级。于是我们有<math>\psi_S(\sigma S\times2)=\alpha</math>。

类似的，我们还可以用<math>\psi_S(\sigma S\times2+\dots)</math>来表示3-投影层级，直到<math>\psi_S(\sigma S\times3)=\beta</math>，最终得到<math>\psi_S(\sigma S\times\omega)=\omega-\text{Projection}</math>。这可以一直向上延伸到<math>\psi_S(\varepsilon_{\sigma S+1})</math>。

因为<math>\psi_S</math>函数不能投影S本身，所以<math>\psi_S(S_{\sigma S+1})</math>会直接补层展开为<math>\psi_S(\alpha \rightarrow \psi_{S_{\sigma S+1}}(\alpha)\rm{fp})</math>。在这之后，因为S能够投影<math>\sigma S_2</math>，所以<math>\psi_S(\sigma S_2)</math>会折叠<math>\psi_S(f(\sigma S))</math>(类比<math>\psi_\alpha(\Omega_{\alpha+2})</math>)。于是就可以将刚才的路重走一遍：

<math>\psi_S(\sigma S_2+\sigma S)</math>

<math>\psi_S(\sigma S_2+\psi_{S_{\sigma S+1}}(S_{\sigma S+1}))</math>

<math>\psi_S(\sigma S_2+\psi_{S_{\sigma S+1}}(\sigma S_2))</math>

<math>\psi_S(\sigma S_2+S_{\sigma S+1})</math>

<math>\psi_S(\sigma S_2+S_{\sigma S+\omega})</math>

<math>\psi_S(\sigma S_2\times2)</math>，这类似于一种更强的2-投影

<math>\psi_S(\sigma S_2\times\omega)</math>

<math>\psi_S(\sigma S_2\times\sigma S)</math>

<math>\psi_S(\sigma S_2^2)</math>

<math>\psi_S(\varepsilon_{\sigma S_2+1})</math>

<math>\psi_S(\sigma S_3)</math>

这样走下去，我们将得到<math>\psi_S(\sigma S_\omega)</math>，这已经是四行BMS中的<math>(0)(1,1,1,1)(2,2,2,1)(3,2,2)</math>。

回忆一下在2-投影中走过的路，<math>\alpha_\omega</math>之后，我们引入了3-投影。在这里，我们同样可以引入<math>\sigma\sigma S</math>（(1,2)-投影）来帮助我们走得更远。类比3-投影折叠2-投影，我们有<math>\psi_{\sigma\sigma S}(\sigma S_{\sigma\sigma S+1}\times\omega)=\sigma S_\omega</math>，而<math>\psi_{\sigma\sigma S}(\sigma S_{\sigma\sigma S+1}^2)</math>将会是(1,1)-投影的(1,1)-投影点。这样走下去，我们还会有<math>\psi_{\sigma\sigma S}(\sigma S_{\sigma\sigma S+\omega})</math>、<math>\psi_{\sigma\sigma S}(\sigma\sigma S_\omega)</math>甚至是<math>\psi_{\sigma\sigma S}(\psi_{\theta S}(\sigma\theta S\times\omega))</math>等等。

终结这一切的是<math>\psi_S(\sigma\sigma S)</math>，因为<math>\sigma\sigma S</math>是<math>\psi_H(H^{H+2})</math>，可以被S投影，所以这是一切<math>\psi(\psi_{\sigma\sigma S}(\alpha))</math>的上确界。于是我们可以继续得到：

<math>\psi_S(\sigma\sigma S+S)</math>

<math>\psi_S(\sigma\sigma S+\psi_{S_2}(\sigma S))</math>

<math>\psi_S(\sigma\sigma S+\psi_{S_2}(\psi_{\sigma\sigma S}(\sigma S_{\sigma\sigma S+1}\times\omega)))</math>

<math>\psi_S(\sigma\sigma S+\psi_{S_2}(\sigma\sigma S))</math>

<math>\psi_S(\sigma\sigma S+S_2)</math>

<math>\psi_S(\sigma\sigma S+\sigma S)</math>

<math>\psi_S(\sigma\sigma S+\psi_{S_{\sigma S+1}}(\sigma\sigma S))</math>

<math>\psi_S(\sigma\sigma S+S_{\sigma S+1})</math>

<math>\psi_S(\sigma\sigma S+S_{\sigma S+\omega})</math>

<math>\psi_S(\sigma\sigma S\times2)</math>

<math>\psi_S(\sigma\sigma S^2)</math>

<math>\psi_S(S_{\sigma\sigma S+1})</math>

<math>\psi_S(\sigma S_{\sigma\sigma S+1})</math>

<math>\psi_S(\sigma\sigma S_2)</math>

<math>\psi_S(\sigma\sigma S_\omega)</math>

<math>\psi_S(\psi_{\sigma\sigma\sigma S}(\sigma\sigma S_{\sigma\sigma\sigma S+1}^2))</math>

<math>\psi_S(\psi_{\sigma\sigma\sigma S}(\sigma\sigma\sigma S_\omega))</math>

<math>\psi_S(\sigma\sigma\sigma S)</math>

<math>\psi_S(\sigma^\omega S)</math>

……

至此，向上投影已经用出了全部的(1,n)-投影，S的层级似乎已经达到了极限，于是我们继续引入(2,0)-投影<math>\theta S</math>。类似于之前的(1,0)-投影，有<math>\psi_{\theta S}(\sigma\theta S\times\omega)=\sigma^\omega S</math>。(2,0)-投影折叠到(1,0)-投影，(3,0)-投影折叠到(2,0)-投影，最后的<math>\theta^\omega S</math>，已经达到了<math>(0)(1,1,1,1)(2,2,2,2)</math>。

想要打败QSS，仅仅使用(n,0)-投影是不够的。引入更强的(a,b,c,d,....)-投影，才能够打败QSS。

[WIP:(1,0,0)-投影的行为]

=== 在 OCF 中的行为 ===
''TO DO: 在 OCF 中的行为''

=== 枚举和强度分析 ===
''主词条：[[投影 VS 反射稳定|投影序数 VS 反射稳定]]，[[非递归BMS分析|非递归 BMS 分析]]，[[投影序数 VS 方括号稳定]]''

对投影序数的强度分析是极端重要的。因为投影序数类似递归记号的规则必须通过扽西才能被人理解。本词条仅列出关键节点。
{| class="wikitable"
!投影序数
!反射稳定
![[非递归BMS|非递归 BMS]]
|-
|<math>\psi_a(0)</math>
|<math>\Omega</math>
|<math>(1,1)</math>
|-
|<math>\psi_a(a)</math>
|<math>\varepsilon_{\Omega+1}</math>
|<math>(1,1)(2,2)</math>
|-
|<math>\psi_a(\Omega_{a+1})</math>
|<math>\Omega_2</math>
|<math>(1,1,1)</math>
|-
|<math>\psi_a(\Omega_{a+1}+a)</math>
|<math>\varepsilon_{\Omega_2+1}</math>
|<math>(1,1,1)(2,2)</math>
|-
|<math>\psi_a(\Omega_{a+1}2)</math>
|<math>\Omega_3</math>
|<math>(1,1,1)(2,2,1)</math>
|-
|<math>\psi_a(\Omega_{a+1}^2)</math>
|<math>2~1-2</math>
|<math>(1,1,1)(2,2,1)(3,2,1)</math>
|-
|<math>\psi_a(\Omega_{a+1}^{\Omega_{a+1}})</math>
|<math>2-2</math>
|<math>(1,1,1)(2,2,1)(3,2,1)(4,2,1)</math>
|-
|<math>\psi_a(a_2)</math>
|<math>\lambda\alpha.(\alpha+1)-\Pi_0</math>
|<math>(1,1,1)(2,2,1)(3,3)</math>
|-
|<math>\psi_a(\Omega_{a_2+1})</math>
|<math>\lambda\alpha.(\Omega_{\alpha+2})-\Pi_1</math>
|<math>(1,1,1)(2,2,1)(3,3,1)</math>
|-
|<math>\psi_a(a_\omega)</math>
|<math>\omega-\pi-\Pi_0</math>
|<math>(1,1,1)(2,2,2)</math>
|-
|<math>\psi(\Omega_{a_\omega+1})</math>
|<math>\omega-\pi-\Pi_1</math>
|<math>(1,1,1)(2,2,2)(3,2,1)</math>
|-
|<math>\psi_a(\psi_b(a_{b+1}^\omega))</math>
|<math>\lambda\alpha.(psd.\Pi_0[\omega])-\Pi_0</math>
|<math>(1,1,1)(2,2,2)(3,2,2)(4,2,2)(4)</math>
|-
|<math>\psi_a(\psi_b(\varepsilon_{a_{b+1}+1}))</math>
|
|<math>(1,1,1)(2,2,2)(3,3)</math>
|-
|<math>\psi_a(\psi_b(\Omega_{a_{b+1}+1}))</math>
|
|<math>(1,1,1)(2,2,2)(3,3,1)</math>
|-
|<math>\psi_a(\psi_b(a_{b+2}))</math>
|
|<math>(1,1,1)(2,2,2)(3,3,2)</math>
|-
|<math>\psi_a(\psi_b(b_\omega))</math>
|
|<math>(1,1,1)(2,2,2)(3,3,3)</math>
|-
|<math>\psi_a(\omega-proj.)</math>
|
|<math>(1,1,1)(2,2,2,1)</math>
|-
|<math>a</math>
|
|<math>(1,1,1,1)</math>
|-
|<math>\Omega_{a+1}</math>
|
|<math>(1,1,1,1)(2,2,1)</math>
|-
|<math>a_2</math>
|
|<math>(1,1,1,1)(2,2,1,1)</math>
|-
|<math>b</math>
|
|<math>(1,1,1,1)(2,2,2,1)</math>
|-
|<math>b_2</math>
|
|<math>(1,1,1,1)(2,2,2,1)(2,2,1,1)(3,3,2,1)</math>
|-
|<math>c</math>
|
|<math>(1,1,1,1)(2,2,2,1)(2,2,2,1)</math>
|-
|<math>\omega-projection</math>
|
|<math>(1,1,1,1)(2,2,2,1)(3)</math>
|}
{{默认排序:非递归记号}}
[[分类:记号]]

大数数学

2026-07-06T10:40:50Z

Baixie01000a7：已将重定向目标从googology更改为Googology

#REDIRECT [[Googology]]

Googology 梗百科

2026-06-13T16:45:56Z

Baixie01000a7：/* 2.扽西 */

本页面收录了一些中文 [[Googology|ggg]] 圈的梗。

== 一、聊天记录类 ==

=== 1.定义没有，牛B吹爆 ===
[[文件:12345B67.jpg|截图日期：2024年8月9日|缩略图]]
起因是 3184 说了句“来点小小的链节余项震撼”，后被 hypcos 回复“定义没有，牛B吹爆”

因为其过于经典而被广为流传。

后来还衍生出了多种版本，如“1234，5B67”和“□□□□，□□□□”，“分析没有，牛B吹爆”等

=== 2.XX给你打了 ===
出自于涵（大数经）对 hypcos 的回复“坦克给你打了”。
[[文件:Tank.jpg|缩略图]]
其中“坦克”指的是 [[LVO]]，这个名词来源于于涵的文件《大数级别段位》（一个数字量级表）中的“掌控者坦克”。另一个较为出名的是“邢天战甲”，被用于指代 [[BO]]。

这个梗中的“坦克”可以被换成任意词，被用于调侃性地表达两个事物间的比较。

此外，受这段聊天记录影响，有一些人在讨论部分内容时也常常使用“我倾向于”表达自己的观点。

详细信息可以参考B站用户 3183丶4139 的[https://b23.tv/ULKDxxw 这期视频]。

=== 3.都在大群拉💩是吧？全都跑不了 ===

出自hypcos在2024年10月25日的发言。

当天00:09qwerty发送“。。。”，随后adm.油手就行复读“。。。”，随后多人复读。09:15后陆续出现“打断复读”、“打断打断复读”、“打断^ω 复读”、“ε(打断+1) 复读”、“2nd 复读”……

随后hypcos发言“都在大群拉💩是吧？全都跑不了”，并分别将real.油手就行，此人不存在等7人分别禁言1,2,4,8,16,32,1分钟。

该聊天记录衍生为“都在___拉_是吧？全都跑不了”与“QSSO+1”(Y序列的1,2,4,8,16,32,1)。

== 二、错字类 ==

=== 1.果糕 ===
果糕是馃槹的谐音版，馃槹是 emoji 表情😰按 UTF-8 编码后用 GBK 解码的结果。

具体可以见[https://2023largenumber.fandom.com/zh/wiki/%F0%9F%98%B0#articleComments/ 此处]。

=== 2.扽西 ===
最早是 PCF 的错字，将“分析”打成了扽西，后来逐渐演变成了一个梗，用于代指不严谨的分析。

该错字衍生出了“森系”(senxi)，“啊恩系”(aenxi)，“ENXI”(CapsLock+enxi)等错字。

=== 3.其他错字 ===
还有一些错字也比较经典，如“狄安娜”指电脑，“周记”指手机，“全业务额是”是“确实”，在此不一一列举。
[[文件:2025-08-11 狄安娜的考验.png|缩略图|疑似对外国友人有点高难度了（对中国人也是）]]
详细可以参考[https://docs.qq.com/sheet/DVnlZSENqbm1CU3FQ?u=7b7ca06006c34e6b84a6bbcc0ac26715&tab=000001 错字辞典]，它较为详细地记载了一些错字。

Mountain Notation

2026-06-12T11:14:01Z

Baixie01000a7：/* MωMN */

=== 定义 ===
山脉系列的矩阵由列组成，它可以表示为 <math>A_1A_2\cdots A_{n-1}A_n</math> 的形式，其中 <math>A_i</math> 为各列，<math>n</math> 是非负整数。把所有列从左到右列出来，列标大为右，最左列的列标是 1。

列由元素组成，它可以表示为 <math>a_1a_2\cdots a_{n-1}a_n</math> 的形式，其中 <math>a_i</math> 为各元素，''<math>n</math>'' 是非负整数。把所有元素从下到上列出来，行标大为上，每一列还额外存在一个元素，位于最下端的行标 0 处。

元素由两部分构成：值、分隔符。值是正整数，代表该元素向左下伸出的左腿要跨越到第几列（左腿元素的行标则小于本元素，且左腿元素是满足条件的所有元素之中的最上者）。分隔符代表元素与它下方一格元素的行标差，这个行标差总是 <math>\omega</math> 的次方，于是该次方数称作本元素的维度（其实维度、分隔符也就是一个意思）。元素的写法是先写分隔符，再写值。至于分隔符的具体表达，则与具体的记号有关。

为了可计算地表达行标，它需要一个记号。（每一列最下端元素的）行标 0 用表达。如果一个元素 <math>a</math> 的行标是 <math>A</math>，它上方一格元素 <math>b</math> 的分隔符是 <math>B</math>，那么 ''<math>b</math>'' 的行标则是 <math>A+B</math>。此处的“+”是“行标加”运算，其定义如下：

<math>[A_1\oplus A_2\cdots\oplus A_n]+B=[A_1\oplus A_2\cdots\oplus A_j\oplus B] \quad j=\max(\{i\leq n|A_i\geq B\}\cup\{0\})</math>

行标的大小比较方式为以分隔符为单位，按字典序比较。至于分隔符的大小关系，则与具体的记号有关。

山脉系列记号同样沿用了山脉图中的一些概念。

* 父元：从一个元素 a 出发，先沿右腿向上一格，再沿左腿向左下一步，就到达 a 的父元。
* 祖先：“父元”关系的[[传递闭包#关系的传递闭包|传递闭包]]。此处祖先不含自身。
* 后代：如果 a 是 b 的祖先，那么 b 是 a 的后代。
* 右上角：最右列中最上端的元素。
* 根元素与具体的记号有关。
* 根元素所在的列是根列，但根列元素并非其字面含义。
* 根列元素指的是根元素及其下方所有元素。注意：不含根元素上方的元素！
* 参考元素与具体的记号有关。但一般而言，一个根列元素会对应一个或更多个参考元素。
* 复制部分是根列以右（不含）、最右列以左（含）的部分。其宽度称为复制宽度。
* magma 元素：任何一个根列元素 a 都对应一个或更多个 magma 元素。a 对应的 magma 元素是（在复制部分中）a 的同行后代。这样的对应可以用到所有根列元素上。把这些 magma 元素都收集起来，就是所有的 magma 元素了。
* 减一操作：在 Y 系列记号中就是简单的把原序列最右元素减去 1，但在山脉系列记号则稍显复杂，而且与具体的记号有关。

==== ωMN ====
ω Mountain Notation（ωMN）是将 [[ω-Y]] 的山脉图显式写出，并作些简化得到的记号。

定义分隔符：分隔符是多重逗号（连续写正整数个逗号），分隔符的大小关系就是逗号数量的大小关系。

ωMN 的简单规则如下：

# 零规则：<math>[n]=n</math>
# 后继规则：<math>A_1A_2\cdots A_X()[n]=A_1A_2\cdots A_X[n^2]</math>

其主流表达式为：<math>f(n)=()(\underbrace{,,\cdots,,1}_n)[n]</math>。由主流表达式展开简单规则所得的矩阵都是标准表达式。

如果一个表达式不能按简单规则处理，就执行一次展开，此时就需要定义根元素、参考元素、减一操作之类的概念。

* 定义根元素：从右上角出发，沿左腿向左下一步，就到达根元素。
* 定义顶元素：除了第 0 行元素以外，其它根列元素都是顶元素。此外，右上角也是顶元素。于是顶元素、根列元素数量相等。二者都从下到上排列，于是形成一一对应。
* 定义参考元素：每一对（根列元素, 顶元素）都对应一个或更多个参考元素。最右列之中，行标（大于等于根列元素行标）且（小于顶元素行标）的那些元素，就是这个配对对应的（也可以说：根列元素对应的）参考元素。

定义减一操作：按下列步骤修改矩阵。

# 设右上角的分隔符是 k 重逗号。右上角沿左腿向左下走一步，到达行标 A；右上角沿右腿向下一格，到达行标 B。
# 如果 k = 1，则删掉右上角，然后跳到第 4 步。如果 k > 1，继续第 3 步。
# 如果 A + (k − 1 重逗号 ) ≤ B，则删掉右上角，否则把右上角的分隔符从 k 重逗号改为 k − 1 重逗号。
# 把根元素上方的元素（不含根元素）都复制到最右列上方。

展开流程如下：

首先确定右上角、根列元素、顶元素。然后做减一操作。然后确定复制部分、复制宽度、magma 元素。对于矩阵 [n]，接下来要做 n 轮延伸，每一轮延伸都有编号：1, 2, . . . , n。

每一轮延伸的步骤如下：

先确定参考元素（注意，此时的矩阵可能已经做了若干延伸，而不再是原来的矩阵或者减一之后的矩阵）。然后，从左到右逐列地把复制部分的元素（称为源元素）复制到右边的新增列中（目标元素）。对于每一个“源元素列”的复制，从下到上应对那些元素。第 0 行的元素需要应对，但它不会作为源元素。最上端的元素不需应对，但它会作为源元素。

非 magma 元素 a。从 a 沿右腿向上一格，到达的元素 x 是待复制的源元素。它只能复制成一个目标元素。此类复制，目标元素的分隔符与 x 相同。如果 x 的值小于根列的列标，那么目标元素的值与 x 相同。如果 x 的值大于等于根列的列标，那么目标元素的值等于 x 的值加上 w · m，其中是 w 复制宽度，m 是延伸的编号。

magma 元素 a。从 a 沿右腿向上一格，到达的元素 x 是待复制的源元素。它可能复制成一个或更多个目标元素。找到 a 所在行的根列元素，然后找到这个根列元素对应的参考元素。每个参考元素将得出一个目标元素。此类复制，目标元素的值等于 x 的值加上 w · m，其中是 w 复制宽度，m 是延伸的编号。对于不是最上端的参考元素，沿右腿向上一格，到达一个元素，其分隔符为 K。于是目标元素的分隔符是 K。对于最上端的参考元素，目标元素的分隔符与 x 相同。

==== TωMN ====
超限 ωMN（Transfinite ω Mountain Notation, TωMN）是 ωMN 的简单扩展，它有 Ω 行的结构。TωMN 之于 ωMN，就好比 Ω 行 BMS 之于 [[BMS]]，它应该说算是一种比较弱的扩展。

定义分隔符：分隔符是非空矩阵。分隔符 <math>\underbrace{()()\cdots()()}_n</math> 也可以简写为 n 重逗号。

元素的大小比较：两元素相比，先比其值，如果值不等，则得出结果；如果值相等，再比分隔符，分隔符的比较结果就是元素的比较结果。

列的大小比较：以元素为单位，按字典序比较。

矩阵的大小比较（也就是分隔符的大小比较）：以列为单位，按字典序比较。

其简单规则如下：

# 零规则：<math>[n]=n</math>
# 后继规则：<math>A_1A_2\cdots A_X()[n]=A_1A_2\cdots A_X[n^2]</math>
#极限维度规则：如果右上角的分隔符是” 最右列不是 ( )” 的矩阵，那么展开此分隔符。

主流表达式：<math>f(n)=A_n[n]</math>，其中 <math>A_0=(),A_{i+1}=()(A_i1)</math>。

如果一个表达式不能按简单规则处理，就执行一次展开。此时就需要定义根元素、参考元素、减一操作之类的概念了。根元素、参考元素的定义与 ωMN 相同。

定义减一操作：按下列步骤修改矩阵。

# 设右上角的分隔符是 <math>M_1M_2\cdots M_X()</math>。右上角沿左腿向左下走一步，到达行标 A；右上角沿右腿向下一格，到达行标 B 。
# 如果 X = 0 ，则删掉右上角，然后跳到第 4 步。如果 X > 0 ，继续第 3 步。
# 如果 <math>A+M_1M_2\cdots M_X\leq B</math>，则删掉右上角，否则把右上角的分隔符从 <math>M_1M_2\cdots M_X</math> 改为 <math>M_1M_2\cdots M_X</math>。
# 把根元素上方的元素（不含根元素）都复制到最右列上方。

其展开流程与 ωMN 完全相同。

==== MωMN ====
变异 ωMN（Mutant ω mountain notation, MωMN）是 ωMN 的改版，增加了一点急模式的特质，但更类似于 mutant matrix，而不像 hyper matrix、sudden matrix 那样整块地比较矩阵大小。

MωMN 的分隔符、简单规则都与 ωMN 相同。

如果一个表达式不能按简单规则处理，就执行一次展开。此时就需要定义根元素、参考元素、减一操作之类的概念了。

* 按下列流程确定根元素：从右上角出发。设右上角的分隔符是 k 重逗号。如果 k = 1，那么沿左腿向左下走一步。到达的元素就是根元素。如果 k > 1，则继续后续的步骤。沿左腿向左下走一步。如果当前元素在第 0 行，则令 i = 0，否则设当前元素的分隔符是 i 重逗号。如果 i ≥ k，则回到步骤 3。否则，当前元素就是根元素。
* 定义参考元素：对于不是根元素的根列元素 a，从 a 沿右腿向上一格，到达根列元素 b。最右列之中，行标（大于等于 a 行标）且（小于 b 行标）的那些元素，就是 a 对应的参考元素。根元素对应的参考元素，是最右列之中，行标（大于等于根元素行标）且（小于等于“从右上角沿右腿向下一格到达的元素”的行标）的那些元素。

减一操作的定义与 ωMN 相同。

其展开流程如下：

对于矩阵 [n]，接下来要做 n 轮延伸。每一轮延伸都有编号：1, 2, . . . , n。最后去掉最右列，才完成整个展开流程。

每一轮延伸的步骤如下：首先确定右上角、根列元素、复制部分、复制宽度、magma 元素。然后做减一操作。然后确定参考元素。然后，从左到右逐列地把复制部分的元素（称为源元素）复制到右边的新增列中（目标元素）。每一列的处理过程，与 ωMN 相同。

MωMN在2026年5月9日被ddfg发现无穷降链：<syntaxhighlight lang="text">
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</syntaxhighlight>

==== MTωMN ====
变异超限 ωMN（Mutant Transfinite ω Mountain Notation, MTωMN）

既然有 MωMN 、有 TωMN ，那么接下来，MTωMN，就融入了"mutant"与"transfinite"两种特质。实质上它是在 TωMN 的基础上，改用 mutant 的方法来找根元素。MTωMN 的分隔符、简单规则都与 TωMN 相同。

如果一个表达式不能按简单规则处理，就执行一次展开。此时就需要定义根元素、减一操作之类的概念了。根元素的定义与 MωMN 完全相同。减一操作的定义与 TωMN 完全相同。展开流程与 MωMN 完全相同。

==== Dω·2MN ====
有缺陷的 ω·2MN（Defective ω·2 Mountain Notation, Dω·2MN）是 ω·2MN 的一个尝试。ω·2MN 的含义，是有 ω·2 种分隔符。

已知 [[Y序列|Y]] 和 [[BTBMS|TBMS]] 都是 [[BMS]] 的扩展，前者只有 ω2 行的结构却能远远超越后者的 Ω 行结构（不止如此，前者甚至还没有用完 ω+1 行结构，就已经在 [[ΩSSO|Y(1,3,4,2,5,8,10)]] 处达到后者的 Ω 行结构）。归根结底，这是由于 Y 具有一种特别的、TBMS 不具有的提升。TBMS 中，极限序数行只意味着最右列会变为极限序数下的大行标，而非最右列没有行标的增长。Y 中，最右列出现极限序数行时，不论是最右列还是非最右列，都存在行标的增加。Y 的这种现象称作 '''eruption'''。同样，为了真正强烈地超越 ωMN，而不是像 TωMN 那样弱，需要引入一种新型的提升：拉伸。在 TωMN 中，极限序数行只意味着最右列的分隔符会变为极限序数下的大分隔符，而非最右列的分隔符没有增长。接下来，在 Dω·2MN（或者其它 >ωMN）中，最右列出现极限序数行时，不论是最右列还是非最右列，都存在分隔符的增加。分隔符的增加意味着同列相邻元素的距离变远了，“拉伸”因而得名。

定义分隔符：

分隔符由两部分组成：（写在左边）0~1个分号、（写在右边）非负整数个逗号。

分隔符的大小关系：两分隔符相比，先比其分号数，如果不等，则得出结果；如果分号数相等，再比逗号数，逗号数的比较结果就是分隔符的比较结果。规定第 0 行元素具有 0 个分号、0 个逗号组成的分隔符。它仍在第0行（行标为[]）。以逗号结尾的分隔符称作后继分隔符（其前继是它去掉结尾的逗号）。否则称作极限分隔符。在本记号中，非空极限分隔符只有“;”一种。

其简单规则如下

# 零规则：<math>[n]=n</math>
# 后继规则：<math>A_1A_2\cdots A_X()[n]=A_1A_2\cdots A_X[n^2]</math>

主流表达式：<math>f(n)=()(;,,\cdots,,1)[n]</math>。由主流表达式展开，用简单规则得到的矩阵都是标准式。

如果一个表达式不能按简单规则处理，就执行一次展开。此时就需要定义根元素、参考元素、减一操作之类的概念了。对于 >ωMN 而言，还要定义拉伸相关的概念。

定义根元素：从右上角出发，沿左腿向左下一步，就到达根元素。（其实这个根元素的定义与 ωMN 相同）

定义拉伸阈：每一对(根列元素,顶元素)都有至多一个拉伸阈。拉伸阈是个分隔符。如果顶元素的分隔符是后继分隔符，则没有拉伸阈。其它情况，顶元素的分隔符是极限分隔符“;”。如果根列元素的分隔符≥顶元素的分隔符，则拉伸阈是1重逗号。设根列元素的分隔符是n重逗号，则拉伸阈是n+1重逗号。

定义拉伸量：每一对(根列元素,顶元素)，有拉伸量。拉伸量是个非负整数。如果没有拉伸阈，则拉伸量为0。如果参考元素只有1个，则拉伸量为0。如果顶元素分隔符>最上参考元素的分隔符≥拉伸阈，设拉伸阈是n重逗号，最上参考元素的分隔符是m重逗号，则拉伸量为m-n+1。其它情况，拉伸量为0。

定义减一操作：按下列步骤修改矩阵。

# 设右上角的分隔符是 M。右上角沿左腿向左下走一步，到达的元素具有分隔符 A、行标 α；右上角沿右腿向下一格，到达的元素具有分隔符 B、行标 β。
# 判断 M 的种类：
## M 是 1 重逗号。删掉右上角，然后跳到（外层的）第 3 步。
## M 是后继分隔符。记 M 的前继为 M'。如果 α+M'≤β，则删掉右上角；否则把右上角的分隔符从 M 改为 M'。然后跳到第 3 步。
## M 是极限分隔符“;”。
### 如果 A≥M 则令 j=1。否则设 A 是 i 重逗号，则令 j=i+1。
### 如果 α<β 且 B 是 ≥j 重逗号，则删掉右上角；否则把右上角的分隔符从 M 改为 j 重逗号。
### 跳到第 3 步。
#把根元素上方的元素（不含根元素）都复制到最右列上方。

以下是展开流程：

对于矩阵 [n]，接下来要做 n 轮延伸。每一轮延伸都有编号：1,2,...,n。最后去掉最右列，才完成整个展开流程。

每一轮延伸的步骤如下：首先确定右上角、根列元素、顶元素、复制部分、复制宽度、magma 元素。然后做减一操作。然后确定参考元素、拉伸阈、拉伸量。然后，从左到右逐列地把复制部分的元素（称为源元素）复制到右边的新增列中（目标元素）。

对于每一个“源元素列”的复制，从下到上应对那些元素。第 0 行的元素需要应对，但它不会作为源元素。最上端的元素不需应对，但它会作为源元素。

非 magma 元素 a。从 a 沿右腿向上一格，到达的元素 x 是待复制的源元素。它只能复制成一个目标元素。如果 x 的值小于根列的列标，那么目标元素的值与x相同。如果 x 的值大于等于根列的列标，那么目标元素的值等于x的值加上复制宽度。如果 x 的分隔符大于等于顶元素分隔符或小于拉伸阈，或者没有拉伸阈，则目标元素的分隔符与x相同。否则，目标元素的分隔符是“x的分隔符后面添加(拉伸量)重逗号”。

magma 元素 a。从 a 沿右腿向上一格，到达的元素 x 是待复制的源元素。它可能复制成一个或更多个目标元素。找到 a 所在行的根列元素，然后找到这个根列元素对应的参考元素。每个参考元素将得出一个目标元素。此类复制，目标元素的值等于 x 的值加上复制宽度。对于不是最上端的参考元素，沿右腿向上一格，到达一个元素，其分隔符为 K。于是目标元素的分隔符是 K。

对于最上端的参考元素。如果 x 的分隔符大于等于顶元素分隔符或小于拉伸阈，或者没有拉伸阈，则目标元素的分隔符与 x 相同。否则，目标元素的分隔符是“x 的分隔符后面添加（拉伸量）重逗号”。

注意到减一操作可能引入左腿跨越“非 ω 的次方”行，即 M 是分号、α+(j重逗号)≤β、但 B<j重逗号的情况。这是 ωMN、TωMN 没有的情况。在此情况下，右上角的分隔符从 M 改成了 j 重逗号，形成新的元素 m。这个元素 m，今后它作为某个根列元素时，在拉伸的判断下显得像j重逗号。然而，元素 m 在展开时，其分隔符却显示出比“β与α的差值”还要大的跨度。这种不匹配的错位（defect）也直接地表现为“左腿跨越非 ω 的次方行”。

典型例子：

<math>()(;1)(,2;1)(,3,3)(,1)(,5;5)(,6,,6;5)(,7,,7,7;5)</math>，粗体为根元素。

初次减一后得 <math>()(;1)(,2;1)(,3,3)(,1)(,5;5)(,6,,6;5)(,7,,7,7,,5)</math>，粗体为根元素及其对应的最上参考元素。

第一轮延伸时，拉伸阈为 2 重逗号，拉伸量为 1。得到 <math>()(;1)(,2;1)(,3,3)(,1)(,5;5)(,6,,6;5)(,7,,7,7,,5)(,8,,8,8,,8;8)(,9,,9,9,,9,,,9;8)(,10,,10,10,,10,,,10,10;8)</math>，粗体为根元素。

最终展开为 <math>()(;1)(,2;1)(,3,3)(,1)(,5;5)(,6,,6;5)(,7,,7,7,,5)(,8,,8,8,,8;8)(,9,,9,9,,9,,,9;8)(,10,,10,10,,10,,,10,10,,,8)(,11,,11,11,,11,,,11,11,,,11;11)(,12,,12,12,,12,,,12,12,,,12,,,,12;11)(,13,,13,13,,13,,,13,13,,,13,,,,13,13,,,,11)\cdots\cdots</math>

关于它的强度以及相对于 TωMN 的提升，参见词条 [[TωMN VS ω·2MN]]。

ω2MN在2026年6月12日被千风诗人笑姐姐发现无穷降链：<syntaxhighlight lang="text">
()(;1)(,2)(,1)(,4;4)(,5,,4)(,4,,4)(,7,,7;7)(,8,,7,,7)(,7,,7;7)(,10,,7,,7)
>
()(;1)(,2)(,1)(,4;4)(,5,,4)(,4,,4)(,7,,7;7)(,8,,7,,7)(,7,,7;7)(,10,,7,7)(,11,,11,11;11)(,12,,11,11,,11)(,11,,11,11,,11)(,14,,14,14,,14;14)(,15,,14,14,,14,,14)(,14,,14,14,,14;14)(,17,,14,14,,14,,14)
>
()(;1)(,2)(,1)(,4;4)(,5,,4)(,4,,4)(,7,,7;7)(,8,,7,,7)(,7,,7;7)(,10,,7,7)(,11,,11,11;11)(,12,,11,11,,11)(,11,,11,11,,11)(,14,,14,14,,14;14)(,15,,14,14,,14,,14)(,14,,14,14,,14;14)(,17,,14,14,,14,14)(,18,,18,18,,18,18;18)(,19,,18,18,,18,18,,18)(,18,,18,18,,18,18,,18)(,21,,21,21,,21,21,,21;21)(,22,,21,21,,21,21,,21,,21)(,21,,21,21,,21,21,,21;21)(,24,,21,21,,21,21,,21,,21)
</syntaxhighlight>

==== Aω·2MN ====
星体 ω·2MN（Astral ω·2 Mountain Notation, Aω·2MN）是 ω·2MN 的另一个尝试。

在 Dω·2MN 中，每个根列元素都成了拉伸的判断依据。要与之匹配，则减一操作时，根元素对应的最上参考元素必须按 Dω·2MN 定义中的那种方式变化，才能让每次最右列出现极限分隔符时有合理的拉伸。然而，还有一种方式来判断拉伸的依据。这种方式需要让一部分元素“不作为判断拉伸的依据”，因此判断的时候要跳过它们，找它们下方的元素。这些元素要有额外的标记，这里就用星号（*）来表示。

于是，每个元素由三部分构成：值、分隔符、星标。值是正整数，代表该元素向左下伸出的左腿要跨越到第几列（左腿元素的行标则小于本元素，且左腿元素是满足条件的所有元素之中的最上者）。分隔符代表元素与它下方一格元素的行标差，这个行标差总是ω的次方。星标是只有“有”“无”取值的布尔值，代表本元素作为判断拉伸的依据之否定。元素的写法是先写分隔符，再（如果有星标则写星号，否则不写任何东西），再写值。

分隔符的定义与 Dω·2MN 相同。简单规则与 Dω·2MN 相同。

如果一个表达式不能按简单规则处理，就执行一次展开。此时就需要定义根元素、参考元素、减一操作、拉伸阈、拉伸量之类的概念了。对于 Aω·2MN，还有额外的标记操作。

根元素的定义与 ωMN 相同。

定义函数 S(a)，其中 a 是元素。如果 a 有星标，则 S(a) 是 S(a沿右腿向下一格)，否则 S(a) 是 a 的分隔符。

定义拉伸阈：每一对 (根列元素,顶元素) 都有至多一个拉伸阈。拉伸阈是个分隔符。如果顶元素的分隔符是后继分隔符，则没有拉伸阈。其它情况，顶元素的分隔符是极限分隔符“;”。如果 S(根列元素)≥顶元素的分隔符，则拉伸阈是 1 重逗号。设 S(根列元素) 是 n 重逗号，则拉伸阈是 n+1 重逗号。

定义拉伸量：每一对 (根列元素,顶元素)，有拉伸量。拉伸量是个非负整数。如果没有拉伸阈，则拉伸量为 0。

其它情况，作下列流程：

# 从最上参考元素出发。
# 如果当前元素与根列元素同行，则拉伸量为 0。结束流程。
# 设当前元素的分隔符是 M。
# 如果顶元素分隔符>M≥拉伸阈，设 M 是 m 重逗号，拉伸阈是 n 重逗号，则拉伸量为 m-n+1。结束流程。
# 沿右腿向下一格。回到步骤 2。

定义减一操作：按下列步骤修改矩阵。

# 设右上角的分隔符是 M。右上角沿左腿向左下走一步，到达的元素 a 具有行标 α；右上角沿右腿向下一格，到达的元素具有分隔符 B、行标 β。
# 判断 M 的种类：
## M 是 1 重逗号。删掉右上角，然后跳到（外层的）第 3 步。
## M 是后继分隔符。记 M 的前继为 M'。如果 α+M'≤β，则删掉右上角；否则把右上角的分隔符从 M 改为 M'。然后跳到第 3 步。
## M 是极限分隔符“;”。
### 如果 S(a)≥M 则令 M'是 1 重逗号。否则设 S(a) 是 i 重逗号，则令 M' 是 i+1 重逗号。
### 如果 α+M'≤β，则删掉右上角；否则把右上角的分隔符从 M 改为 M'。
### 跳到第 3 步。
# 把根元素上方的元素（不含根元素）都复制到最右列上方。

定义标记操作：对于每一对 (根列元素,顶元素)，都按下列步骤修改矩阵。

# 从最上参考元素出发。
# 如果当前元素与根列元素同行，则结束流程。
# 设当前元素的分隔符是 M。
# 如果 M<拉伸阈，则把当前元素设为“有星标”。
# 如果顶元素>M≥拉伸阈，则结束流程。
#沿右腿向下一格。回到步骤 2。

以下是展开流程：

对于矩阵 [n]，接下来要做 n 轮延伸。每一轮延伸都有编号：1,2,...,n。最后去掉最右列，才完成整个展开流程。

每一轮延伸的步骤如下：首先确定右上角、根列元素、顶元素、复制部分、复制宽度、magma 元素。然后做减一操作。然后确定参考元素、拉伸阈、拉伸量，再做标记操作。然后，从左到右逐列地把复制部分的元素（称为源元素）复制到右边的新增列中（目标元素）。

对于每一个“源元素列”的复制，从下到上应对那些元素。第0行的元素需要应对，但它不会作为源元素。最上端的元素不需应对，但它会作为源元素。

非 magma 元素 a。从 a 沿右腿向上一格，到达的元素 x 是待复制的源元素。它只能复制成一个目标元素。如果 x 的值小于根列的列标，那么目标元素的值与 x 相同。如果 x 的值大于等于根列的列标，那么目标元素的值等于 x 的值加上复制宽度。如果 x 的分隔符大于等于顶元素分隔符或小于拉伸阈，或者没有拉伸阈，则目标元素的分隔符与x相同。否则，目标元素的分隔符是“x 的分隔符后面添加(拉伸量)重逗号”。目标元素的星标与 x 相同。

magma 元素 a。从 a 沿右腿向上一格，到达的元素 x 是待复制的源元素。它可能复制成一个或更多个目标元素。找到 a 所在行的根列元素，然后找到这个根列元素对应的参考元素。每个参考元素将得出一个目标元素。此类复制，目标元素的值等于 x 的值加上复制宽度。

对于不是最上端的参考元素，沿右腿向上一格，到达一个元素k。于是目标元素的分隔符、星标与 k 相同。对于最上端的参考元素。如果x的分隔符大于等于顶元素分隔符或小于拉伸阈，或者没有拉伸阈，则目标元素的分隔符与x相同。否则，目标元素的分隔符是“x 的分隔符后面添加(拉伸量)重逗号”。

目标元素的星标与 x 相同。

在 Dω·2MN 中，每个根列元素都成了拉伸的判断依据；与之匹配的是最上端的参考元素。

而在 Aω·2MN 中，最上端的参考元素可能不够大，便用它下方最近的“足够大”的参考元素作为拉伸的判断依据。由此，要想与之匹配，根列元素就需要星标，延续“它下方最近的足够大的参考元素”这一思想。

典例分析：<math>()(;1)(,2;1)(,3,3)(,1)(,5;5)(,6,,6;5)(,7,,7,7;5)</math>，粗体为根元素。

减一后得 <math>()(;1)(,2;1)(,3,3)(,1)(,5;5)(,6,,6;5)(,7,,7,7)</math>，粗体为根元素及其对应的最上参考元素。

拉伸阈为 2 重逗号，拉伸量为 1。

标记后得 <math>()(;1)(,2;1)(,3,3)(,1)(,5;5)(,6,,6;5)(,7,,7,*7)</math>。然后延伸出更多列。

最终展开为 <math>()(;1)(,2;1)(,3,3)(,1)(,5;5)(,6,,6;5)(,7,,7,*7)(,8,,8,*8;8)(,9,,9,*9,,,9;8)(,10,,10,*10,,,10,*10)(,11,,11,*11,,,11,*11;11)(,12,,12,*12,,,12,*12,,,,12;11)(,13,,13,*13,,,13,*13,,,,13,*13)</math>……

==== Dω2MN ====
有缺陷的 ω2MN（Defective ω2 Mountain Notation, Dω2MN）是 Dω·2MN 的进一步扩展，是 ω2MN 的一种尝试。因为 Astral 型定义比较复杂，所以我选用了 Defective 型的定义。虽不太完美，但好在定义比 astral 简单一点点。ω2MN，意思是有 ω2 种分隔符的 MN。

Dω·2MN 有一种极限分隔符“;”，由此有一种拉伸：一部分小于分号的分隔符（有拉伸阈的要求）扩大了，但仍小于分号。在 ω2MN 中，那就有 ω 种极限分隔符，它们是 n 重分号，由此有拉伸：一部分小于 n 重分号的分隔符（有拉伸阈的要求）扩大了，但仍小于 n 重分号。

定义分隔符：分隔符由两部分组成：（写在左边）非负整数个分号、（写在右边）非负整数个逗号。分隔符的大小关系：两分隔符相比，先比其分号数，如果不等，则得出结果；如果分号数相等，再比逗号数，逗号数的比较结果就是分隔符的比较结果。规定第 0 行元素具有 0 个分号、0 个逗号组成的分隔符。它仍在第 0 行（行标为 []）。以逗号结尾的分隔符称作后继分隔符（其前继是它去掉结尾的逗号）。否则称作极限分隔符。

简单规则与 Dω·2MN 相同。

主流表达式：<math>f(n)=()(;;;\cdots;;1)[n]</math>。

由主流表达式展开，用简单规则得到的矩阵都是标准式。

如果一个表达式不能按简单规则处理，就执行一次展开。此时就需要定义根元素、减一操作、拉伸阈、拉伸量之类的概念了。

对于极限分隔符 M=n重分号，记 M[i] = n-1 重分号后跟 i 重逗号（i 只取正整数）。

根元素的定义与 ωMN 相同：从右上角出发，沿左腿向左下一步，就到达根元素。

定义拉伸阈：每一对 (根列元素,顶元素) 都有至多一个拉伸阈。拉伸阈是个分隔符。如果顶元素的分隔符是后继分隔符，则没有拉伸阈。其它情况，顶元素的分隔符是极限分隔符——设它是 M。如果根列元素的分隔符≥M，则拉伸阈是 M[1]。如果根列元素的分隔符<M，则拉伸阈是 M[n]，其中 n 是使得“M[i]>根列元素的分隔符”的最小正整数 i。

定义拉伸量：每一对 (根列元素,顶元素)，有拉伸量。拉伸量是个非负整数。如果没有拉伸阈，则拉伸量为 0。如果参考元素只有 1 个，则拉伸量为 0。如果顶元素分隔符 > 最上参考元素的分隔符≥拉伸阈：设拉伸阈是 n 重分号后跟 m 重逗号，最上参考元素的分隔符是 n 重分号后跟 k 重逗号，则拉伸量为 k-m+1。其它情况，拉伸量为 0。

定义减一操作：按下列步骤修改矩阵。

# 设右上角的分隔符是 M。右上角沿左腿向左下走一步，到达的元素具有分隔符 A、行标 α；右上角沿右腿向下一格，到达的元素具有分隔符 B、行标 β。
# 判断 M 的种类：
## M 是 1 重逗号。删掉右上角，然后跳到（外层的）第 3 步。
## M 是后继分隔符。记 M 的前继为 M'。如果 α+M'≤β，则删掉右上角；否则把右上角的分隔符从 M 改为 M'。然后跳到第 3 步。
## M 是极限分隔符。
### 如果 A≥M 则令j=1。否则令 j=(使得 M[i]>A 的最小正整数 i)。
### 如果 α<β 且 B≥M[j]，则删掉右上角；否则把右上角的分隔符从 M 改为 M[j]。
### 跳到第 3 步。
# 把根元素上方的元素（不含根元素）都复制到最右列上方。

以下是展开流程：

对于矩阵 [n]，接下来要做 n 轮延伸。每一轮延伸都有编号：1,2,...,n。最后去掉最右列，才完成整个展开流程。

每一轮延伸的步骤如下：首先确定右上角、根列元素、顶元素、复制部分、复制宽度、magma 元素。然后做减一操作。然后确定参考元素、拉伸阈、拉伸量。然后，从左到右逐列地把复制部分的元素（称为源元素）复制到右边的新增列中（目标元素）。

对于每一个“源元素列”的复制，从下到上应对那些元素。第 0 行的元素需要应对，但它不会作为源元素。最上端的元素不需应对，但它会作为源元素。

非 magma 元素 a。从 a 沿右腿向上一格，到达的元素 x 是待复制的源元素。它只能复制成一个目标元素。确定目标元素的值：如果 x 的值小于根列的列标，那么目标元素的值与 x 相同；如果 x 的值大于等于根列的列标，那么目标元素的值等于 x 的值加上复制宽度。确定目标元素的分隔符：如果 x 的分隔符大于等于顶元素分隔符或小于拉伸阈，或者没有拉伸阈，则目标元素的分隔符与 x 相同；否则，目标元素的分隔符是“x 的分隔符后面添加(拉伸量)重逗号”。

magma 元素 a。从 a 沿右腿向上一格，到达的元素x是待复制的源元素。它可能复制成一个或更多个目标元素。找到 a 所在行的根列元素，然后找到这个根列元素对应的参考元素。每个参考元素将得出一个目标元素。

确定目标元素的值：此类复制，目标元素的值等于 x 的值加上复制宽度。

确定目标元素的分隔符：对于不是最上端的参考元素，沿右腿向上一格，到达一个元素，其分隔符为 K。于是目标元素的分隔符是 K。对于最上端的参考元素，如果 x 的分隔符大于等于顶元素分隔符或小于拉伸阈，或者没有拉伸阈，则目标元素的分隔符与 x 相同；否则，目标元素的分隔符是“x 的分隔符后面添加(拉伸量)重逗号”。

==== DωωMN ====
有缺陷的 ωωMN（Defective ωω Mountain Notation, DωωMN）是 Dω2MN 的进一步扩展，是 ωωMN 的一种尝试。

DωωMN 中的分隔符有 ωω 种。其中，第 α+1 种都是后继分隔符；第 α+ω 种分隔符与 Dω2MN 中的分隔符类似，以它为顶元素发生拉伸的时候，被拉伸的分隔符总是在末尾添加若干个逗号（即分隔符的种类序数增加一个正整数）；而更大的第<math>\alpha+\omega^2</math>种分隔符则是新东西，以它为顶元素发生拉伸的时候，被拉伸的分隔符要从第<math>\alpha+\omega\times n+m</math>种分隔符拉伸到第<math>\alpha+\omega\times(n+k)+m</math>种分隔符，这不是简单的“加一个序数”，而是连末尾的整数部分也保留着。

由于分隔符的种类较多，DωωMN 将像 TωMN 那样，用记号自身来表达分隔符。只不过，分隔符的大小有上限。

定义分隔符：分隔符是小于 <math>()(,1)(,2)</math> 的非空矩阵。分隔符也可以简写为 n 重逗号。

（以下分隔符概念与 TωMN 相同）

元素的大小比较：两元素相比，先比其值，如果值不等，则得出结果；如果值相等，再比分隔符，分隔符的比较结果就是元素的比较结果。

列的大小比较：以元素为单位，按字典序比较。

矩阵的大小比较（也就是分隔符的大小比较）：以列为单位，按字典序比较。

规定第0行元素具有空矩阵分隔符。它仍在第 0 行（行标为 []）。

以结尾的分隔符称作后继分隔符（其前继是它去掉结尾的）。否则称作极限分隔符。

简单规则与 Dω·2MN 相同。

主流表达式：<math>f(n)=()(,1)(,2()(,1)(,1)\cdots(,1)2)[n]</math>。由主流表达式展开，用简单规则得到的矩阵都是标准式。

如果一个表达式不能按简单规则处理，就执行一次展开。此时就需要定义根元素、减一操作、拉伸阈、拉伸量之类的概念了。

对于分隔符 M 而言，它可以作为矩阵长展开为 M[n]（n 为非负整数），我们也定义长展开的 M[-1] 是 M 去掉根列右侧（不含根列）的所有列。以下所有定义中，M[n] 都采用长展开而非短展开。

根元素的定义与 ωMN 相同，从右上角出发，沿左腿向左下一步，就到达根元素。

定义拉伸阈：每一对 (根列元素,顶元素) 都有至多一个拉伸阈。拉伸阈是个分隔符。如果顶元素的分隔符是后继分隔符，则没有拉伸阈。其它情况，顶元素的分隔符是极限分隔符，设它是 M。如果根列元素的分隔符≥M，则拉伸阈是 M[-1]。如果根列元素的分隔符<M，则拉伸阈是 M[n]，其中 n 是满足“M[n]>根列元素的分隔符”的最小值。

定义拉伸量：每一对 (根列元素,顶元素)，有拉伸量。拉伸量是个非负整数。如果没有拉伸阈，则拉伸量为 0。如果参考元素只有1个，则拉伸量为0。如果顶元素分隔符>最上参考元素的分隔符≥拉伸阈：设顶元素分隔符是 M，拉伸阈是 M[n]，最上参考元素的分隔符是 K，k 是满足 K≥M[k] 的最大值，则拉伸量为 k-n+1。其它情况，拉伸量为 0。

定义减一操作：按下列步骤修改矩阵。

# 设右上角的分隔符是 M。右上角沿左腿向左下走一步，到达的元素具有分隔符 A、行标 α；右上角沿右腿向下一格，到达的元素具有分隔符 B、行标 β。
# 判断 M 的种类：
## M 是 1 重逗号。删掉右上角，然后跳到（外层的）第 3 步。
## M 是后继分隔符。记 M 的前继为 M'。如果 α+M'≤β，则删掉右上角；否则把右上角的分隔符从 M 改为 M'。然后跳到第 3 步。
## M 是极限分隔符。
### 如果 A≥M 则令 j=-1。否则令 j=(使得 M[i]>A 的最小 i)。
### 如果 α<β 且 B≥M[j]，则删掉右上角；否则把右上角的分隔符从 M 改为 M[j]。
### 跳到第 3 步。
# 把根元素上方的元素（不含根元素）都复制到最右列上方。

以下是展开流程。

对于矩阵 [n]，接下来要做 n 轮延伸。每一轮延伸都有编号：1,2,...,n。延伸完毕后，如果是长展开，则再做一次减一操作；如果是短展开，则去掉最右列。这才完成整个展开流程。

每一轮延伸的步骤如下：首先确定右上角、根列元素、顶元素、复制部分、复制宽度、magma 元素。然后做减一操作。然后确定参考元素、拉伸阈、拉伸量。然后，从左到右逐列地把复制部分的元素（称为源元素）复制到右边的新增列中（目标元素）。

对于每一个“源元素列”的复制，从下到上应对那些元素。第 0 行的元素需要应对，但它不会作为源元素。最上端的元素不需应对，但它会作为源元素。

非 magma 元素 a。从 a 沿右腿向上一格，到达的元素 x 是待复制的源元素（分隔符为 X）。它只能复制成一个目标元素。确定目标元素的值：如果 x 的值小于根列的列标，那么目标元素的值与 x 相同；如果 x 的值大于等于根列的列标，那么目标元素的值等于 x 的值加上复制宽度。确定目标元素的分隔符：如果 X 大于等于顶元素分隔符或小于拉伸阈，或者没有拉伸阈，则目标元素的分隔符是 X；否则，记顶元素分隔符为 M、拉伸量为 k。设 s 满足 X≤M[s]。从最左列数起，X 与 M[s] 的最长公共部分（一整列一整列地数）为 N。再取 t 是满足 M[t] 是 X 从最左列开始的部分的最大值，Y 是 X 去掉 M[t] 后剩余的部分。设 M 的根列在第 u 列。将 Y 中所有大于等于 u 的元素值都加上 (M 的复制宽度)·k。于是，目标元素的分隔符是 M[t+k] 右边跟着 Y。

magma 元素a。从 a 沿右腿向上一格，到达的元素x是待复制的源元素。它可能复制成一个或更多个目标元素。找到a所在行的根列元素，然后找到这个根列元素对应的参考元素。每个参考元素将得出一个目标元素。

确定目标元素的值：此类复制，目标元素的值等于x的值加上复制宽度。

确定目标元素的分隔符：对于不是最上端的参考元素，沿右腿向上一格，到达一个元素，其分隔符为 K。于是目标元素的分隔符是 K。对于最上端的参考元素，如果 x 的分隔符大于等于顶元素分隔符或小于拉伸阈，或者没有拉伸阈，则目标元素的分隔符与 x 相同；否则，设 x 的分隔符是 X，记顶元素分隔符为 M、拉伸量为 k。设 s 满足 X≤M[s]。从最左列数起，X 与 M[s] 的最长公共部分（一整列一整列地数）为 N。再取t是满足“M[t] 是 X 从最左列开始的部分”的最大值，Y 是 X 去掉 M[t] 后剩余的部分。设 M 的根列在第 u 列。将 Y 中所有大于等于 u 的元素值都加上 (M的复制宽度)·k。于是，目标元素的分隔符是 M[t+k] 右边跟着 Y。

==== TωωMN ====
超限 ωωMN（Transfinite ωω Mountain Notation, TωωMN）是 DωωMN 的进一步扩展。不确定更高层次的 αMN 是否需要更“新型”的提升/eruption/拉伸/etc. 概念才能完成。这里暂用 transfinite 这个形容词来表示分隔符种类之多——TωωMN 中的分隔符种类数与该记号的极限相当。看到这里，我们知道，TωωMN 最关键的问题在于如何拉伸。我们仍规定只有当顶元素分隔符>待拉伸分隔符≥拉伸阈的时候才有可能拉伸。所有其他定义都要配合这一准则。

一个非平凡的拉伸发生在“顶元素具有第 ωω 种分隔符”的情形。被拉伸的分隔符要从第 <math>\omega^n</math> 种分隔符拉伸到第 <math>\omega^{n+k}</math> 种分隔符。但如果分隔符的种类序数不是 ω 的整次方呢？比如，被拉伸的分隔符是第 <math>\omega^n\times2</math> 种分隔符，按照 DωωMN 的拉伸方法，它将变成第 <math>\omega^{n+k}+\omega^n</math> 种分隔符，只取“最左侧”的一个部分发生拉伸。另一个非平凡的拉伸发生在“顶元素具有分隔符<math>()(,1)(,2,,2)</math>”的情形。此时分隔符在展开时出现 eruption，那么拉伸就不是按照 DωωMN 定义的那种“仅仅向右平移、元素值增加”能完成的了。我们需要把被拉伸的分隔符也纳入顶元素分隔符的延伸过程中，把（被拉伸的分隔符中的）根列右方的列当作被复制的东西，连同主要的延伸过程一起复制、一起向右移动、一起 eruption、一起拉伸。

TωωMN 的分隔符与 TωMN 相同。

简单规则与 Dω·2MN 相同。

主流表达式：<math>f(n)=A_n[n],\text{其中}A_0=(),A_i=A_{i-1}(A_0iA_1i\cdots A_{i-1}i)</math>。由主流表达式展开，用简单规则得到的矩阵都是标准式。

如果一个表达式不能按简单规则处理，就执行一次展开。此时就需要定义根元素、减一操作、拉伸阈、拉伸量之类的概念了。

对于分隔符 M 而言，它可以作为矩阵长展开为 M[n]（n 为非负整数），我们也定义长展开的 M[-1] 是 M 去掉根列右侧（不含根列）的所有列。以下所有定义中，M[n] 都采用长展开而非短展开。此外，对于分隔符 M>N 而言，把它们作为矩阵，可以将 M 延伸，同时 N 作为“附加列”也一起延伸。带附加列的延伸流程将在“展开流程”一节阐述。

根元素的定义与 ωMN 相同——从右上角出发，沿左腿向左下一步，就到达根元素。

定义拉伸阈：每一对 (根列元素,顶元素)都有至多一个拉伸阈。拉伸阈是个分隔符。如果顶元素的分隔符是后继分隔符，则没有拉伸阈。其它情况，顶元素的分隔符是极限分隔符——设它是 M。如果根列元素的分隔符≥M，则拉伸阈是 M[-1]。此时定义预拉伸量为 0。如果根列元素的分隔符<M，则拉伸阈是M[n]，其中 n 是满足 M[n]>根列元素的分隔符的最小值。此时定义预拉伸量为 n+1。

定义拉伸量：每一对 (根列元素,顶元素)，有拉伸量。拉伸量是个非负整数。如果没有拉伸阈，则拉伸量为 0。如果参考元素只有 1 个，则拉伸量为 0。如果顶元素分隔符>最上参考元素的分隔符≥拉伸阈，设顶元素分隔符是 M，预拉伸量是 n，最上参考元素的分隔符是 K，k 是满足 M[k]>K 的最小值，则拉伸量为 k-n+1。其它情况，拉伸量为 0。

减一操作的定义与 DωωMN 相同。

以下是展开流程：

对于矩阵[n]，接下来要做n轮延伸。每一轮延伸都有编号：1、2……、n。
延伸完毕后，如果是长展开，则再做一次减一操作；如果是短展开，则去掉最右列。这才完成整个展开流程。

每一轮延伸，可能是单独一个矩阵的延伸，也可能是“A 附加 B 延伸”（A,B 都是矩阵。此处 A 称作主矩阵，B 称作附加矩阵）。步骤如下：

# 首先是附加矩阵的预处理。A,B 的最长公共部分（一整列一整列地数）记作 C。B 删去 C 这个部分，余下的部分作为后续步骤中的“附加矩阵”。
# 主矩阵确定右上角、根列元素、顶元素、复制部分、复制宽度。
# 附加矩阵的复制部分是根列以右（不含根列）的所有列，列标甚至能超过主矩阵的列数。
# 主矩阵、附加矩阵都（按照主矩阵的根列元素）确定 magma 元素。
# 主矩阵做减一操作，不含附加矩阵。
# 主矩阵确定参考元素、拉伸阈、预拉伸量、拉伸量。
# 从左到右逐列地把主矩阵、附加矩阵复制部分的元素（称为源元素）复制到右边的新增列中（目标元素）。
# 如果要得到附加矩阵 D，那么把“现有的附加矩阵”作为 D 最右边的部分，D 左边空余的列从主矩阵取得。

对于每一个“源元素列”的复制，从下到上应对那些元素。第 0 行的元素需要应对，但它不会作为源元素。最上端的元素不需应对，但它会作为源元素。

非 magma 元素 a。从 a 沿右腿向上一格，到达的元素 x 是待复制的源元素（分隔符为 X）。它只能复制成一个目标元素。确定目标元素的值：如果 x 的值小于根列的列标，那么目标元素的值与 x 相同；如果 x 的值大于等于根列的列标，那么目标元素的值等于 x 的值加上复制宽度。确定目标元素的分隔符：如果 X 大于等于顶元素分隔符或小于拉伸阈，或者没有拉伸阈，则目标元素的分隔符是 X；否则，记顶元素分隔符为 M、预拉伸量为 m、拉伸量为 k，M 延伸 m 轮得到 N。目标元素的分隔符是“N 附加 X 延伸 k 轮之后得到的附加矩阵。

magma 元素 a。从 a 沿右腿向上一格，到达的元素 x 是待复制的源元素。它可能复制成一个或更多个目标元素。找到 a 所在行的根列元素，然后找到这个根列元素对应的参考元素。每个参考元素将得出一个目标元素。

确定目标元素的值：此类复制，目标元素的值等于 x 的值加上复制宽度。

确定目标元素的分隔符：

# 对于不是最上端的参考元素，沿右腿向上一格，到达一个元素，其分隔符为 K。于是目标元素的分隔符是 K。
# 对于最上端的参考元素。
## 如果 x 的分隔符大于等于顶元素分隔符或小于拉伸阈，或者没有拉伸阈，则目标元素的分隔符与 x 相同。
## 否则，设 x 的分隔符是 X，记顶元素分隔符为 M、预拉伸量为 m、拉伸量为 k。M 延伸 m 轮得到 N。目标元素的分隔符是“N 附加 X 延伸”k 轮之后得到的附加矩阵。

=== 与 Y 系列记号的区别 ===
Y 系列记号的表达式是个正整数序列，每个元素都压缩了许多信息，不能立即辨认，需要画出山脉图才可以看到其结构。山脉图分为行、列，列标与行标的二元组可以定位山脉图中的一个元素。列标是正整数，每一列对应原来序列的一个元素。行标则是序数，理想中 α-Y 山脉图的行标是小于 <math>\omega^{1+\alpha}</math> 的序数。相比之下，山脉系列记号则显式地表达山脉图，而无需像 Y 系列记号那样需要解压、压缩。山脉系列记号的表达式是矩阵[n]，此 n 也就是展开时的基本列项数。

相比于 Y 系列记号而言，山脉系列记号具有如下的优点：

# 显式地表达山脉图，无需解压（画山脉图）、压缩（从山脉图还原为正整数序列）就可看出结构。
# 表达式可以更加自由（不受解压、压缩的限制），从而可以简化。尽管与 Y 同样有许多非标准表达。
# 可以规避压扁现象——山脉记号中特定行标的元素总可以存在。这是第二点优势的延伸。
# 可以规避 Y 系列作超限简单扩展时“极限序数行标的 1 与极限序数值不匹配”的问题。

但同时它有如下的不足：

# 表达式比较长，不如 Y 系列简短。
# 难以提取，而 Y 系列却可以简单地提取任何可以形成正整数序列的东西。
{{默认排序:序数记号}}
[[分类:记号]]

Mountain Notation

2026-06-12T11:13:34Z

Baixie01000a7：

=== 定义 ===
山脉系列的矩阵由列组成，它可以表示为 <math>A_1A_2\cdots A_{n-1}A_n</math> 的形式，其中 <math>A_i</math> 为各列，<math>n</math> 是非负整数。把所有列从左到右列出来，列标大为右，最左列的列标是 1。

列由元素组成，它可以表示为 <math>a_1a_2\cdots a_{n-1}a_n</math> 的形式，其中 <math>a_i</math> 为各元素，''<math>n</math>'' 是非负整数。把所有元素从下到上列出来，行标大为上，每一列还额外存在一个元素，位于最下端的行标 0 处。

元素由两部分构成：值、分隔符。值是正整数，代表该元素向左下伸出的左腿要跨越到第几列（左腿元素的行标则小于本元素，且左腿元素是满足条件的所有元素之中的最上者）。分隔符代表元素与它下方一格元素的行标差，这个行标差总是 <math>\omega</math> 的次方，于是该次方数称作本元素的维度（其实维度、分隔符也就是一个意思）。元素的写法是先写分隔符，再写值。至于分隔符的具体表达，则与具体的记号有关。

为了可计算地表达行标，它需要一个记号。（每一列最下端元素的）行标 0 用表达。如果一个元素 <math>a</math> 的行标是 <math>A</math>，它上方一格元素 <math>b</math> 的分隔符是 <math>B</math>，那么 ''<math>b</math>'' 的行标则是 <math>A+B</math>。此处的“+”是“行标加”运算，其定义如下：

<math>[A_1\oplus A_2\cdots\oplus A_n]+B=[A_1\oplus A_2\cdots\oplus A_j\oplus B] \quad j=\max(\{i\leq n|A_i\geq B\}\cup\{0\})</math>

行标的大小比较方式为以分隔符为单位，按字典序比较。至于分隔符的大小关系，则与具体的记号有关。

山脉系列记号同样沿用了山脉图中的一些概念。

* 父元：从一个元素 a 出发，先沿右腿向上一格，再沿左腿向左下一步，就到达 a 的父元。
* 祖先：“父元”关系的[[传递闭包#关系的传递闭包|传递闭包]]。此处祖先不含自身。
* 后代：如果 a 是 b 的祖先，那么 b 是 a 的后代。
* 右上角：最右列中最上端的元素。
* 根元素与具体的记号有关。
* 根元素所在的列是根列，但根列元素并非其字面含义。
* 根列元素指的是根元素及其下方所有元素。注意：不含根元素上方的元素！
* 参考元素与具体的记号有关。但一般而言，一个根列元素会对应一个或更多个参考元素。
* 复制部分是根列以右（不含）、最右列以左（含）的部分。其宽度称为复制宽度。
* magma 元素：任何一个根列元素 a 都对应一个或更多个 magma 元素。a 对应的 magma 元素是（在复制部分中）a 的同行后代。这样的对应可以用到所有根列元素上。把这些 magma 元素都收集起来，就是所有的 magma 元素了。
* 减一操作：在 Y 系列记号中就是简单的把原序列最右元素减去 1，但在山脉系列记号则稍显复杂，而且与具体的记号有关。

==== ωMN ====
ω Mountain Notation（ωMN）是将 [[ω-Y]] 的山脉图显式写出，并作些简化得到的记号。

定义分隔符：分隔符是多重逗号（连续写正整数个逗号），分隔符的大小关系就是逗号数量的大小关系。

ωMN 的简单规则如下：

# 零规则：<math>[n]=n</math>
# 后继规则：<math>A_1A_2\cdots A_X()[n]=A_1A_2\cdots A_X[n^2]</math>

其主流表达式为：<math>f(n)=()(\underbrace{,,\cdots,,1}_n)[n]</math>。由主流表达式展开简单规则所得的矩阵都是标准表达式。

如果一个表达式不能按简单规则处理，就执行一次展开，此时就需要定义根元素、参考元素、减一操作之类的概念。

* 定义根元素：从右上角出发，沿左腿向左下一步，就到达根元素。
* 定义顶元素：除了第 0 行元素以外，其它根列元素都是顶元素。此外，右上角也是顶元素。于是顶元素、根列元素数量相等。二者都从下到上排列，于是形成一一对应。
* 定义参考元素：每一对（根列元素, 顶元素）都对应一个或更多个参考元素。最右列之中，行标（大于等于根列元素行标）且（小于顶元素行标）的那些元素，就是这个配对对应的（也可以说：根列元素对应的）参考元素。

定义减一操作：按下列步骤修改矩阵。

# 设右上角的分隔符是 k 重逗号。右上角沿左腿向左下走一步，到达行标 A；右上角沿右腿向下一格，到达行标 B。
# 如果 k = 1，则删掉右上角，然后跳到第 4 步。如果 k > 1，继续第 3 步。
# 如果 A + (k − 1 重逗号 ) ≤ B，则删掉右上角，否则把右上角的分隔符从 k 重逗号改为 k − 1 重逗号。
# 把根元素上方的元素（不含根元素）都复制到最右列上方。

展开流程如下：

首先确定右上角、根列元素、顶元素。然后做减一操作。然后确定复制部分、复制宽度、magma 元素。对于矩阵 [n]，接下来要做 n 轮延伸，每一轮延伸都有编号：1, 2, . . . , n。

每一轮延伸的步骤如下：

先确定参考元素（注意，此时的矩阵可能已经做了若干延伸，而不再是原来的矩阵或者减一之后的矩阵）。然后，从左到右逐列地把复制部分的元素（称为源元素）复制到右边的新增列中（目标元素）。对于每一个“源元素列”的复制，从下到上应对那些元素。第 0 行的元素需要应对，但它不会作为源元素。最上端的元素不需应对，但它会作为源元素。

非 magma 元素 a。从 a 沿右腿向上一格，到达的元素 x 是待复制的源元素。它只能复制成一个目标元素。此类复制，目标元素的分隔符与 x 相同。如果 x 的值小于根列的列标，那么目标元素的值与 x 相同。如果 x 的值大于等于根列的列标，那么目标元素的值等于 x 的值加上 w · m，其中是 w 复制宽度，m 是延伸的编号。

magma 元素 a。从 a 沿右腿向上一格，到达的元素 x 是待复制的源元素。它可能复制成一个或更多个目标元素。找到 a 所在行的根列元素，然后找到这个根列元素对应的参考元素。每个参考元素将得出一个目标元素。此类复制，目标元素的值等于 x 的值加上 w · m，其中是 w 复制宽度，m 是延伸的编号。对于不是最上端的参考元素，沿右腿向上一格，到达一个元素，其分隔符为 K。于是目标元素的分隔符是 K。对于最上端的参考元素，目标元素的分隔符与 x 相同。

==== TωMN ====
超限 ωMN（Transfinite ω Mountain Notation, TωMN）是 ωMN 的简单扩展，它有 Ω 行的结构。TωMN 之于 ωMN，就好比 Ω 行 BMS 之于 [[BMS]]，它应该说算是一种比较弱的扩展。

定义分隔符：分隔符是非空矩阵。分隔符 <math>\underbrace{()()\cdots()()}_n</math> 也可以简写为 n 重逗号。

元素的大小比较：两元素相比，先比其值，如果值不等，则得出结果；如果值相等，再比分隔符，分隔符的比较结果就是元素的比较结果。

列的大小比较：以元素为单位，按字典序比较。

矩阵的大小比较（也就是分隔符的大小比较）：以列为单位，按字典序比较。

其简单规则如下：

# 零规则：<math>[n]=n</math>
# 后继规则：<math>A_1A_2\cdots A_X()[n]=A_1A_2\cdots A_X[n^2]</math>
#极限维度规则：如果右上角的分隔符是” 最右列不是 ( )” 的矩阵，那么展开此分隔符。

主流表达式：<math>f(n)=A_n[n]</math>，其中 <math>A_0=(),A_{i+1}=()(A_i1)</math>。

如果一个表达式不能按简单规则处理，就执行一次展开。此时就需要定义根元素、参考元素、减一操作之类的概念了。根元素、参考元素的定义与 ωMN 相同。

定义减一操作：按下列步骤修改矩阵。

# 设右上角的分隔符是 <math>M_1M_2\cdots M_X()</math>。右上角沿左腿向左下走一步，到达行标 A；右上角沿右腿向下一格，到达行标 B 。
# 如果 X = 0 ，则删掉右上角，然后跳到第 4 步。如果 X > 0 ，继续第 3 步。
# 如果 <math>A+M_1M_2\cdots M_X\leq B</math>，则删掉右上角，否则把右上角的分隔符从 <math>M_1M_2\cdots M_X</math> 改为 <math>M_1M_2\cdots M_X</math>。
# 把根元素上方的元素（不含根元素）都复制到最右列上方。

其展开流程与 ωMN 完全相同。

==== MωMN ====
变异 ωMN（Mutant ω mountain notation, MωMN）是 ωMN 的改版，增加了一点急模式的特质，但更类似于 mutant matrix，而不像 hyper matrix、sudden matrix 那样整块地比较矩阵大小。

MωMN 的分隔符、简单规则都与 ωMN 相同。

如果一个表达式不能按简单规则处理，就执行一次展开。此时就需要定义根元素、参考元素、减一操作之类的概念了。

* 按下列流程确定根元素：从右上角出发。设右上角的分隔符是 k 重逗号。如果 k = 1，那么沿左腿向左下走一步。到达的元素就是根元素。如果 k > 1，则继续后续的步骤。沿左腿向左下走一步。如果当前元素在第 0 行，则令 i = 0，否则设当前元素的分隔符是 i 重逗号。如果 i ≥ k，则回到步骤 3。否则，当前元素就是根元素。
* 定义参考元素：对于不是根元素的根列元素 a，从 a 沿右腿向上一格，到达根列元素 b。最右列之中，行标（大于等于 a 行标）且（小于 b 行标）的那些元素，就是 a 对应的参考元素。根元素对应的参考元素，是最右列之中，行标（大于等于根元素行标）且（小于等于“从右上角沿右腿向下一格到达的元素”的行标）的那些元素。

减一操作的定义与 ωMN 相同。

其展开流程如下：

对于矩阵 [n]，接下来要做 n 轮延伸。每一轮延伸都有编号：1, 2, . . . , n。最后去掉最右列，才完成整个展开流程。

每一轮延伸的步骤如下：首先确定右上角、根列元素、复制部分、复制宽度、magma 元素。然后做减一操作。然后确定参考元素。然后，从左到右逐列地把复制部分的元素（称为源元素）复制到右边的新增列中（目标元素）。每一列的处理过程，与 ωMN 相同。

MωMN在2026年5月9日被ddfg发现无穷降链：<syntaxhighlight lang="text">
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</syntaxhighlight>

MTωMN
变异超限 ωMN（Mutant Transfinite ω Mountain Notation, MTωMN）

既然有 MωMN 、有 TωMN ，那么接下来，MTωMN，就融入了"mutant"与"transfinite"两种特质。实质上它是在 TωMN 的基础上，改用 mutant 的方法来找根元素。MTωMN 的分隔符、简单规则都与 TωMN 相同。

如果一个表达式不能按简单规则处理，就执行一次展开。此时就需要定义根元素、减一操作之类的概念了。根元素的定义与 MωMN 完全相同。减一操作的定义与 TωMN 完全相同。展开流程与 MωMN 完全相同。

==== Dω·2MN ====
有缺陷的 ω·2MN（Defective ω·2 Mountain Notation, Dω·2MN）是 ω·2MN 的一个尝试。ω·2MN 的含义，是有 ω·2 种分隔符。

已知 [[Y序列|Y]] 和 [[BTBMS|TBMS]] 都是 [[BMS]] 的扩展，前者只有 ω2 行的结构却能远远超越后者的 Ω 行结构（不止如此，前者甚至还没有用完 ω+1 行结构，就已经在 [[ΩSSO|Y(1,3,4,2,5,8,10)]] 处达到后者的 Ω 行结构）。归根结底，这是由于 Y 具有一种特别的、TBMS 不具有的提升。TBMS 中，极限序数行只意味着最右列会变为极限序数下的大行标，而非最右列没有行标的增长。Y 中，最右列出现极限序数行时，不论是最右列还是非最右列，都存在行标的增加。Y 的这种现象称作 '''eruption'''。同样，为了真正强烈地超越 ωMN，而不是像 TωMN 那样弱，需要引入一种新型的提升：拉伸。在 TωMN 中，极限序数行只意味着最右列的分隔符会变为极限序数下的大分隔符，而非最右列的分隔符没有增长。接下来，在 Dω·2MN（或者其它 >ωMN）中，最右列出现极限序数行时，不论是最右列还是非最右列，都存在分隔符的增加。分隔符的增加意味着同列相邻元素的距离变远了，“拉伸”因而得名。

定义分隔符：

分隔符由两部分组成：（写在左边）0~1个分号、（写在右边）非负整数个逗号。

分隔符的大小关系：两分隔符相比，先比其分号数，如果不等，则得出结果；如果分号数相等，再比逗号数，逗号数的比较结果就是分隔符的比较结果。规定第 0 行元素具有 0 个分号、0 个逗号组成的分隔符。它仍在第0行（行标为[]）。以逗号结尾的分隔符称作后继分隔符（其前继是它去掉结尾的逗号）。否则称作极限分隔符。在本记号中，非空极限分隔符只有“;”一种。

其简单规则如下

# 零规则：<math>[n]=n</math>
# 后继规则：<math>A_1A_2\cdots A_X()[n]=A_1A_2\cdots A_X[n^2]</math>

主流表达式：<math>f(n)=()(;,,\cdots,,1)[n]</math>。由主流表达式展开，用简单规则得到的矩阵都是标准式。

如果一个表达式不能按简单规则处理，就执行一次展开。此时就需要定义根元素、参考元素、减一操作之类的概念了。对于 >ωMN 而言，还要定义拉伸相关的概念。

定义根元素：从右上角出发，沿左腿向左下一步，就到达根元素。（其实这个根元素的定义与 ωMN 相同）

定义拉伸阈：每一对(根列元素,顶元素)都有至多一个拉伸阈。拉伸阈是个分隔符。如果顶元素的分隔符是后继分隔符，则没有拉伸阈。其它情况，顶元素的分隔符是极限分隔符“;”。如果根列元素的分隔符≥顶元素的分隔符，则拉伸阈是1重逗号。设根列元素的分隔符是n重逗号，则拉伸阈是n+1重逗号。

定义拉伸量：每一对(根列元素,顶元素)，有拉伸量。拉伸量是个非负整数。如果没有拉伸阈，则拉伸量为0。如果参考元素只有1个，则拉伸量为0。如果顶元素分隔符>最上参考元素的分隔符≥拉伸阈，设拉伸阈是n重逗号，最上参考元素的分隔符是m重逗号，则拉伸量为m-n+1。其它情况，拉伸量为0。

定义减一操作：按下列步骤修改矩阵。

# 设右上角的分隔符是 M。右上角沿左腿向左下走一步，到达的元素具有分隔符 A、行标 α；右上角沿右腿向下一格，到达的元素具有分隔符 B、行标 β。
# 判断 M 的种类：
## M 是 1 重逗号。删掉右上角，然后跳到（外层的）第 3 步。
## M 是后继分隔符。记 M 的前继为 M'。如果 α+M'≤β，则删掉右上角；否则把右上角的分隔符从 M 改为 M'。然后跳到第 3 步。
## M 是极限分隔符“;”。
### 如果 A≥M 则令 j=1。否则设 A 是 i 重逗号，则令 j=i+1。
### 如果 α<β 且 B 是 ≥j 重逗号，则删掉右上角；否则把右上角的分隔符从 M 改为 j 重逗号。
### 跳到第 3 步。
#把根元素上方的元素（不含根元素）都复制到最右列上方。

以下是展开流程：

对于矩阵 [n]，接下来要做 n 轮延伸。每一轮延伸都有编号：1,2,...,n。最后去掉最右列，才完成整个展开流程。

每一轮延伸的步骤如下：首先确定右上角、根列元素、顶元素、复制部分、复制宽度、magma 元素。然后做减一操作。然后确定参考元素、拉伸阈、拉伸量。然后，从左到右逐列地把复制部分的元素（称为源元素）复制到右边的新增列中（目标元素）。

对于每一个“源元素列”的复制，从下到上应对那些元素。第 0 行的元素需要应对，但它不会作为源元素。最上端的元素不需应对，但它会作为源元素。

非 magma 元素 a。从 a 沿右腿向上一格，到达的元素 x 是待复制的源元素。它只能复制成一个目标元素。如果 x 的值小于根列的列标，那么目标元素的值与x相同。如果 x 的值大于等于根列的列标，那么目标元素的值等于x的值加上复制宽度。如果 x 的分隔符大于等于顶元素分隔符或小于拉伸阈，或者没有拉伸阈，则目标元素的分隔符与x相同。否则，目标元素的分隔符是“x的分隔符后面添加(拉伸量)重逗号”。

magma 元素 a。从 a 沿右腿向上一格，到达的元素 x 是待复制的源元素。它可能复制成一个或更多个目标元素。找到 a 所在行的根列元素，然后找到这个根列元素对应的参考元素。每个参考元素将得出一个目标元素。此类复制，目标元素的值等于 x 的值加上复制宽度。对于不是最上端的参考元素，沿右腿向上一格，到达一个元素，其分隔符为 K。于是目标元素的分隔符是 K。

对于最上端的参考元素。如果 x 的分隔符大于等于顶元素分隔符或小于拉伸阈，或者没有拉伸阈，则目标元素的分隔符与 x 相同。否则，目标元素的分隔符是“x 的分隔符后面添加（拉伸量）重逗号”。

注意到减一操作可能引入左腿跨越“非 ω 的次方”行，即 M 是分号、α+(j重逗号)≤β、但 B<j重逗号的情况。这是 ωMN、TωMN 没有的情况。在此情况下，右上角的分隔符从 M 改成了 j 重逗号，形成新的元素 m。这个元素 m，今后它作为某个根列元素时，在拉伸的判断下显得像j重逗号。然而，元素 m 在展开时，其分隔符却显示出比“β与α的差值”还要大的跨度。这种不匹配的错位（defect）也直接地表现为“左腿跨越非 ω 的次方行”。

典型例子：

<math>()(;1)(,2;1)(,3,3)(,1)(,5;5)(,6,,6;5)(,7,,7,7;5)</math>，粗体为根元素。

初次减一后得 <math>()(;1)(,2;1)(,3,3)(,1)(,5;5)(,6,,6;5)(,7,,7,7,,5)</math>，粗体为根元素及其对应的最上参考元素。

第一轮延伸时，拉伸阈为 2 重逗号，拉伸量为 1。得到 <math>()(;1)(,2;1)(,3,3)(,1)(,5;5)(,6,,6;5)(,7,,7,7,,5)(,8,,8,8,,8;8)(,9,,9,9,,9,,,9;8)(,10,,10,10,,10,,,10,10;8)</math>，粗体为根元素。

最终展开为 <math>()(;1)(,2;1)(,3,3)(,1)(,5;5)(,6,,6;5)(,7,,7,7,,5)(,8,,8,8,,8;8)(,9,,9,9,,9,,,9;8)(,10,,10,10,,10,,,10,10,,,8)(,11,,11,11,,11,,,11,11,,,11;11)(,12,,12,12,,12,,,12,12,,,12,,,,12;11)(,13,,13,13,,13,,,13,13,,,13,,,,13,13,,,,11)\cdots\cdots</math>

关于它的强度以及相对于 TωMN 的提升，参见词条 [[TωMN VS ω·2MN]]。

ω2MN在2026年6月12日被千风诗人笑姐姐发现无穷降链：<syntaxhighlight lang="text">
()(;1)(,2)(,1)(,4;4)(,5,,4)(,4,,4)(,7,,7;7)(,8,,7,,7)(,7,,7;7)(,10,,7,,7)
>
()(;1)(,2)(,1)(,4;4)(,5,,4)(,4,,4)(,7,,7;7)(,8,,7,,7)(,7,,7;7)(,10,,7,7)(,11,,11,11;11)(,12,,11,11,,11)(,11,,11,11,,11)(,14,,14,14,,14;14)(,15,,14,14,,14,,14)(,14,,14,14,,14;14)(,17,,14,14,,14,,14)
>
()(;1)(,2)(,1)(,4;4)(,5,,4)(,4,,4)(,7,,7;7)(,8,,7,,7)(,7,,7;7)(,10,,7,7)(,11,,11,11;11)(,12,,11,11,,11)(,11,,11,11,,11)(,14,,14,14,,14;14)(,15,,14,14,,14,,14)(,14,,14,14,,14;14)(,17,,14,14,,14,14)(,18,,18,18,,18,18;18)(,19,,18,18,,18,18,,18)(,18,,18,18,,18,18,,18)(,21,,21,21,,21,21,,21;21)(,22,,21,21,,21,21,,21,,21)(,21,,21,21,,21,21,,21;21)(,24,,21,21,,21,21,,21,,21)
</syntaxhighlight>

==== Aω·2MN ====
星体 ω·2MN（Astral ω·2 Mountain Notation, Aω·2MN）是 ω·2MN 的另一个尝试。

在 Dω·2MN 中，每个根列元素都成了拉伸的判断依据。要与之匹配，则减一操作时，根元素对应的最上参考元素必须按 Dω·2MN 定义中的那种方式变化，才能让每次最右列出现极限分隔符时有合理的拉伸。然而，还有一种方式来判断拉伸的依据。这种方式需要让一部分元素“不作为判断拉伸的依据”，因此判断的时候要跳过它们，找它们下方的元素。这些元素要有额外的标记，这里就用星号（*）来表示。

于是，每个元素由三部分构成：值、分隔符、星标。值是正整数，代表该元素向左下伸出的左腿要跨越到第几列（左腿元素的行标则小于本元素，且左腿元素是满足条件的所有元素之中的最上者）。分隔符代表元素与它下方一格元素的行标差，这个行标差总是ω的次方。星标是只有“有”“无”取值的布尔值，代表本元素作为判断拉伸的依据之否定。元素的写法是先写分隔符，再（如果有星标则写星号，否则不写任何东西），再写值。

分隔符的定义与 Dω·2MN 相同。简单规则与 Dω·2MN 相同。

如果一个表达式不能按简单规则处理，就执行一次展开。此时就需要定义根元素、参考元素、减一操作、拉伸阈、拉伸量之类的概念了。对于 Aω·2MN，还有额外的标记操作。

根元素的定义与 ωMN 相同。

定义函数 S(a)，其中 a 是元素。如果 a 有星标，则 S(a) 是 S(a沿右腿向下一格)，否则 S(a) 是 a 的分隔符。

定义拉伸阈：每一对 (根列元素,顶元素) 都有至多一个拉伸阈。拉伸阈是个分隔符。如果顶元素的分隔符是后继分隔符，则没有拉伸阈。其它情况，顶元素的分隔符是极限分隔符“;”。如果 S(根列元素)≥顶元素的分隔符，则拉伸阈是 1 重逗号。设 S(根列元素) 是 n 重逗号，则拉伸阈是 n+1 重逗号。

定义拉伸量：每一对 (根列元素,顶元素)，有拉伸量。拉伸量是个非负整数。如果没有拉伸阈，则拉伸量为 0。

其它情况，作下列流程：

# 从最上参考元素出发。
# 如果当前元素与根列元素同行，则拉伸量为 0。结束流程。
# 设当前元素的分隔符是 M。
# 如果顶元素分隔符>M≥拉伸阈，设 M 是 m 重逗号，拉伸阈是 n 重逗号，则拉伸量为 m-n+1。结束流程。
# 沿右腿向下一格。回到步骤 2。

定义减一操作：按下列步骤修改矩阵。

# 设右上角的分隔符是 M。右上角沿左腿向左下走一步，到达的元素 a 具有行标 α；右上角沿右腿向下一格，到达的元素具有分隔符 B、行标 β。
# 判断 M 的种类：
## M 是 1 重逗号。删掉右上角，然后跳到（外层的）第 3 步。
## M 是后继分隔符。记 M 的前继为 M'。如果 α+M'≤β，则删掉右上角；否则把右上角的分隔符从 M 改为 M'。然后跳到第 3 步。
## M 是极限分隔符“;”。
### 如果 S(a)≥M 则令 M'是 1 重逗号。否则设 S(a) 是 i 重逗号，则令 M' 是 i+1 重逗号。
### 如果 α+M'≤β，则删掉右上角；否则把右上角的分隔符从 M 改为 M'。
### 跳到第 3 步。
# 把根元素上方的元素（不含根元素）都复制到最右列上方。

定义标记操作：对于每一对 (根列元素,顶元素)，都按下列步骤修改矩阵。

# 从最上参考元素出发。
# 如果当前元素与根列元素同行，则结束流程。
# 设当前元素的分隔符是 M。
# 如果 M<拉伸阈，则把当前元素设为“有星标”。
# 如果顶元素>M≥拉伸阈，则结束流程。
#沿右腿向下一格。回到步骤 2。

以下是展开流程：

对于矩阵 [n]，接下来要做 n 轮延伸。每一轮延伸都有编号：1,2,...,n。最后去掉最右列，才完成整个展开流程。

每一轮延伸的步骤如下：首先确定右上角、根列元素、顶元素、复制部分、复制宽度、magma 元素。然后做减一操作。然后确定参考元素、拉伸阈、拉伸量，再做标记操作。然后，从左到右逐列地把复制部分的元素（称为源元素）复制到右边的新增列中（目标元素）。

对于每一个“源元素列”的复制，从下到上应对那些元素。第0行的元素需要应对，但它不会作为源元素。最上端的元素不需应对，但它会作为源元素。

非 magma 元素 a。从 a 沿右腿向上一格，到达的元素 x 是待复制的源元素。它只能复制成一个目标元素。如果 x 的值小于根列的列标，那么目标元素的值与 x 相同。如果 x 的值大于等于根列的列标，那么目标元素的值等于 x 的值加上复制宽度。如果 x 的分隔符大于等于顶元素分隔符或小于拉伸阈，或者没有拉伸阈，则目标元素的分隔符与x相同。否则，目标元素的分隔符是“x 的分隔符后面添加(拉伸量)重逗号”。目标元素的星标与 x 相同。

magma 元素 a。从 a 沿右腿向上一格，到达的元素 x 是待复制的源元素。它可能复制成一个或更多个目标元素。找到 a 所在行的根列元素，然后找到这个根列元素对应的参考元素。每个参考元素将得出一个目标元素。此类复制，目标元素的值等于 x 的值加上复制宽度。

对于不是最上端的参考元素，沿右腿向上一格，到达一个元素k。于是目标元素的分隔符、星标与 k 相同。对于最上端的参考元素。如果x的分隔符大于等于顶元素分隔符或小于拉伸阈，或者没有拉伸阈，则目标元素的分隔符与x相同。否则，目标元素的分隔符是“x 的分隔符后面添加(拉伸量)重逗号”。

目标元素的星标与 x 相同。

在 Dω·2MN 中，每个根列元素都成了拉伸的判断依据；与之匹配的是最上端的参考元素。

而在 Aω·2MN 中，最上端的参考元素可能不够大，便用它下方最近的“足够大”的参考元素作为拉伸的判断依据。由此，要想与之匹配，根列元素就需要星标，延续“它下方最近的足够大的参考元素”这一思想。

典例分析：<math>()(;1)(,2;1)(,3,3)(,1)(,5;5)(,6,,6;5)(,7,,7,7;5)</math>，粗体为根元素。

减一后得 <math>()(;1)(,2;1)(,3,3)(,1)(,5;5)(,6,,6;5)(,7,,7,7)</math>，粗体为根元素及其对应的最上参考元素。

拉伸阈为 2 重逗号，拉伸量为 1。

标记后得 <math>()(;1)(,2;1)(,3,3)(,1)(,5;5)(,6,,6;5)(,7,,7,*7)</math>。然后延伸出更多列。

最终展开为 <math>()(;1)(,2;1)(,3,3)(,1)(,5;5)(,6,,6;5)(,7,,7,*7)(,8,,8,*8;8)(,9,,9,*9,,,9;8)(,10,,10,*10,,,10,*10)(,11,,11,*11,,,11,*11;11)(,12,,12,*12,,,12,*12,,,,12;11)(,13,,13,*13,,,13,*13,,,,13,*13)</math>……

==== Dω2MN ====
有缺陷的 ω2MN（Defective ω2 Mountain Notation, Dω2MN）是 Dω·2MN 的进一步扩展，是 ω2MN 的一种尝试。因为 Astral 型定义比较复杂，所以我选用了 Defective 型的定义。虽不太完美，但好在定义比 astral 简单一点点。ω2MN，意思是有 ω2 种分隔符的 MN。

Dω·2MN 有一种极限分隔符“;”，由此有一种拉伸：一部分小于分号的分隔符（有拉伸阈的要求）扩大了，但仍小于分号。在 ω2MN 中，那就有 ω 种极限分隔符，它们是 n 重分号，由此有拉伸：一部分小于 n 重分号的分隔符（有拉伸阈的要求）扩大了，但仍小于 n 重分号。

定义分隔符：分隔符由两部分组成：（写在左边）非负整数个分号、（写在右边）非负整数个逗号。分隔符的大小关系：两分隔符相比，先比其分号数，如果不等，则得出结果；如果分号数相等，再比逗号数，逗号数的比较结果就是分隔符的比较结果。规定第 0 行元素具有 0 个分号、0 个逗号组成的分隔符。它仍在第 0 行（行标为 []）。以逗号结尾的分隔符称作后继分隔符（其前继是它去掉结尾的逗号）。否则称作极限分隔符。

简单规则与 Dω·2MN 相同。

主流表达式：<math>f(n)=()(;;;\cdots;;1)[n]</math>。

由主流表达式展开，用简单规则得到的矩阵都是标准式。

如果一个表达式不能按简单规则处理，就执行一次展开。此时就需要定义根元素、减一操作、拉伸阈、拉伸量之类的概念了。

对于极限分隔符 M=n重分号，记 M[i] = n-1 重分号后跟 i 重逗号（i 只取正整数）。

根元素的定义与 ωMN 相同：从右上角出发，沿左腿向左下一步，就到达根元素。

定义拉伸阈：每一对 (根列元素,顶元素) 都有至多一个拉伸阈。拉伸阈是个分隔符。如果顶元素的分隔符是后继分隔符，则没有拉伸阈。其它情况，顶元素的分隔符是极限分隔符——设它是 M。如果根列元素的分隔符≥M，则拉伸阈是 M[1]。如果根列元素的分隔符<M，则拉伸阈是 M[n]，其中 n 是使得“M[i]>根列元素的分隔符”的最小正整数 i。

定义拉伸量：每一对 (根列元素,顶元素)，有拉伸量。拉伸量是个非负整数。如果没有拉伸阈，则拉伸量为 0。如果参考元素只有 1 个，则拉伸量为 0。如果顶元素分隔符 > 最上参考元素的分隔符≥拉伸阈：设拉伸阈是 n 重分号后跟 m 重逗号，最上参考元素的分隔符是 n 重分号后跟 k 重逗号，则拉伸量为 k-m+1。其它情况，拉伸量为 0。

定义减一操作：按下列步骤修改矩阵。

# 设右上角的分隔符是 M。右上角沿左腿向左下走一步，到达的元素具有分隔符 A、行标 α；右上角沿右腿向下一格，到达的元素具有分隔符 B、行标 β。
# 判断 M 的种类：
## M 是 1 重逗号。删掉右上角，然后跳到（外层的）第 3 步。
## M 是后继分隔符。记 M 的前继为 M'。如果 α+M'≤β，则删掉右上角；否则把右上角的分隔符从 M 改为 M'。然后跳到第 3 步。
## M 是极限分隔符。
### 如果 A≥M 则令j=1。否则令 j=(使得 M[i]>A 的最小正整数 i)。
### 如果 α<β 且 B≥M[j]，则删掉右上角；否则把右上角的分隔符从 M 改为 M[j]。
### 跳到第 3 步。
# 把根元素上方的元素（不含根元素）都复制到最右列上方。

以下是展开流程：

对于矩阵 [n]，接下来要做 n 轮延伸。每一轮延伸都有编号：1,2,...,n。最后去掉最右列，才完成整个展开流程。

每一轮延伸的步骤如下：首先确定右上角、根列元素、顶元素、复制部分、复制宽度、magma 元素。然后做减一操作。然后确定参考元素、拉伸阈、拉伸量。然后，从左到右逐列地把复制部分的元素（称为源元素）复制到右边的新增列中（目标元素）。

对于每一个“源元素列”的复制，从下到上应对那些元素。第 0 行的元素需要应对，但它不会作为源元素。最上端的元素不需应对，但它会作为源元素。

非 magma 元素 a。从 a 沿右腿向上一格，到达的元素 x 是待复制的源元素。它只能复制成一个目标元素。确定目标元素的值：如果 x 的值小于根列的列标，那么目标元素的值与 x 相同；如果 x 的值大于等于根列的列标，那么目标元素的值等于 x 的值加上复制宽度。确定目标元素的分隔符：如果 x 的分隔符大于等于顶元素分隔符或小于拉伸阈，或者没有拉伸阈，则目标元素的分隔符与 x 相同；否则，目标元素的分隔符是“x 的分隔符后面添加(拉伸量)重逗号”。

magma 元素 a。从 a 沿右腿向上一格，到达的元素x是待复制的源元素。它可能复制成一个或更多个目标元素。找到 a 所在行的根列元素，然后找到这个根列元素对应的参考元素。每个参考元素将得出一个目标元素。

确定目标元素的值：此类复制，目标元素的值等于 x 的值加上复制宽度。

确定目标元素的分隔符：对于不是最上端的参考元素，沿右腿向上一格，到达一个元素，其分隔符为 K。于是目标元素的分隔符是 K。对于最上端的参考元素，如果 x 的分隔符大于等于顶元素分隔符或小于拉伸阈，或者没有拉伸阈，则目标元素的分隔符与 x 相同；否则，目标元素的分隔符是“x 的分隔符后面添加(拉伸量)重逗号”。

==== DωωMN ====
有缺陷的 ωωMN（Defective ωω Mountain Notation, DωωMN）是 Dω2MN 的进一步扩展，是 ωωMN 的一种尝试。

DωωMN 中的分隔符有 ωω 种。其中，第 α+1 种都是后继分隔符；第 α+ω 种分隔符与 Dω2MN 中的分隔符类似，以它为顶元素发生拉伸的时候，被拉伸的分隔符总是在末尾添加若干个逗号（即分隔符的种类序数增加一个正整数）；而更大的第<math>\alpha+\omega^2</math>种分隔符则是新东西，以它为顶元素发生拉伸的时候，被拉伸的分隔符要从第<math>\alpha+\omega\times n+m</math>种分隔符拉伸到第<math>\alpha+\omega\times(n+k)+m</math>种分隔符，这不是简单的“加一个序数”，而是连末尾的整数部分也保留着。

由于分隔符的种类较多，DωωMN 将像 TωMN 那样，用记号自身来表达分隔符。只不过，分隔符的大小有上限。

定义分隔符：分隔符是小于 <math>()(,1)(,2)</math> 的非空矩阵。分隔符也可以简写为 n 重逗号。

（以下分隔符概念与 TωMN 相同）

元素的大小比较：两元素相比，先比其值，如果值不等，则得出结果；如果值相等，再比分隔符，分隔符的比较结果就是元素的比较结果。

列的大小比较：以元素为单位，按字典序比较。

矩阵的大小比较（也就是分隔符的大小比较）：以列为单位，按字典序比较。

规定第0行元素具有空矩阵分隔符。它仍在第 0 行（行标为 []）。

以结尾的分隔符称作后继分隔符（其前继是它去掉结尾的）。否则称作极限分隔符。

简单规则与 Dω·2MN 相同。

主流表达式：<math>f(n)=()(,1)(,2()(,1)(,1)\cdots(,1)2)[n]</math>。由主流表达式展开，用简单规则得到的矩阵都是标准式。

如果一个表达式不能按简单规则处理，就执行一次展开。此时就需要定义根元素、减一操作、拉伸阈、拉伸量之类的概念了。

对于分隔符 M 而言，它可以作为矩阵长展开为 M[n]（n 为非负整数），我们也定义长展开的 M[-1] 是 M 去掉根列右侧（不含根列）的所有列。以下所有定义中，M[n] 都采用长展开而非短展开。

根元素的定义与 ωMN 相同，从右上角出发，沿左腿向左下一步，就到达根元素。

定义拉伸阈：每一对 (根列元素,顶元素) 都有至多一个拉伸阈。拉伸阈是个分隔符。如果顶元素的分隔符是后继分隔符，则没有拉伸阈。其它情况，顶元素的分隔符是极限分隔符，设它是 M。如果根列元素的分隔符≥M，则拉伸阈是 M[-1]。如果根列元素的分隔符<M，则拉伸阈是 M[n]，其中 n 是满足“M[n]>根列元素的分隔符”的最小值。

定义拉伸量：每一对 (根列元素,顶元素)，有拉伸量。拉伸量是个非负整数。如果没有拉伸阈，则拉伸量为 0。如果参考元素只有1个，则拉伸量为0。如果顶元素分隔符>最上参考元素的分隔符≥拉伸阈：设顶元素分隔符是 M，拉伸阈是 M[n]，最上参考元素的分隔符是 K，k 是满足 K≥M[k] 的最大值，则拉伸量为 k-n+1。其它情况，拉伸量为 0。

定义减一操作：按下列步骤修改矩阵。

# 设右上角的分隔符是 M。右上角沿左腿向左下走一步，到达的元素具有分隔符 A、行标 α；右上角沿右腿向下一格，到达的元素具有分隔符 B、行标 β。
# 判断 M 的种类：
## M 是 1 重逗号。删掉右上角，然后跳到（外层的）第 3 步。
## M 是后继分隔符。记 M 的前继为 M'。如果 α+M'≤β，则删掉右上角；否则把右上角的分隔符从 M 改为 M'。然后跳到第 3 步。
## M 是极限分隔符。
### 如果 A≥M 则令 j=-1。否则令 j=(使得 M[i]>A 的最小 i)。
### 如果 α<β 且 B≥M[j]，则删掉右上角；否则把右上角的分隔符从 M 改为 M[j]。
### 跳到第 3 步。
# 把根元素上方的元素（不含根元素）都复制到最右列上方。

以下是展开流程。

对于矩阵 [n]，接下来要做 n 轮延伸。每一轮延伸都有编号：1,2,...,n。延伸完毕后，如果是长展开，则再做一次减一操作；如果是短展开，则去掉最右列。这才完成整个展开流程。

每一轮延伸的步骤如下：首先确定右上角、根列元素、顶元素、复制部分、复制宽度、magma 元素。然后做减一操作。然后确定参考元素、拉伸阈、拉伸量。然后，从左到右逐列地把复制部分的元素（称为源元素）复制到右边的新增列中（目标元素）。

对于每一个“源元素列”的复制，从下到上应对那些元素。第 0 行的元素需要应对，但它不会作为源元素。最上端的元素不需应对，但它会作为源元素。

非 magma 元素 a。从 a 沿右腿向上一格，到达的元素 x 是待复制的源元素（分隔符为 X）。它只能复制成一个目标元素。确定目标元素的值：如果 x 的值小于根列的列标，那么目标元素的值与 x 相同；如果 x 的值大于等于根列的列标，那么目标元素的值等于 x 的值加上复制宽度。确定目标元素的分隔符：如果 X 大于等于顶元素分隔符或小于拉伸阈，或者没有拉伸阈，则目标元素的分隔符是 X；否则，记顶元素分隔符为 M、拉伸量为 k。设 s 满足 X≤M[s]。从最左列数起，X 与 M[s] 的最长公共部分（一整列一整列地数）为 N。再取 t 是满足 M[t] 是 X 从最左列开始的部分的最大值，Y 是 X 去掉 M[t] 后剩余的部分。设 M 的根列在第 u 列。将 Y 中所有大于等于 u 的元素值都加上 (M 的复制宽度)·k。于是，目标元素的分隔符是 M[t+k] 右边跟着 Y。

magma 元素a。从 a 沿右腿向上一格，到达的元素x是待复制的源元素。它可能复制成一个或更多个目标元素。找到a所在行的根列元素，然后找到这个根列元素对应的参考元素。每个参考元素将得出一个目标元素。

确定目标元素的值：此类复制，目标元素的值等于x的值加上复制宽度。

确定目标元素的分隔符：对于不是最上端的参考元素，沿右腿向上一格，到达一个元素，其分隔符为 K。于是目标元素的分隔符是 K。对于最上端的参考元素，如果 x 的分隔符大于等于顶元素分隔符或小于拉伸阈，或者没有拉伸阈，则目标元素的分隔符与 x 相同；否则，设 x 的分隔符是 X，记顶元素分隔符为 M、拉伸量为 k。设 s 满足 X≤M[s]。从最左列数起，X 与 M[s] 的最长公共部分（一整列一整列地数）为 N。再取t是满足“M[t] 是 X 从最左列开始的部分”的最大值，Y 是 X 去掉 M[t] 后剩余的部分。设 M 的根列在第 u 列。将 Y 中所有大于等于 u 的元素值都加上 (M的复制宽度)·k。于是，目标元素的分隔符是 M[t+k] 右边跟着 Y。

==== TωωMN ====
超限 ωωMN（Transfinite ωω Mountain Notation, TωωMN）是 DωωMN 的进一步扩展。不确定更高层次的 αMN 是否需要更“新型”的提升/eruption/拉伸/etc. 概念才能完成。这里暂用 transfinite 这个形容词来表示分隔符种类之多——TωωMN 中的分隔符种类数与该记号的极限相当。看到这里，我们知道，TωωMN 最关键的问题在于如何拉伸。我们仍规定只有当顶元素分隔符>待拉伸分隔符≥拉伸阈的时候才有可能拉伸。所有其他定义都要配合这一准则。

一个非平凡的拉伸发生在“顶元素具有第 ωω 种分隔符”的情形。被拉伸的分隔符要从第 <math>\omega^n</math> 种分隔符拉伸到第 <math>\omega^{n+k}</math> 种分隔符。但如果分隔符的种类序数不是 ω 的整次方呢？比如，被拉伸的分隔符是第 <math>\omega^n\times2</math> 种分隔符，按照 DωωMN 的拉伸方法，它将变成第 <math>\omega^{n+k}+\omega^n</math> 种分隔符，只取“最左侧”的一个部分发生拉伸。另一个非平凡的拉伸发生在“顶元素具有分隔符<math>()(,1)(,2,,2)</math>”的情形。此时分隔符在展开时出现 eruption，那么拉伸就不是按照 DωωMN 定义的那种“仅仅向右平移、元素值增加”能完成的了。我们需要把被拉伸的分隔符也纳入顶元素分隔符的延伸过程中，把（被拉伸的分隔符中的）根列右方的列当作被复制的东西，连同主要的延伸过程一起复制、一起向右移动、一起 eruption、一起拉伸。

TωωMN 的分隔符与 TωMN 相同。

简单规则与 Dω·2MN 相同。

主流表达式：<math>f(n)=A_n[n],\text{其中}A_0=(),A_i=A_{i-1}(A_0iA_1i\cdots A_{i-1}i)</math>。由主流表达式展开，用简单规则得到的矩阵都是标准式。

如果一个表达式不能按简单规则处理，就执行一次展开。此时就需要定义根元素、减一操作、拉伸阈、拉伸量之类的概念了。

对于分隔符 M 而言，它可以作为矩阵长展开为 M[n]（n 为非负整数），我们也定义长展开的 M[-1] 是 M 去掉根列右侧（不含根列）的所有列。以下所有定义中，M[n] 都采用长展开而非短展开。此外，对于分隔符 M>N 而言，把它们作为矩阵，可以将 M 延伸，同时 N 作为“附加列”也一起延伸。带附加列的延伸流程将在“展开流程”一节阐述。

根元素的定义与 ωMN 相同——从右上角出发，沿左腿向左下一步，就到达根元素。

定义拉伸阈：每一对 (根列元素,顶元素)都有至多一个拉伸阈。拉伸阈是个分隔符。如果顶元素的分隔符是后继分隔符，则没有拉伸阈。其它情况，顶元素的分隔符是极限分隔符——设它是 M。如果根列元素的分隔符≥M，则拉伸阈是 M[-1]。此时定义预拉伸量为 0。如果根列元素的分隔符<M，则拉伸阈是M[n]，其中 n 是满足 M[n]>根列元素的分隔符的最小值。此时定义预拉伸量为 n+1。

定义拉伸量：每一对 (根列元素,顶元素)，有拉伸量。拉伸量是个非负整数。如果没有拉伸阈，则拉伸量为 0。如果参考元素只有 1 个，则拉伸量为 0。如果顶元素分隔符>最上参考元素的分隔符≥拉伸阈，设顶元素分隔符是 M，预拉伸量是 n，最上参考元素的分隔符是 K，k 是满足 M[k]>K 的最小值，则拉伸量为 k-n+1。其它情况，拉伸量为 0。

减一操作的定义与 DωωMN 相同。

以下是展开流程：

对于矩阵[n]，接下来要做n轮延伸。每一轮延伸都有编号：1、2……、n。
延伸完毕后，如果是长展开，则再做一次减一操作；如果是短展开，则去掉最右列。这才完成整个展开流程。

每一轮延伸，可能是单独一个矩阵的延伸，也可能是“A 附加 B 延伸”（A,B 都是矩阵。此处 A 称作主矩阵，B 称作附加矩阵）。步骤如下：

# 首先是附加矩阵的预处理。A,B 的最长公共部分（一整列一整列地数）记作 C。B 删去 C 这个部分，余下的部分作为后续步骤中的“附加矩阵”。
# 主矩阵确定右上角、根列元素、顶元素、复制部分、复制宽度。
# 附加矩阵的复制部分是根列以右（不含根列）的所有列，列标甚至能超过主矩阵的列数。
# 主矩阵、附加矩阵都（按照主矩阵的根列元素）确定 magma 元素。
# 主矩阵做减一操作，不含附加矩阵。
# 主矩阵确定参考元素、拉伸阈、预拉伸量、拉伸量。
# 从左到右逐列地把主矩阵、附加矩阵复制部分的元素（称为源元素）复制到右边的新增列中（目标元素）。
# 如果要得到附加矩阵 D，那么把“现有的附加矩阵”作为 D 最右边的部分，D 左边空余的列从主矩阵取得。

对于每一个“源元素列”的复制，从下到上应对那些元素。第 0 行的元素需要应对，但它不会作为源元素。最上端的元素不需应对，但它会作为源元素。

非 magma 元素 a。从 a 沿右腿向上一格，到达的元素 x 是待复制的源元素（分隔符为 X）。它只能复制成一个目标元素。确定目标元素的值：如果 x 的值小于根列的列标，那么目标元素的值与 x 相同；如果 x 的值大于等于根列的列标，那么目标元素的值等于 x 的值加上复制宽度。确定目标元素的分隔符：如果 X 大于等于顶元素分隔符或小于拉伸阈，或者没有拉伸阈，则目标元素的分隔符是 X；否则，记顶元素分隔符为 M、预拉伸量为 m、拉伸量为 k，M 延伸 m 轮得到 N。目标元素的分隔符是“N 附加 X 延伸 k 轮之后得到的附加矩阵。

magma 元素 a。从 a 沿右腿向上一格，到达的元素 x 是待复制的源元素。它可能复制成一个或更多个目标元素。找到 a 所在行的根列元素，然后找到这个根列元素对应的参考元素。每个参考元素将得出一个目标元素。

确定目标元素的值：此类复制，目标元素的值等于 x 的值加上复制宽度。

确定目标元素的分隔符：

# 对于不是最上端的参考元素，沿右腿向上一格，到达一个元素，其分隔符为 K。于是目标元素的分隔符是 K。
# 对于最上端的参考元素。
## 如果 x 的分隔符大于等于顶元素分隔符或小于拉伸阈，或者没有拉伸阈，则目标元素的分隔符与 x 相同。
## 否则，设 x 的分隔符是 X，记顶元素分隔符为 M、预拉伸量为 m、拉伸量为 k。M 延伸 m 轮得到 N。目标元素的分隔符是“N 附加 X 延伸”k 轮之后得到的附加矩阵。

=== 与 Y 系列记号的区别 ===
Y 系列记号的表达式是个正整数序列，每个元素都压缩了许多信息，不能立即辨认，需要画出山脉图才可以看到其结构。山脉图分为行、列，列标与行标的二元组可以定位山脉图中的一个元素。列标是正整数，每一列对应原来序列的一个元素。行标则是序数，理想中 α-Y 山脉图的行标是小于 <math>\omega^{1+\alpha}</math> 的序数。相比之下，山脉系列记号则显式地表达山脉图，而无需像 Y 系列记号那样需要解压、压缩。山脉系列记号的表达式是矩阵[n]，此 n 也就是展开时的基本列项数。

相比于 Y 系列记号而言，山脉系列记号具有如下的优点：

# 显式地表达山脉图，无需解压（画山脉图）、压缩（从山脉图还原为正整数序列）就可看出结构。
# 表达式可以更加自由（不受解压、压缩的限制），从而可以简化。尽管与 Y 同样有许多非标准表达。
# 可以规避压扁现象——山脉记号中特定行标的元素总可以存在。这是第二点优势的延伸。
# 可以规避 Y 系列作超限简单扩展时“极限序数行标的 1 与极限序数值不匹配”的问题。

但同时它有如下的不足：

# 表达式比较长，不如 Y 系列简短。
# 难以提取，而 Y 系列却可以简单地提取任何可以形成正整数序列的东西。
{{默认排序:序数记号}}
[[分类:记号]]

SSS 分析

2026-06-08T13:22:30Z

Baixie01000a7：/* Part 7 */

本条目展示 SSS（单行 [[BSM]]）分析。

=== Part 1 ===
* <math>0=1</math>
* <math>0,0=2</math>
* <math>0,0,0=3</math>
* <math>0,1=\omega</math>
* <math>0,1,0=\omega+1</math>
* <math>0,1,0,0=\omega+2</math>
* <math>0,1,0,0,1=\omega\times2</math>
* <math>0,1,0,0,1,0,0,1=\omega\times3</math>
* <math>0,1,0,1=\omega^2</math>
* <math>0,1,0,1,0,0,1=\omega^2+\omega</math>
* <math>0,1,0,1,0,0,1,0,0,1=\omega^2+\omega\times2</math>
* <math>0,1,0,1,0,0,1,0,1=\omega^2\times2</math>
* <math>0,1,0,1,0,0,1,0,1,0,0,1,0,1=\omega^2\times3</math>
* <math>0,1,0,1,0,1=\omega^3</math>
* <math>0,1,0,1,0,1,0,1=\omega^4</math>
* <math>0,1,1=\omega^\omega</math>
* <math>0,1,1,0,0,1,0,1=\omega^\omega+\omega^2</math>
* <math>0,1,1,0,0,1,1=\omega^\omega\times2</math>
* <math>0,1,1,0,1=\omega^{\omega+1}</math>
* <math>0,1,1,0,1,0,0,1,1,0,1=\omega^{\omega+1}\times2</math>
* <math>0,1,1,0,1,0,1=\omega^{\omega+2}</math>
* <math>0,1,1,0,1,0,1,1=\omega^{\omega\times2}</math>
* <math>0,1,1,0,1,0,1,1,0,1=\omega^{\omega\times2+1}</math>
* <math>0,1,1,0,1,0,1,1,0,1,0,1,1=\omega^{\omega\times3}</math>
* <math>0,1,1,0,1,1=\omega^{\omega^2}</math>
* <math>0,1,1,0,1,1,0,1=\omega^{\omega^2+1}</math>
* <math>0,1,1,0,1,1,0,1,0,1,1,0,1,1=\omega^{\omega^2\times2}</math>
* <math>0,1,1,0,1,1,0,1,1=\omega^{\omega^3}</math>
* <math>0,1,1,1=\omega^{\omega^\omega}</math>
* <math>0,1,1,1,1=\omega^{\omega^{\omega^\omega}}</math>
* <math>0,1,1,2=\psi(0)</math>

=== Part 2 ===
* <math>0,1,1,2,0,0,1=\psi(0)+\omega</math>
* <math>0,1,1,2,0,0,1,0,1=\psi(0)+\omega^2</math>
* <math>0,1,1,2,0,0,1,1=\psi(0)+\omega^\omega</math>
* <math>0,1,1,2,0,0,1,1,2=\psi(0)\times2</math>
* <math>0,1,1,2,0,1=\psi(0)\times\omega</math>
* <math>0,1,1,2,0,1,0,0,1,1,2,0,1=\psi(0)\times\omega\times2</math>
* <math>0,1,1,2,0,1,0,1=\psi(0)\times\omega^2</math>
* <math>0,1,1,2,0,1,0,1,1=\psi(0)\times\omega^\omega</math>
* <math>0,1,1,2,0,1,0,1,1,2=\psi(0)^2</math>
* <math>0,1,1,2,0,1,0,1,1,2,0,1=\psi(0)^2\times\omega</math>
* <math>0,1,1,2,0,1,0,1,1,2,0,1,0,1,1,2=\psi(0)^3</math>
* <math>0,1,1,2,0,1,1=\psi(0)^\omega</math>
* <math>0,1,1,2,0,1,1,0,1,0,1,1,2=\psi(0)^{\omega+1}</math>
* <math>0,1,1,2,0,1,1,0,1,0,1,1,2,0,1,1=\psi(0)^{\omega\times2}</math>
* <math>0,1,1,2,0,1,1,0,1,1=\psi(0)^{\omega^2}</math>
* <math>0,1,1,2,0,1,1,0,1,1,1=\psi(0)^{\omega^\omega}</math>
* <math>0,1,1,2,0,1,1,0,1,1,2=\psi(0)^{\psi(0)}</math>
* <math>0,1,1,2,0,1,1,1=\psi(0)^{\psi(0)^\omega}</math>
* <math>0,1,1,2,0,1,1,2=\psi(1)</math>
* <math>0,1,1,2,0,1,1,2,0,1,1,2=\psi(2)</math>
* <math>0,1,1,2,1=\psi(\omega)</math>
* <math>0,1,1,2,1,0,1=\psi(\omega)\times\omega</math>
* <math>0,1,1,2,1,0,1,0,1,1,2=\psi(\omega)\times\psi(0)</math>
* <math>0,1,1,2,1,0,1,0,1,1,2,0,1,1,2=\psi(\omega)\times\psi(1)</math>
* <math>0,1,1,2,1,0,1,0,1,1,2,1=\psi(\omega)^2</math>
* <math>0,1,1,2,1,0,1,0,1,1,2,1,0,1,0,1,1,2,1=\psi(\omega)^3</math>
* <math>0,1,1,2,1,0,1,1=\psi(\omega)^\omega</math>
* <math>0,1,1,2,1,0,1,1,0,1,1,2=\psi(\omega)^{\psi(\omega)}</math>
* <math>0,1,1,2,1,0,1,1,1=\psi(\omega)^{\psi(\omega)^{\omega}}</math>
* <math>0,1,1,2,1,0,1,1,2=\psi(\omega+1)</math>
* <math>0,1,1,2,1,0,1,1,2,0,1,1,2=\psi(\omega+2)</math>
* <math>0,1,1,2,1,0,1,1,2,0,1,1,2,1=\psi(\omega\times2)</math>
* <math>0,1,1,2,1,0,1,1,2,1=\psi(\omega^2)</math>
* <math>0,1,1,2,1,0,1,1,2,1,0,1,1,2=\psi(\omega^2+1)</math>
* <math>0,1,1,2,1,0,1,1,2,1,0,1,1,2,0,1,1,2,1=\psi(\omega^2+\omega)</math>
* <math>0,1,1,2,1,0,1,1,2,1,0,1,1,2,0,1,1,2,1,0,1,1,2,1=\psi(\omega^2\times2)</math>
* <math>0,1,1,2,1,0,1,1,2,1,0,1,1,2,1=\psi(\omega^3)</math>
* <math>0,1,1,2,1,1=\psi(\omega^\omega)</math>
* <math>0,1,1,2,1,1,1=\psi(\omega^{\omega^\omega})</math>
* <math>0,1,1,2,1,1,2=\psi(\psi(0))</math>
* <math>0,1,1,2,1,1,2,0,1=\psi(\psi(0))\times\omega</math>
* <math>0,1,1,2,1,1,2,0,1,1,2=\psi(\psi(0)+1)</math>
* <math>0,1,1,2,1,1,2,0,1,1,2,0,1,1,2,1,1,2=\psi(\psi(0)\times2)</math>
* <math>0,1,1,2,1,1,2,0,1,1,2,1=\psi(\psi(0)\times\omega)</math>
* <math>0,1,1,2,1,1,2,0,1,1,2,1,1=\psi(\psi(0)^\omega)</math>
* <math>0,1,1,2,1,1,2,0,1,1,2,1,1,2=\psi(\psi(1))</math>
* <math>0,1,1,2,1,1,2,1=\psi(\psi(\omega))</math>
* <math>0,1,1,2,1,1,2,1,0,1,1,2,1,1,2,1=\psi(\psi(\omega^2))</math>
* <math>0,1,1,2,1,1,2,1,1=\psi(\psi(\omega^\omega))</math>
* <math>0,1,1,2,1,1,2,1,1,2=\psi(\psi(\psi(0)))</math>
* <math>0,1,1,2,1,2=\psi(\Omega)</math>

=== Part 3 ===
* <math>0,1,1,2,1,2,0,1,1,2=\psi(\Omega+1)</math>
* <math>0,1,1,2,1,2,0,1,1,2,0,1,1,2,1=\psi(\Omega+\omega)</math>
* <math>0,1,1,2,1,2,0,1,1,2,0,1,1,2,1,1,2=\psi(\Omega+\psi(0))</math>
* <math>0,1,1,2,1,2,0,1,1,2,0,1,1,2,1,1,2,1,1,2=\psi(\Omega+\psi(\psi(0)))</math>
* <math>0,1,1,2,1,2,0,1,1,2,0,1,1,2,1,2=\psi(\Omega+\psi(\Omega))</math>
* <math>0,1,1,2,1,2,0,1,1,2,0,1,1,2,1,2,0,1,1,2=\psi(\Omega+\psi(\Omega)+1)</math>
* <math>0,1,1,2,1,2,0,1,1,2,1=\psi(\Omega+\psi(\Omega)\times\omega)</math>
* <math>0,1,1,2,1,2,0,1,1,2,1,0,1,1,2=\psi(\Omega+\psi(\Omega)\times\omega+1)</math>
* <math>0,1,1,2,1,2,0,1,1,2,1,0,1,1,2,0,1,1,2,1,2,0,1,1,2,1=\psi(\Omega+\psi(\Omega)\times\omega\times2)</math>
* <math>0,1,1,2,1,2,0,1,1,2,1,0,1,1,2,1=\psi(\Omega+\psi(\Omega)\times\omega^2)</math>
* <math>0,1,1,2,1,2,0,1,1,2,1,0,1,1,2,1,1=\psi(\Omega+\psi(\Omega)\times\omega^\omega)</math>
* <math>0,1,1,2,1,2,0,1,1,2,1,0,1,1,2,1,1,2=\psi(\Omega+\psi(\Omega)\times\psi(0))</math>
* <math>0,1,1,2,1,2,0,1,1,2,1,0,1,1,2,1,1,2,1=\psi(\Omega+\psi(\Omega)\times\psi(\omega))</math>
* <math>0,1,1,2,1,2,0,1,1,2,1,0,1,1,2,1,2=\psi(\Omega+\psi(\Omega)^2)</math>
* <math>0,1,1,2,1,2,0,1,1,2,1,1=\psi(\Omega+\psi(\Omega)^\omega)</math>
* <math>0,1,1,2,1,2,0,1,1,2,1,1,2=\psi(\Omega+\psi(\Omega+1))</math>
* <math>0,1,1,2,1,2,0,1,1,2,1,1,2,1=\psi(\Omega+\psi(\Omega+\psi(\Omega)\times\omega))</math>
* <math>0,1,1,2,1,2,0,1,1,2,1,1,2,1,1=\psi(\Omega+\psi(\Omega+\psi(\Omega)^\omega))</math>
* <math>0,1,1,2,1,2,0,1,1,2,1,1,2,1,1,2=\psi(\Omega+\psi(\Omega+\psi(\Omega+1)))</math>
* <math>0,1,1,2,1,2,0,1,1,2,1,2=\psi(\Omega\times2)</math>
* <math>0,1,1,2,1,2,0,1,1,2,1,2,0,1,1,2,1,2=\psi(\Omega\times3)</math>
* <math>0,1,1,2,1,2,1=\psi(\Omega\times\omega)</math>
* <math>0,1,1,2,1,2,1,0,1,1,2,1,2=\psi(\Omega\times\omega+\Omega)</math>
* <math>0,1,1,2,1,2,1,0,1,1,2,1,2,0,1,1,2,1,2,1=\psi(\Omega\times\omega\times2)</math>
* <math>0,1,1,2,1,2,1,0,1,1,2,1,2,1=\psi(\Omega\times\omega^2)</math>
* <math>0,1,1,2,1,2,1,1=\psi(\Omega\times\omega^\omega)</math>
* <math>0,1,1,2,1,2,1,1,2=\psi(\Omega\times\psi(0))</math>
* <math>0,1,1,2,1,2,1,1,2,0,1,1,2,1,2=\psi(\Omega\times\psi(0)+\Omega)</math>
* <math>0,1,1,2,1,2,1,1,2,0,1,1,2,1,2,1=\psi(\Omega\times\psi(0)\times\omega)</math>
* <math>0,1,1,2,1,2,1,1,2,0,1,1,2,1,2,1,0,1,1,2,1,2,1,1=\psi(\Omega\times\psi(0)\times\omega^2)</math>
* <math>0,1,1,2,1,2,1,1,2,0,1,1,2,1,2,1,0,1,1,2,1,2,1,1,2=\psi(\Omega\times\psi(0)^2)</math>
* <math>0,1,1,2,1,2,1,1,2,0,1,1,2,1,2,1,1=\psi(\Omega\times\psi(0)^\omega)</math>
* <math>0,1,1,2,1,2,1,1,2,0,1,1,2,1,2,1,1,2=\psi(\Omega\times\psi(1))</math>
* <math>0,1,1,2,1,2,1,1,2,1=\psi(\Omega\times\psi(\omega))</math>
* <math>0,1,1,2,1,2,1,1,2,1,1=\psi(\Omega\times\psi(\omega^\omega))</math>
* <math>0,1,1,2,1,2,1,1,2,1,1,2=\psi(\Omega\times\psi(\psi(0)))</math>
* <math>0,1,1,2,1,2,1,1,2,1,2=\psi(\Omega\times\psi(\Omega))</math>
* <math>0,1,1,2,1,2,1,1,2,1,2,0,1,1,2,1,2=\psi(\Omega\times\psi(\Omega)+\Omega)</math>
* <math>0,1,1,2,1,2,1,1,2,1,2,0,1,1,2,1,2,1=\psi(\Omega\times\psi(\Omega)\times\omega)</math>
* <math>0,1,1,2,1,2,1,1,2,1,2,0,1,1,2,1,2,1,1,2=\psi(\Omega\times\psi(\Omega+1))</math>
* <math>0,1,1,2,1,2,1,1,2,1,2,0,1,1,2,1,2,1,1,2,1,2=\psi(\Omega\times\psi(\Omega\times2))</math>
* <math>0,1,1,2,1,2,1,1,2,1,2,1=\psi(\Omega\times\psi(\Omega\times\omega))</math>
* <math>0,1,1,2,1,2,1,2=\psi(\Omega^2)</math>
* <math>0,1,1,2,1,2,1,2,0,1,1,2,1,2=\psi(\Omega^2+\Omega)</math>
* <math>0,1,1,2,1,2,1,2,0,1,1,2,1,2,1,2=\psi(\Omega^2\times2)</math>
* <math>0,1,1,2,1,2,1,2,1=\psi(\Omega^2\times\omega)</math>
* <math>0,1,1,2,1,2,1,2,1,1,2=\psi(\Omega^2\times\psi(0))</math>
* <math>0,1,1,2,1,2,1,2,1,1,2,1,2=\psi(\Omega^2\times\psi(\Omega))</math>
* <math>0,1,1,2,1,2,1,2,1,1,2,1,2,1,2=\psi(\Omega^2\times\psi(\Omega^2))</math>
* <math>0,1,1,2,1,2,1,2,1,1,2,1,2,1,2,1,1,2=\psi(\Omega^2\times\psi(\Omega^2\times\psi(0)))</math>
* <math>0,1,1,2,1,2,1,2,1,2=\psi(\Omega^3)</math>
* <math>0,1,1,2,1,2,1,2,1,2,1,2=\psi(\Omega^4)</math>
* <math>0,1,1,2,2=\psi(\Omega^\omega)</math>
* <math>0,1,1,2,2,0,1,1,2=\psi(\Omega^\omega+1)</math>
* <math>0,1,1,2,2,0,1,1,2,1,2=\psi(\Omega^\omega+\Omega^2)</math>
* <math>0,1,1,2,2,0,1,1,2,1,2,1,2=\psi(\Omega^\omega+\Omega^3)</math>
* <math>0,1,1,2,2,0,1,1,2,2=\psi(\Omega^\omega\times2)</math>
* <math>0,1,1,2,2,1=\psi(\Omega^\omega\times\omega)</math>
* <math>0,1,1,2,2,1,1,2=\psi(\Omega^\omega\times\psi(0))</math>
* <math>0,1,1,2,2,1,1,2,1,2=\psi(\Omega^\omega\times\psi(\Omega))</math>
* <math>0,1,1,2,2,1,1,2,1,2,1,2=\psi(\Omega^\omega\times\psi(\Omega^2))</math>
* <math>0,1,1,2,2,1,1,2,1,2,2=\psi(\Omega^\omega\times\psi(\Omega^\omega))</math>
* <math>0,1,1,2,2,1,2=\psi(\Omega^{\omega+1})</math>
* <math>0,1,1,2,2,1,2,1,2=\psi(\Omega^{\omega+2})</math>
* <math>0,1,1,2,2,1,2,1,2,2=\psi(\Omega^{\omega\times2})</math>
* <math>0,1,1,2,2,1,2,2=\psi(\Omega^{\omega^2})</math>
* <math>0,1,1,2,2,2=\psi(\Omega^{\omega^\omega})</math>
* <math>0,1,1,2,2,2,1,2,2=\psi(\Omega^{\omega^{\omega+1}})</math>
* <math>0,1,1,2,2,3=\psi(\Omega^{\psi(0)})</math>
* <math>0,1,1,2,2,3,1,2=\psi(\Omega^{\psi(0)+1})</math>
* <math>0,1,1,2,2,3,1,2,1,2,2,3=\psi(\Omega^{\psi(0)\times2})</math>
* <math>0,1,1,2,2,3,1,2,2=\psi(\Omega^{\psi(0)\times\omega})</math>
* <math>0,1,1,2,2,3,1,2,2,2=\psi(\Omega^{\psi(0)^\omega})</math>
* <math>0,1,1,2,2,3,1,2,2,3=\psi(\Omega^{\psi(1)})</math>
* <math>0,1,1,2,2,3,2=\psi(\Omega^{\psi(\omega)})</math>
* <math>0,1,1,2,2,3,2,2,3=\psi(\Omega^{\psi(\psi(0))})</math>
* <math>0,1,1,2,2,3,2,2,3,2,2,3=\psi(\Omega^{\psi(\psi(\psi(0)))})</math>
* <math>0,1,1,2,2,3,2,3=\psi(\Omega^{\psi(\Omega)})</math>
* <math>0,1,1,2,2,3,2,3,2,3=\psi(\Omega^{\psi(\Omega^2)})</math>
* <math>0,1,1,2,2,3,3=\psi(\Omega^{\psi(\Omega^\omega)})</math>
* <math>0,1,1,2,2,3,3,3=\psi(\Omega^{\psi(\Omega^{\omega^\omega})})</math>
* <math>0,1,1,2,2,3,3,4=\psi(\Omega^{\psi(\Omega^{\psi(0)})})</math>
* <math>0,1,2=\psi(\Omega^\Omega)</math>

=== Part 4 ===
* <math>0,1,2,0,0,1,1=\psi(\Omega^\Omega)+\omega^2</math>
* <math>0,1,2,0,0,1,1,2=\psi(\Omega^\Omega)+\psi(0)</math>
* <math>0,1,2,0,0,1,2=\psi(\Omega^\Omega)\times2</math>
* <math>0,1,2,0,1=\psi(\Omega^\Omega)\times\omega</math>
* <math>0,1,2,0,1,0,1,1,2=\psi(\Omega^\Omega)\times\psi(0)</math>
* <math>0,1,2,0,1,0,1,1,2,2,3=\psi(\Omega^\Omega)\times\psi(\Omega^{\psi(0)})</math>
* <math>0,1,2,\color{green}{0,1,0,1,1,2,3}=\psi(\Omega^\Omega)^2</math>
* <math>0,1,2,\color{green}{0,1,0,1,1,2,3,}0,1,0,1,1,2,3=\psi(\Omega^\Omega)^3</math>
* <math>0,1,2,\color{green}{0,1,0,1,1,2,3,}0,1,1=\psi(\Omega^\Omega)^\omega</math>
* <math>0,1,2,\color{green}{0,1,0,1,1,2,3,}0,1,1,0,1,0,1,1,2,3=\psi(\Omega^\Omega)^{\omega+1}</math>
* <math>0,1,2,\color{green}{0,1,0,1,1,2,3,}0,1,1,0,1,0,1,1,2,3,0,1,1=\psi(\Omega^\Omega)^{\omega\times2}</math>
* <math>0,1,2,\color{green}{0,1,0,1,1,2,3,}0,1,1,0,1,1=\psi(\Omega^\Omega)^{\omega^2}</math>
* <math>0,1,2,\color{green}{0,1,0,1,1,2,3,}0,1,1,0,1,1,2,3=\psi(\Omega^\Omega)^{\psi(\Omega^\Omega)}</math>
* <math>0,1,2,\color{green}{0,1,0,1,1,2,3,}0,1,1,1=\psi(\Omega^\Omega)^{\psi(\Omega^\Omega)^\omega}</math>
* <math>0,1,2,\color{green}{0,1,0,1,1,2,3,}0,1,1,2=\psi(\Omega^\Omega+1)</math>
* <math>0,1,2,\color{green}{0,1,0,1,1,2,3},0,1,1,2,0,1,1,2=\psi(\Omega^\Omega+2)</math>
* <math>0,1,2,\color{green}{0,1,0,1,1,2,3},0,1,1,2,0,1,1,2,1=\psi(\Omega^\Omega+\omega)</math>
* <math>0,1,2,\color{green}{0,1,0,1,1,2,3},0,1,1,2,0,1,1,2,1,1,2=\psi(\Omega^\Omega+\psi(0))</math>
* <math>0,1,2,\color{green}{0,1,0,1,1,2,3},0,1,1,2,0,1,1,2,3=\psi(\Omega^\Omega+\psi(\Omega^\Omega))</math>
* <math>0,1,2,\color{green}{0,1,0,1,1,2,3},0,1,1,2,1=\psi(\Omega^\Omega+\psi(\Omega^\Omega)\times\omega)</math>
* <math>0,1,2,\color{green}{0,1,0,1,1,2,3},0,1,1,2,1,0,1,1,2,3=\psi(\Omega^\Omega+\psi(\Omega^\Omega)^2)</math>
* <math>0,1,2,\color{green}{0,1,0,1,1,2,3},0,1,1,2,1,1=\psi(\Omega^\Omega+\psi(\Omega^\Omega)^\omega)</math>
* <math>0,1,2,\color{green}{0,1,0,1,1,2,3},0,1,1,2,1,1,2=\psi(\Omega^\Omega+\psi(\Omega^\Omega+1))</math>
* <math>0,1,2,\color{green}{0,1,0,1,1,2,3},0,1,1,2,1,1,2,1=\psi(\Omega^\Omega+\psi(\Omega^\Omega+\psi(\Omega^\Omega)\times\omega))</math>
* <math>0,1,2,\color{green}{0,1,0,1,1,2,3},0,1,1,2,1,2=\psi(\Omega^\Omega+\Omega)</math>
* <math>0,1,2,\color{green}{0,1,0,1,1,2,3},0,1,1,2,1,2,0,1,1,2,1,2=\psi(\Omega^\Omega+\Omega\times2)</math>
* <math>0,1,2,\color{green}{0,1,0,1,1,2,3},0,1,1,2,1,2,1=\psi(\Omega^\Omega+\Omega\times\omega)</math>
* <math>0,1,2,\color{green}{0,1,0,1,1,2,3},0,1,1,2,1,2,1,2=\psi(\Omega^\Omega+\Omega^2)</math>
* <math>0,1,2,0,1,0,1,1,2,3,0,1,1,2,3=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)})</math>
* <math>0,1,2,0,1,0,1,1,2,3,0,1,1,2,3,0,1,1,2,3=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)}\times2)</math>
* <math>0,1,2,0,1,0,1,1,2,3,1=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)}\times\omega)</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,0,1,1,2,3,0,1,1,2,3,1=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)}\times\omega\times2)</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,0,1,1,2,3,1=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)}\times\omega^2)</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,1=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)}\times\omega^\omega)</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,1,2=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)}\times\psi(0))</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,1,2,0,1,1,2,3,0,1,1,2,3,1,1,2=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)}\times\psi(0)^2)</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,1,2,0,1,1,2,3,1=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)}\times\psi(0)^\omega)</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,1,2,1=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)}\times\psi(\omega))</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,1,2,1,2=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)}\times\psi(\Omega))</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,1,2,1,2,1,2=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)}\times\psi(\Omega^2))</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,1,2,2=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)}\times\psi(\Omega^\omega))</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,1,2,3=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)}\times\psi(\Omega^\Omega))</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,2=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)+1})</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,2,1,2=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)+2})</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,2,1,2,2,3,4=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)\times2})</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,2,1,2,2,3,4,1,2,2=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)\times\omega})</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,2,1,2,2,3,4,1,2,2,1,2,2=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)\times\omega^2})</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,2,1,2,2,3,4,1,2,2,1,2,2,3,4=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)^2})</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,2,1,2,2,3,4,1,2,2,2=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)^\omega})</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,2,1,2,2,3,4,1,2,2,3=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega+1)})</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,2,1,2,2,3,4,1,2,2,3,2,3=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega+\Omega)})</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,2,1,2,2,3,4,1,2,2,3,4=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)})})</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,2,1,2,2,3,4,2=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)}\times\omega)})</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,2,1,2,2,3,4,2,2,3=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)}\times\psi(0))})</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,2,1,2,2,3,4,2,3=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)+1}})</math>
* <math>0,1,2,0,1,0,1,1,2,3,1,2,1,2,2,3,4,2,3,2,3,3,4,5=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)\times2})})</math>
* <math>0,1,2,0,1,0,1,2=\psi(\Omega^\Omega\times 2)</math>

=== Part 5 ===
* <math>0,1,2,0,1,0,1,2,0,1=\psi(\Omega^\Omega\times2)\times\omega</math>
* <math>0,1,2,0,1,0,1,2,0,1,0,1=\psi(\Omega^\Omega\times2)\times\omega^2</math>
* <math>0,1,2,0,1,0,1,2,0,1,0,1,1=\psi(\Omega^\Omega\times2)\times\omega^\omega</math>
* <math>0,1,2,0,1,0,1,2,0,1,0,1,1,2=\psi(\Omega^\Omega\times2)\times\psi(0)</math>
* <math>0,1,2,0,1,0,1,2,0,1,0,1,1,2,3,1,2,1,2,3=\psi(\Omega^\Omega\times2)^2</math>
* <math>0,1,2,0,1,0,1,2,0,1,0,1,1,2,3,1,2,1,2,3,0,1,1,2=\psi(\Omega^\Omega\times2+1)</math>
* <math>0,1,2,0,1,0,1,2,0,1,0,1,1,2,3,1,2,1,2,3,0,1,1,2,3,1,2,1,2,3=\psi(\Omega^\Omega\times2+\Omega^{\psi(\Omega^\Omega\times2)})</math>
* <math>0,1,2,0,1,0,1,2,0,1,0,1,1,2,3,1,2,1,2,3,1=\psi(\Omega^\Omega\times2+\Omega^{\psi(\Omega^\Omega\times2)}\times\omega)</math>
* <math>0,1,2,0,1,0,1,2,0,1,0,1,1,2,3,1,2,1,2,3,1,2=\psi(\Omega^\Omega\times2+\Omega^{\psi(\Omega^\Omega\times2)+1})</math>
* <math>0,1,2,0,1,0,1,2,0,1,0,1,1,2,3,1,2,1,2,3,1,2,1,2,2=\psi(\Omega^\Omega\times2+\Omega^{\psi(\Omega^\Omega\times2)+\omega})</math>
* <math>0,1,2,0,1,0,1,2,0,1,0,1,1,2,3,1,2,1,2,3,1,2,1,2,2,3,4=\psi(\Omega^\Omega\times2+\Omega^{\psi(\Omega^\Omega\times2)\times2})</math>
* <math>0,1,2,0,1,0,1,2,0,1,0,1,1,2,3,1,2,1,2,3,1,2,1,2,2,3,4,1,2,2=\psi(\Omega^\Omega\times2+\Omega^{\psi(\Omega^\Omega\times2)\times\omega})</math>
* <math>0,1,2,0,1,0,1,2,0,1,0,1,1,2,3,1,2,1,2,3,1,2,1,2,2,3,4,1,2,2,2=\psi(\Omega^\Omega\times2+\Omega^{\psi(\Omega^\Omega\times2)^\omega})</math>
* <math>0,1,2,0,1,0,1,2,0,1,0,1,1,2,3,1,2,1,2,3,1,2,1,2,2,3,4,1,2,2,3=\psi(\Omega^\Omega\times2+\Omega^{\psi(\Omega^\Omega\times2+1)})</math>
* <math>0,1,2,0,1,0,1,2,0,1,0,1,1,2,3,1,2,1,2,3,1,2,1,2,2,3,4,1,2,2,3,4=\psi(\Omega^\Omega\times2+\Omega^{\psi(\Omega^\Omega\times2+\Omega^{\psi(\Omega^\Omega)})})</math>
* <math>0,1,2,0,1,0,1,2,0,1,0,1,1,2,3,1,2,1,2,3,1,2,1,2,2,3,4,2,3,2,3,4=\psi(\Omega^\Omega\times2+\Omega^{\psi(\Omega^\Omega\times2+\Omega^{\psi(\Omega^\Omega\times2)})})</math>
* <math>0,1,2,0,1,0,1,2,0,1,0,1,2=\psi(\Omega^\Omega\times3)</math>
* <math>0,1,2,0,1,0,1,2,0,1,0,1,2,0,1,0,1,2=\psi(\Omega^\Omega\times4)</math>
* <math>0,1,2,0,1,1=\psi(\Omega^\Omega\times\omega)</math>
* <math>0,1,2,0,1,1,0,1,0,1,2=\psi(\Omega^\Omega\times\omega+\Omega^\Omega)</math>
* <math>0,1,2,0,1,1,0,1,0,1,2,0,1,1=\psi(\Omega^\Omega\times\omega\times2)</math>
* <math>0,1,2,0,1,1,0,1,1=\psi(\Omega^\Omega\times\omega^2)</math>
* <math>0,1,2,0,1,1,0,1,1,2=\psi(\Omega^\Omega\times\psi(0))</math>
* <math>0,1,2,0,1,1,0,1,1,2,3=\psi(\Omega^\Omega\times\psi(\Omega^\Omega))</math>
* <math>0,1,2,0,1,1,0,1,1,2,3,1,2,2=\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times\omega))</math>
* <math>0,1,2,0,1,1,0,1,1,2,3,1,2,2,0,1,1=\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times\omega)\times\omega)</math>
* <math>0,1,2,0,1,1,0,1,1,2,3,1,2,2,0,1,1,0,1,1,2,3,1,2,2=\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times\omega)^2)</math>
* <math>0,1,2,0,1,1,0,1,1,2,3,1,2,2,0,1,1,1=\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times\omega)^\omega)</math>
* <math>0,1,2,0,1,1,0,1,1,2,3,1,2,2,0,1,1,2=\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times\omega+1))</math>
* <math>0,1,2,0,1,1,0,1,1,2,3,1,2,2,0,1,1,2,0,1,1,2,1=\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times\omega+\omega))</math>
* <math>0,1,2,0,1,1,0,1,1,2,3,1,2,2,0,1,1,2,0,1,1,2,3,1,2,2=\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times\omega+\psi(\Omega^\Omega\times\omega)))</math>
* <math>0,1,2,0,1,1,0,1,1,2,3,1,2,2,0,1,1,2,1=\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times\omega+\psi(\Omega^\Omega\times\omega)\times\omega))</math>
* <math>0,1,2,0,1,1,0,1,1,2,3,1,2,2,0,1,1,2,1,1,2=\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times\omega+\psi(\Omega^\Omega\times\omega+1)))</math>
* <math>0,1,2,0,1,1,0,1,1,2,3,1,2,2,0,1,1,2,1,2=\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times\omega+\Omega))</math>
* <math>0,1,2,0,1,1,0,1,1,2,3,1,2,2,0,1,1,2,2=\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times\omega+\Omega^\omega))</math>
* <math>0,1,2,0,1,1,0,1,1,2,3,1,2,2,0,1,1,2,3=\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times\omega+\Omega^{\psi(\Omega^\Omega)}))</math>
* <math>0,1,2,0,1,1,0,1,1,2,3,1,2,2,0,1,1,2,3,1,2,1,2,3=\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times\omega+\Omega^{\psi(\Omega^\Omega\times2)}))</math>
* <math>0,1,2,0,1,1,0,1,1,2,3,1,2,2,0,1,1,2,3,1,2,2=\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times\omega+\Omega^{\psi(\Omega^\Omega\times\omega)}))</math>
* <math>0,1,2,0,1,1,0,1,1,2,3,1,2,2,1=\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times\omega+\Omega^{\psi(\Omega^\Omega\times\omega)}\times\omega))</math>
* <math>0,1,2,0,1,1,0,1,1,2,3,1,2,2,1,2=\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times\omega+\Omega^{\psi(\Omega^\Omega\times\omega)+1}))</math>
* <math>0,1,2,0,1,1,0,1,1,2,3,1,2,2,1,2,1,2,2=\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times\omega+\Omega^{\psi(\Omega^\Omega\times\omega)+\omega}))</math>
* <math>0,1,2,0,1,1,0,1,1,2,3,1,2,2,1,2,1,2,3=\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times\omega+\Omega^\Omega))</math>
* <math>0,1,2,0,1,1,0,1,1,2,3,1,2,2,1,2,1,2,3,1,2,2=\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times\omega\times2))</math>
* <math>0,1,2,0,1,1,0,1,1,2,3,1,2,2,1,2,2=\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times\omega^2))</math>
* <math>0,1,2,0,1,1,0,1,1,2,3,1,2,2,1,2,2,3=\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times\psi(0)))</math>
* <math>0,1,2,0,1,1,0,1,2=\psi(\Omega^{\Omega+1})</math>

=== Part 6 ===
* <math>0,1,2,0,1,1,0,1,2,0,1=\psi(\Omega^{\Omega+1})\times\omega</math>
* <math>0,1,2,0,1,1,0,1,2,0,1,0,1,1,2,3=\psi(\Omega^{\Omega+1})\times\psi(\Omega^\Omega)</math>
* <math>0,1,2,0,1,1,0,1,2,0,1,0,1,1,2,3,1,2,2,1,2,3=\psi(\Omega^{\Omega+1})^2</math>
* <math>0,1,2,0,1,1,0,1,2,0,1,0,1,1,2,3,1,2,2,1,2,3,0,1,1=\psi(\Omega^{\Omega+1})^\omega</math>
* <math>0,1,2,0,1,1,0,1,2,0,1,0,1,1,2,3,1,2,2,1,2,3,0,1,1,2=\psi(\Omega^{\Omega+1}+1)</math>
* <math>0,1,2,0,1,1,0,1,2,0,1,0,1,1,2,3,1,2,2,1,2,3,0,1,1,2,1,2=\psi(\Omega^{\Omega+1}+\Omega)</math>
* <math>0,1,2,0,1,1,0,1,2,0,1,0,1,1,2,3,1,2,2,1,2,3,0,1,1,2,1,2,1,2=\psi(\Omega^{\Omega+1}+\Omega^2)</math>
* <math>0,1,2,0,1,1,0,1,2,0,1,0,1,1,2,3,1,2,2,1,2,3,0,1,1,2,3=\psi(\Omega^{\Omega+1}+\Omega^{\psi(\Omega^\Omega)})</math>
* <math>0,1,2,0,1,1,0,1,2,0,1,0,1,1,2,3,1,2,2,1,2,3,0,1,1,2,3,1,2,2,1,2,3=\psi(\Omega^{\Omega+1}+\Omega^{\psi(\Omega^{\Omega+1})})</math>
* <math>0,1,2,0,1,1,0,1,2,0,1,0,1,1,2,3,1,2,2,1,2,3,1=\psi(\Omega^{\Omega+1}+\Omega^{\psi(\Omega^{\Omega+1})}\times\omega)</math>
* <math>0,1,2,0,1,1,0,1,2,0,1,0,1,1,2,3,1,2,2,1,2,3,1,2=\psi(\Omega^{\Omega+1}+\Omega^{\psi(\Omega^{\Omega+1})+1})</math>
* <math>0,1,2,0,1,1,0,1,2,0,1,0,1,1,2,3,1,2,2,1,2,3,1,2,2,3,4,2,3,3,2,3,4=\psi(\Omega^{\Omega+1}+\Omega^{\psi(\Omega^{\Omega+1})\times2})</math>
* <math>0,1,2,0,1,1,0,1,2,0,1,0,1,2=\psi(\Omega^{\Omega+1}+\Omega^\Omega)</math>
* <math>0,1,2,0,1,1,0,1,2,0,1,0,1,2,0,1,0,1,2=\psi(\Omega^{\Omega+1}+\Omega^\Omega\times2)</math>
* <math>0,1,2,0,1,1,0,1,2,0,1,0,1,2,0,1,1=\psi(\Omega^{\Omega+1}+\Omega^\Omega\times\omega)</math>
* <math>0,1,2,0,1,1,0,1,2,0,1,0,1,2,0,1,1,0,1,2=\psi(\Omega^{\Omega+1}\times2)</math>
* <math>0,1,2,0,1,1,0,1,2,0,1,1=\psi(\Omega^{\Omega+1}\times\omega)</math>
* <math>0,1,2,0,1,1,0,1,2,0,1,1,0,1,1,2=\psi(\Omega^{\Omega+1}\times\psi(0))</math>
* <math>0,1,2,0,1,1,0,1,2,0,1,1,0,1,1,2,3=\psi(\Omega^{\Omega+1}\times\psi(\Omega^\Omega))</math>
* <math>0,1,2,0,1,1,0,1,2,0,1,1,0,1,1,2,3,1,2,2,1,2,3=\psi(\Omega^{\Omega+1}\times\psi(\Omega^{\Omega+1}))</math>
* <math>0,1,2,0,1,1,0,1,2,0,1,1,0,1,1,2,3,1,2,2,1,2,3,1,2,2=\psi(\Omega^{\Omega+1}\times\psi(\Omega^{\Omega+1}\times\omega))</math>
* <math>0,1,2,0,1,1,0,1,2,0,1,1,0,1,2=\psi(\Omega^{\Omega+2})</math>
* <math>0,1,2,0,1,1,0,1,2,0,1,1,0,1,2,0,1,1,0,1,2=\psi(\Omega^{\Omega+3})</math>
* <math>0,1,2,0,1,1,1=\psi(\Omega^{\Omega+\omega})</math>
* <math>0,1,2,0,1,1,1,0,1,1,0,1,2=\psi(\Omega^{\Omega+\omega+1})</math>
* <math>0,1,2,0,1,1,1,0,1,1,0,1,2,0,1,1,1=\psi(\Omega^{\Omega+\omega\times2})</math>
* <math>0,1,2,0,1,1,1,0,1,1,1=\psi(\Omega^{\Omega+\omega^2})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2=\psi(\Omega^{\Omega+\psi(0)})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega})})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,0,1,1,1,0,1,1,2,3,1,2,2,2=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega})\times2})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,0,1,1,1,1=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega})\times\omega})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,0,1,1,1,1,0,1,1,2,3,1,2,2,2=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega})^2})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,0,1,1,1,1,1=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega})^\omega})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,0,1,1,2=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega}+1)})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,0,1,1,2,1,2=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega}+\Omega)})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,0,1,1,2,3=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega}+\Omega^{\psi(\Omega^\Omega)})})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,0,1,1,2,3,1,2,2,2=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega}+\Omega^{\psi(\Omega^{\Omega+\omega})})})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,1=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega}+\Omega^{\psi(\Omega^{\Omega+\omega})}\times\omega)})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,1,1,2=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega}+\Omega^{\psi(\Omega^{\Omega+\omega})}\times\psi(0))})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,1,2=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega}+\Omega^{\psi(\Omega^{\Omega+\omega})+1})})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,1,2,1,2=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega}+\Omega^{\psi(\Omega^{\Omega+\omega})+2})})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,1,2,1,2,2,3,4=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega}+\Omega^{\psi(\Omega^{\Omega+\omega})+\psi(\Omega^\Omega)})})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,1,2,1,2,2,3,4,2,3,3,3=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega}+\Omega^{\psi(\Omega^{\Omega+\omega})\times2})})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,1,2,1,2,3=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega}+\Omega^\Omega)})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,1,2,1,2,3,1,2,2=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega}+\Omega^\Omega\times\omega)})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,1,2,1,2,3,1,2,2,1,2,3=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega}+\Omega^{\Omega+1})})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,1,2,1,2,3,1,2,2,2=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega}\times2)})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,1,2,2=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega}\times\omega)})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,1,2,2,1,2,3=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega+1})})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,1,2,2,1,2,3,1,2,2,2=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega\times2})})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,1,2,2,2=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega\times\omega})})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,1,2,2,3=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\psi(0)})})</math>
* <math>0,1,2,0,1,1,1,0,1,1,2,3,1,2,2,2,1,2,2,3,4,2,3,3,3=\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega})})})</math>
* <math>0,1,2,0,1,1,1,0,1,2=\psi(\Omega^{\Omega\times2})</math>
* <math>0,1,2,0,1,1,1,0,1,2,0,1,0,1,2,0,1,1,1,0,1,2=\psi(\Omega^{\Omega\times2}\times2)</math>
* <math>0,1,2,0,1,1,1,0,1,2,0,1,1=\psi(\Omega^{\Omega\times2}\times\omega)</math>
* <math>0,1,2,0,1,1,1,0,1,2,0,1,1,0,1,2=\psi(\Omega^{\Omega\times2+1})</math>
* <math>0,1,2,0,1,1,1,0,1,2,0,1,1,0,1,2,0,1,1,1=\psi(\Omega^{\Omega\times2+\omega})</math>
* <math>0,1,2,0,1,1,1,0,1,2,0,1,1,0,1,2,0,1,1,1,0,1,1,1=\psi(\Omega^{\Omega\times2+\omega^2})</math>
* <math>0,1,2,0,1,1,1,0,1,2,0,1,1,0,1,2,0,1,1,1,0,1,2=\psi(\Omega^{\Omega\times3})</math>
* <math>0,1,2,0,1,1,1,0,1,2,0,1,1,1=\psi(\Omega^{\Omega\times\omega})</math>
* <math>0,1,2,0,1,1,1,0,1,2,0,1,1,1,0,1,2=\psi(\Omega^{\Omega^2})</math>
* <math>0,1,2,0,1,1,1,0,1,2,0,1,1,1,0,1,2,0,1,1,1=\psi(\Omega^{\Omega^2\times\omega})</math>
* <math>0,1,2,0,1,1,1,0,1,2,0,1,1,1,0,1,2,0,1,1,1,0,1,2=\psi(\Omega^{\Omega^3})</math>
* <math>0,1,2,0,1,1,1,1=\psi(\Omega^{\Omega^\omega})=\mathrm{SVO}</math>
* <math>0,1,2,0,1,1,1,1,0,1,2=\psi(\Omega^{\Omega^\Omega})=\mathrm{LVO}</math>

=== Part 7 ===
* <math>0,1,2,0,1,1,1,1,0,1,2,0,1,1,1=\psi(\Omega^{\Omega^\Omega\times\omega})</math>
* <math>0,1,2,0,1,1,1,1,0,1,2,0,1,1,1,0,1,2=\psi(\Omega^{\Omega^{\Omega+1}})</math>
* <math>0,1,2,0,1,1,1,1,0,1,2,0,1,1,1,0,1,2,0,1,1,1,1=\psi(\Omega^{\Omega^{\Omega+\omega}})</math>
* <math>0,1,2,0,1,1,1,1,0,1,2,0,1,1,1,0,1,2,0,1,1,1,1,0,1,2=\psi(\Omega^{\Omega^{\Omega\times2}})</math>
* <math>0,1,2,0,1,1,1,1,0,1,2,0,1,1,1,1=\psi(\Omega^{\Omega^{\Omega\times\omega}})</math>
* <math>0,1,2,0,1,1,1,1,0,1,2,0,1,1,1,1,0,1,2=\psi(\Omega^{\Omega^{\Omega^2}})</math>
* <math>0,1,2,0,1,1,1,1,1=\psi(\Omega^{\Omega^{\Omega^\omega}})</math>
* <math>0,1,2,0,1,1,2=\psi(\psi_1(0))</math>
* <math>0,1,2,0,1,1,2,0,1,0,1,2=\psi(\psi_1(0)+\Omega^\Omega)</math>
* <math>0,1,2,0,1,1,2,0,1,0,1,2,0,1,0,1,2=\psi(\psi_1(0)+\Omega^\Omega\times2)</math>
* <math>0,1,2,0,1,1,2,0,1,0,1,2,0,1,1=\psi(\psi_1(0)+\Omega^\Omega\times\omega)</math>
* <math>0,1,2,0,1,1,2,0,1,0,1,2,0,1,1,0,1,2=\psi(\psi_1(0)+\Omega^{\Omega+1})</math>
* <math>0,1,2,0,1,1,2,0,1,0,1,2,0,1,1,0,1,2,0,1,0,1,2,0,1,1,0,1,2=\psi(\psi_1(0)+\Omega^{\Omega+1}\times2)</math>
* <math>0,1,2,0,1,1,2,0,1,0,1,2,0,1,1,0,1,2,0,1,1,0,1,2=\psi(\psi_1(0)+\Omega^{\Omega+2})</math>
* <math>0,1,2,0,1,1,2,0,1,0,1,2,0,1,1,1=\psi(\psi_1(0)+\Omega^{\Omega+\omega})</math>
* <math>0,1,2,0,1,1,2,0,1,0,1,2,0,1,1,1,0,1,2=\psi(\psi_1(0)+\Omega^{\Omega\times2})</math>
* <math>0,1,2,0,1,1,2,0,1,0,1,2,0,1,1,2=\psi(\psi_1(0)\times2)</math>
* <math>0,1,2,0,1,1,2,0,1,0,1,2,0,1,1,2,0,1,0,1,2,0,1,1,2=\psi(\psi_1(0)\times3)</math>
* <math>0,1,2,0,1,1,2,0,1,1=\psi(\psi_1(0)\times\omega)</math>
* <math>0,1,2,0,1,1,2,0,1,1,0,1,2=\psi(\psi_1(0)\times\Omega)</math>
* <math>0,1,2,0,1,1,2,0,1,1,0,1,2,0,1,1,1=\psi(\psi_1(0)\times\Omega^\omega)</math>
* <math>0,1,2,0,1,1,2,0,1,1,0,1,2,0,1,1,1,0,1,2=\psi(\psi_1(0)\times\Omega^\Omega)</math>
* <math>0,1,2,0,1,1,2,0,1,1,0,1,2,0,1,1,1,1=\psi(\psi_1(0)\times\Omega^{\Omega^\omega})</math>
* <math>0,1,2,0,1,1,2,0,1,1,0,1,2,0,1,1,2=\psi(\psi_1(0)^2)</math>
* <math>0,1,2,0,1,1,2,0,1,1,0,1,2,0,1,1,2,0,1,1,0,1,2=\psi(\psi_1(0)^2\times\Omega)</math>
* <math>0,1,2,0,1,1,2,0,1,1,0,1,2,0,1,1,2,0,1,1,0,1,2,0,1,1,2=\psi(\psi_1(0)^3)</math>
* <math>0,1,2,0,1,1,2,0,1,1,1=\psi(\psi_1(0)^\omega)</math>
* <math>0,1,2,0,1,1,2,0,1,1,1,0,1,1,0,1,2,0,1,1,2,0,1,1=\psi(\psi_1(0)^{\omega\times2})</math>
* <math>0,1,2,0,1,1,2,0,1,1,1,0,1,1,1=\psi(\psi_1(0)^{\omega^2})</math>
* <math>0,1,2,0,1,1,2,0,1,1,1,0,1,2=\psi(\psi_1(0)^{\Omega})</math>
* <math>0,1,2,0,1,1,2,0,1,1,1,0,1,2,0,1,1,2=\psi(\psi_1(0)^{\psi_1(0)})</math>
* <math>0,1,2,0,1,1,2,0,1,1,1,0,1,2,0,1,1,2,0,1,1,1=\psi(\psi_1(0)^{\psi_1(0)\times\omega})</math>
* <math>0,1,2,0,1,1,2,0,1,1,1,0,1,2,0,1,1,2,0,1,1,1,0,1,2,0,1,1,2=\psi(\psi_1(0)^{\psi_1(0)^2})</math>
* <math>0,1,2,0,1,1,2,0,1,1,1,1=\psi(\psi_1(0)^{\psi_1(0)^\omega})</math>
* <math>0,1,2,0,1,1,2,0,1,1,2=\psi(\psi_1(1))</math>
* <math>0,1,2,0,1,1,2,0,1,1,2,0,1,1,2=\psi(\psi_1(2))</math>
* <math>0,1,2,0,1,1,2,0,1,1,2,1=\psi(\psi_1(\omega))</math>
* <math>0,1,2,0,1,1,2,0,1,1,2,3=\psi(\psi_1(\psi(\Omega^\Omega)))</math>
* <math>0,1,2,0,1,1,2,0,1,1,2,3,0,1,1,2=\psi(\psi_1(\psi(\Omega^\Omega)+1))</math>
* <math>0,1,2,0,1,1,2,0,1,1,2,3,0,1,1,2,0,1,1,2,3=\psi(\psi_1(\psi(\Omega^\Omega)\times2))</math>
* <math>0,1,2,0,1,1,2,0,1,1,2,3,0,1,1,2,1=\psi(\psi_1(\psi(\Omega^\Omega)\times\omega))</math>
* <math>0,1,2,0,1,1,2,0,1,1,2,3,0,1,1,2,1,0,1,1,2,1=\psi(\psi_1(\psi(\Omega^\Omega)\times\omega^2))</math>
* <math>0,1,2,0,1,1,2,0,1,1,2,3,0,1,1,2,1,0,1,1,2,3=\psi(\psi_1(\psi(\Omega^\Omega)^2))</math>
* <math>0,1,2,0,1,1,2,0,1,1,2,3,0,1,1,2,1,1=\psi(\psi_1(\psi(\Omega^\Omega)^\omega))</math>
* <math>0,1,2,0,1,1,2,0,1,1,2,3,0,1,1,2,1,1,2=\psi(\psi_1(\psi(\Omega^\Omega+1)))</math>
* <math>0,1,2,0,1,1,2,0,1,1,2,3,0,1,1,2,3=\psi(\psi_1(\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)})))</math>
* <math>0,1,2,0,1,1,2,0,1,1,2,3,1=\psi(\psi_1(\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)}\times\omega)))</math>
* <math>0,1,2,0,1,1,2,0,1,1,2,3,1,2,1,2,3=\psi(\psi_1(\psi(\Omega^\Omega\times2)))</math>
* <math>0,1,2,0,1,1,2,0,1,1,2,3,1,2,2=\psi(\psi_1(\psi(\Omega^\Omega\times\omega)))</math>
* <math>0,1,2,0,1,1,2,0,1,1,2,3,1,2,2,1,2,3=\psi(\psi_1(\psi(\Omega^{\Omega+1})))</math>
* <math>0,1,2,0,1,1,2,0,1,1,2,3,1,2,2,3=\psi(\psi_1(\psi(\psi_1(0))))</math>
* <math>0,1,2,0,1,1,2,0,1,2=\psi(\psi_1(\Omega))</math>
* <math>0,1,2,0,1,1,2,0,1,2,0,1,1,2=\psi(\psi_1(\Omega+1))</math>
* <math>0,1,2,0,1,1,2,0,1,2,0,1,1,2,0,1,2=\psi(\psi_1(\Omega\times2))</math>
* <math>0,1,2,0,1,1,2,1=\psi(\psi_1(\Omega\times\omega))</math>
* <math>0,1,2,0,1,1,2,1,0,1,1,2,0,1,2=\psi(\psi_1(\Omega\times\omega+\Omega))</math>
* <math>0,1,2,0,1,1,2,1,0,1,1,2,0,1,2,0,1,1,2,1=\psi(\psi_1(\Omega\times\omega\times2))</math>
* <math>0,1,2,0,1,1,2,1,0,1,1,2,1=\psi(\psi_1(\Omega\times\omega^2))</math>
* <math>0,1,2,0,1,1,2,1,0,1,2=\psi(\psi_1(\Omega^2))</math>
* <math>0,1,2,0,1,1,2,1,0,1,2,0,1,1,2,0,1,2=\psi(\psi_1(\Omega^3))</math>
* <math>0,1,2,0,1,1,2,1,1=\psi(\psi_1(\Omega^\omega))</math>
* <math>0,1,2,0,1,1,2,1,1,1=\psi(\psi_1(\Omega^{\Omega^\omega}))</math>
* <math>0,1,2,0,1,1,2,1,1,2=\psi(\psi_1(\psi_1(0)))</math>
* <math>0,1,2,0,1,1,2,1,2=\psi(\Omega_2)</math>
* <math>0,1,2,0,1,1,2,1,2,0,1,1,2,1,2=\psi(\Omega_2\times2)</math>
* <math>0,1,2,0,1,1,2,1,2,0,1,2=\psi(\Omega_2\times\Omega)</math>
* <math>0,1,2,0,1,1,2,1,2,1=\psi(\Omega_2\times\Omega\times\omega)</math>
* <math>0,1,2,0,1,1,2,1,2,1,0,1,2=\psi(\Omega_2\times\Omega^2)</math>
* <math>0,1,2,0,1,1,2,1,2,1,1,2=\psi(\Omega_2\times\psi_1(0))</math>
* <math>0,1,2,0,1,1,2,1,2,1,2=\psi(\Omega_2^2)</math>
* <math>0,1,2,0,1,1,2,2=\psi(\Omega_2^\omega)</math>
* <math>0,1,2,0,1,1,2,2,0,1,1,2,2=\psi(\Omega_2^\omega\times2)</math>
* <math>0,1,2,0,1,1,2,2,0,1,2=\psi(\Omega_2^\omega\times\Omega)</math>
* <math>0,1,2,0,1,1,2,2,1=\psi(\Omega_2^\omega\times\Omega\times\omega)</math>
* <math>0,1,2,0,1,1,2,2,1,1,2=\psi(\Omega_2^\omega\times\psi_1(0))</math>
* <math>0,1,2,0,1,1,2,2,1,1,2,1,2=\psi(\Omega_2^\omega\times\psi_1(\Omega_2))</math>
* <math>0,1,2,0,1,1,2,2,1,1,2,2=\psi(\Omega_2^\omega\times\psi_1(\Omega_2\times\omega))</math>
* <math>0,1,2,0,1,1,2,2,1,2=\psi(\Omega_2^{\omega+1})</math>
* <math>0,1,2,0,1,1,2,2,1,2,1,2,2=\psi(\Omega_2^{\omega\times2})</math>
* <math>0,1,2,0,1,1,2,2,1,2,2=\psi(\Omega_2^{\omega^2})</math>
* <math>0,1,2,0,1,1,2,2,2=\psi(\Omega_2^{\omega^\omega})</math>
* <math>0,1,2,0,1,1,2,2,3=\psi(\Omega_2^{\psi(0)})</math>
* <math>0,1,2,0,1,1,2,3=\psi(\Omega_2^{\psi(\Omega_\Omega)})</math>
* <math>0,1,2,0,1,1,2,3,1,2,2,3=\psi(\Omega_2^{\psi(\psi_1(0))})</math>
* <math>0,1,2,0,1,1,2,3,1,2,2,3,1,2,2,3=\psi(\Omega_2^{\psi(\psi_1(1))})</math>
* <math>0,1,2,0,1,1,2,3,1,2,2,3,2,3=\psi(\Omega_2^{\psi(\Omega_2)})</math>
* <math>0,1,2,0,1,1,2,3,1,2,2,3,3=\psi(\Omega_2^{\psi(\Omega_2^\omega)})</math>
* <math>0,1,2,0,1,1,2,3,1,2,2,3,3,4=\psi(\Omega_2^{\psi(\Omega_2^{\psi(0)})})</math>
* <math>0,1,2,0,1,2=\psi(\Omega_2^\Omega)</math>

=== Part 8 ===
* <math>0,1,2,0,1,2,0,1=\psi(\Omega_2^\Omega)\times\omega</math>
* <math>0,1,2,0,1,2,0,1,0,1,1,2,3=\psi(\Omega_2^\Omega)\times\psi(\Omega^\Omega)</math>
* <math>0,1,2,0,1,2,0,1,0,1,1,2,3,1,2,3=\psi(\Omega_2^\Omega)^2</math>
* <math>0,1,2,0,1,2,0,1,0,1,1,2,3,1,2,3,0,1,0,1,1,2,3,1,2,3=\psi(\Omega_2^\Omega)^3</math>
* <math>0,1,2,0,1,2,0,1,0,1,1,2,3,1,2,3,0,1,1=\psi(\Omega_2^\Omega)^\omega</math>
* <math>0,1,2,0,1,2,0,1,0,1,1,2,3,1,2,3,0,1,1,0,1,1=\psi(\Omega_2^\Omega)^{\omega^2}</math>
* <math>0,1,2,0,1,2,0,1,0,1,1,2,3,1,2,3,0,1,1,1=\psi(\Omega_2^\Omega)^{\psi(\Omega_2^\Omega)^\omega}</math>
* <math>0,1,2,0,1,2,0,1,0,1,1,2,3,1,2,3,0,1,1,2=\psi(\Omega_2^\Omega+1)</math>
* <math>0,1,2,0,1,2,0,1,0,1,1,2,3,1,2,3,0,1,1,2,0,1,1,2,3,1,2,3=\psi(\Omega_2^\Omega+\psi(\Omega_2^\Omega))</math>
* <math>0,1,2,0,1,2,0,1,0,1,1,2,3,1,2,3,0,1,1,2,1=\psi(\Omega_2^\Omega+\psi(\Omega_2^\Omega)\times\omega)</math>
* <math>0,1,2,0,1,2,0,1,0,1,1,2,3,1,2,3,0,1,1,2,1,1,2=\psi(\Omega_2^\Omega+\psi(\Omega_2^\Omega+1))</math>
* <math>0,1,2,0,1,2,0,1,0,1,1,2,3,1,2,3,0,1,1,2,1,2=\psi(\Omega_2^\Omega+\Omega)</math>
* <math>0,1,2,0,1,2,0,1,0,1,1,2,3,1,2,3,0,1,1,2,1,2,1,2=\psi(\Omega_2^\Omega+\Omega^2)</math>
* <math>0,1,2,0,1,2,0,1,0,1,1,2,3,1,2,3,0,1,1,2,3=\psi(\Omega_2^\Omega+\Omega^{\psi(\Omega^\Omega)})</math>
* <math>0,1,2,0,1,2,0,1,0,1,1,2,3,1,2,3,0,1,1,2,3,1,2,3=\psi(\Omega_2^\Omega+\Omega^{\psi(\Omega_2^\Omega)})</math>
* <math>0,1,2,0,1,2,0,1,0,1,1,2,3,1,2,3,0,1,1,2,3,1,2,3,0,1,1,2=\psi(\Omega_2^\Omega+\Omega^{\psi(\Omega_2^\Omega)}+1)</math>
* <math>0,1,2,0,1,2,0,1,0,1,1,2,3,1,2,3,0,1,1,2,3,1,2,3,0,1,1,2,3,1,2,3=\psi(\Omega_2^\Omega+\Omega^{\psi(\Omega_2^\Omega)}\times2)</math>
* <math>0,1,2,0,1,2,0,1,0,1,1,2,3,1,2,3,1=\psi(\Omega_2^\Omega+\Omega^{\psi(\Omega_2^\Omega)}\times\omega)</math>
* <math>0,1,2,0,1,2,0,1,0,1,1,2,3,1,2,3,1,1,2=\psi(\Omega_2^\Omega+\Omega^{\psi(\Omega_2^\Omega)}\times\psi(0))</math>
* <math>0,1,2,0,1,2,0,1,0,1,1,2,3,1,2,3,1,2=\psi(\Omega_2^\Omega+\Omega^{\psi(\Omega_2^\Omega)+1})</math>
* <math>0,1,2,0,1,2,0,1,0,1,1,2,3,1,2,3,1,2,1,2=\psi(\Omega_2^\Omega+\Omega^{\psi(\Omega_2^\Omega)+2})</math>
* <math>0,1,2,0,1,2,0,1,0,1,1,2,3,1,2,3,1,2,1,2,2=\psi(\Omega_2^\Omega+\Omega^{\psi(\Omega_2^\Omega)+\omega})</math>
* <math>0,1,2,0,1,2,0,1,0,1,1,2,3,1,2,3,1,2,1,2,2,3,4,2,3,4=\psi(\Omega_2^\Omega+\Omega^{\psi(\Omega_2^\Omega)\times2})</math>
* <math>0,1,2,0,1,2,0,1,0,1,2=\psi(\Omega_2^\Omega+\Omega^\Omega)</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,0,1,2=\psi(\Omega_2^\Omega+\Omega^\Omega\times2)</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1=\psi(\Omega_2^\Omega+\Omega^\Omega\times\omega)</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,0,1,0,1,2=\psi(\Omega_2^\Omega+\Omega^\Omega\times\omega+\Omega^\Omega)</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,0,1,0,1,2=\psi(\Omega_2^\Omega+\Omega^\Omega\times\omega+\Omega^\Omega)</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,0,1,0,1,2,0,1,1=\psi(\Omega_2^\Omega+\Omega^\Omega\times\omega\times2)</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,0,1,1=\psi(\Omega_2^\Omega+\Omega^\Omega\times\omega^2)</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,0,1,1,0,1,1,2,3,1,2,3=\psi(\Omega_2^\Omega+\Omega^\Omega\times\psi(\Omega_2^\Omega))</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,0,1,2=\psi(\Omega_2^\Omega+\Omega^{\Omega+1})</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,1=\psi(\Omega_2^\Omega+\Omega^{\Omega+\omega})</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,1,0,1,2=\psi(\Omega_2^\Omega+\Omega^{\Omega\times2})</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,1,0,1,2,0,1,1,0,1,2=\psi(\Omega_2^\Omega+\Omega^{\Omega\times2+1})</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,1,0,1,2,0,1,1,0,1,2=\psi(\Omega_2^\Omega+\Omega^{\Omega\times2+1})</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,1,0,1,2,0,1,1,0,1,2,0,1,1,1=\psi(\Omega_2^\Omega+\Omega^{\Omega\times2+\omega})</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,1,0,1,2,0,1,1,0,1,2,0,1,1,1,0,1,2=\psi(\Omega_2^\Omega+\Omega^{\Omega\times3})</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,1,0,1,2,0,1,1,1=\psi(\Omega_2^\Omega+\Omega^{\Omega\times\omega})</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,1,0,1,2,0,1,1,1,0,1,2=\psi(\Omega_2^\Omega+\Omega^{\Omega^2})</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,1,1=\psi(\Omega_2^\Omega+\Omega^{\Omega^\omega})</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,2=\psi(\Omega_2^\Omega+\psi_1(0))</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,2,0,1,1,2,1=\psi(\Omega_2^\Omega+\psi_1(\omega))</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,2,0,1,1,2,3=\psi(\Omega_2^\Omega+\psi_1(\psi(\Omega^\Omega)))</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,2,0,1,2=\psi(\Omega_2^\Omega+\psi_1(\Omega))</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,2,1=\psi(\Omega_2^\Omega+\psi_1(\Omega\times\omega))</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,2,1,1=\psi(\Omega_2^\Omega+\psi_1(\Omega^\omega))</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,2,1,1,2=\psi(\Omega_2^\Omega+\psi_1(\psi_1(0)))</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,2,1,2=\psi(\Omega_2^\Omega+\psi_1(\Omega_2))</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,2,1,2,1,2=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^2))</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,1,2,3=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^{\psi(\Omega^\Omega)}))</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,2=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega))</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,2,0,1,0,1,2=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)+\Omega^\Omega)</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,2,0,1,0,1,2,0,1,1,1=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)+\Omega^{\Omega+\omega})</math>
* <math>0,1,2,0,1,2,0,1,0,1,2,0,1,2,0,1,0,1,2,0,1,2=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)\times2)</math>
* <math>0,1,2,0,1,2,0,1,1=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)\times\omega)</math>
* <math>0,1,2,0,1,2,0,1,1,0,1,0,1,2,0,1,2=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)\times\omega+\psi_1(\Omega_2^\Omega))</math>
* <math>0,1,2,0,1,2,0,1,1,0,1,0,1,2,0,1,2,0,1,1=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)\times\omega\times2)</math>
* <math>0,1,2,0,1,2,0,1,1,0,1,1=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)\times\omega^2)</math>
* <math>0,1,2,0,1,2,0,1,1,0,1,2=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)\times\Omega)</math>
* <math>0,1,2,0,1,2,0,1,1,0,1,2,0,1,1,1=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)\times\Omega^\omega)</math>
* <math>0,1,2,0,1,2,0,1,1,0,1,2,0,1,1,2=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)\times\psi_1(0))</math>
* <math>0,1,2,0,1,2,0,1,1,0,1,2,0,1,1,2,0,1,1,2=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)\times\psi_1(1))</math>
* <math>0,1,2,0,1,2,0,1,1,0,1,2,0,1,2=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)^2)</math>

=== Part 9 ===
* <math>0,1,2,0,1,2,0,1,1,1=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)^\omega)</math>
* <math>0,1,2,0,1,2,0,1,1,1,0,1,1,0,1,2,0,1,2=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)^{\omega\times2})</math>
* <math>0,1,2,0,1,2,0,1,1,1,0,1,1,1=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)^{\omega^2})</math>
* <math>0,1,2,0,1,2,0,1,1,1,0,1,2=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)^{\Omega})</math>
* <math>0,1,2,0,1,2,0,1,1,1,0,1,2,0,1,2=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)^{\psi_1(\Omega_2^\Omega)})</math>
* <math>0,1,2,0,1,2,0,1,1,1,1=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)^{\psi_1(\Omega_2^\Omega)^\omega})</math>
* <math>0,1,2,0,1,2,0,1,1,2=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega+1))</math>
* <math>0,1,2,0,1,2,0,1,1,2,0,1,1,2=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega+2))</math>
* <math>0,1,2,0,1,2,0,1,1,2,0,1,2=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega+\Omega))</math>
* <math>0,1,2,0,1,2,0,1,1,2,0,1,2,0,1,1,2,1=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega+\Omega\times\omega))</math>
* <math>0,1,2,0,1,2,0,1,1,2,0,1,2,0,1,1,2,1,2=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega+\psi_1(\Omega_2)))</math>
* <math>0,1,2,0,1,2,0,1,1,2,0,1,2,0,1,1,2,3=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega+\psi_1(\Omega_2^{\psi(\Omega^\Omega)})))</math>
* <math>0,1,2,0,1,2,0,1,1,2,0,1,2,0,1,1,2,3,1,2,3=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega+\psi_1(\Omega_2^{\psi(\Omega_2^\Omega)})))</math>
* <math>0,1,2,0,1,2,0,1,1,2,0,1,2,0,1,2=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)))</math>
* <math>0,1,2,0,1,2,0,1,1,2,0,1,2,0,1,2,0,1,1,2=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)+1))</math>
* <math>0,1,2,0,1,2,0,1,1,2,1=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)\times\omega))</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,1,2=\psi(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega+1)))</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,2=\psi(\Omega_2^\Omega+\Omega_2)</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,2,0,1,0,1,2=\psi(\Omega_2^\Omega+\Omega_2+\Omega^\Omega)</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,2,0,1,0,1,2,0,1,2=\psi(\Omega_2^\Omega+\Omega_2+\psi_1(\Omega_2^\Omega))</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,2,0,1,0,1,2,0,1,2,0,1,1,2=\psi(\Omega_2^\Omega+\Omega_2+\psi_1(\Omega_2^\Omega+1))</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,2,0,1,0,1,2,0,1,2,0,1,1,2,1,2=\psi(\Omega_2^\Omega+\Omega_2+\psi_1(\Omega_2^\Omega+\Omega_2))</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,2,0,1,1=\psi(\Omega_2^\Omega+\Omega_2+\psi_1(\Omega_2^\Omega+\Omega_2)\times\omega)</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,2,0,1,1,2=\psi(\Omega_2^\Omega+\Omega_2+\psi_1(\Omega_2^\Omega+\Omega_2+1))</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,2,0,1,1,2,1,2=\psi(\Omega_2^\Omega+\Omega_2\times2)</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,2,0,1,2=\psi(\Omega_2^\Omega+\Omega_2\times\Omega)</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,2,0,1,2,0,1,1,2,1,2,0,1,2=\psi(\Omega_2^\Omega+\Omega_2\times\Omega\times2)</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,2,0,1,2,0,1,1,2,1,2,1=\psi(\Omega_2^\Omega+\Omega_2\times\Omega\times\omega)</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,2,0,1,2,0,1,1,2,1,2,1,1,2=\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(0))</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,2,0,1,2,0,1,1,2,1,2,1,1,2,1,2,0,1,1,2,1,2,1,1,2,1,2=\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_2\times2))</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,2,0,1,2,0,1,1,2,1,2,1,1,2,1,2,0,1,2=\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_2\times\Omega))</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,2,0,1,2,0,1,1,2,1,2,1,1,2,1,2,1=\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_2\times\Omega\times\omega))</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,2,0,1,2,0,1,1,2,1,2,1,2=\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_2^2))</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,2,0,1,2,0,1,1,2,2=\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_2^\omega))</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,2,0,1,2,0,1,2=\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_2^\Omega))</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,2,1,1,2=\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_2^\Omega+1))</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,2,1,1,2,1,2=\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_2^\Omega+\Omega_2))</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,2,1,1,2,1,2,0,1,2=\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_2^\Omega+\Omega_2\times\Omega))</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,2,1,1,2,1,2,0,1,2,0,1,2=\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_2^\Omega)))</math>
* <math>0,1,2,0,1,2,0,1,1,2,1,2,1,2=\psi(\Omega_2^\Omega+\Omega_2^2)</math>
* <math>0,1,2,0,1,2,0,1,1,2,2=\psi(\Omega_2^\Omega+\Omega_2^\omega)</math>
* <math>0,1,2,0,1,2,0,1,1,2,3,1,2,3=\psi(\Omega_2^\Omega+\Omega_2^{\psi(\Omega_2^\Omega)})</math>
* <math>0,1,2,0,1,2,0,1,2=\psi(\Omega_2^\Omega\times2)</math>
* <math>0,1,2,0,1,2,0,1,2,0,1,2=\psi(\Omega_2^\Omega\times3)</math>
* <math>0,1,2,1=\psi(\Omega_2^\Omega\times\omega)</math>

=== Part 10 ===
* <math>0,1,2,1,0,1,1,2=\psi(\Omega_2^\Omega\times\omega+\psi_1(\Omega_2^\Omega+1))</math>
* <math>0,1,2,1,0,1,1,2,1,2=\psi(\Omega_2^\Omega\times\omega+\Omega_2)</math>
* <math>0,1,2,1,0,1,1,2,1,2,1,2=\psi(\Omega_2^\Omega\times\omega+\Omega_2^2)</math>
* <math>0,1,2,1,0,1,1,2,1,2,1,2=\psi(\Omega_2^\Omega\times\omega+\Omega_2^2)</math>
* <math>0,1,2,1,0,1,1,2,2=\psi(\Omega_2^\Omega\times\omega+\Omega_2^\omega)</math>
* <math>0,1,2,1,0,1,1,2,3=\psi(\Omega_2^\Omega\times\omega+\Omega_2^{\psi(\Omega^\Omega)})</math>
* <math>0,1,2,1,0,1,1,2,3,2=\psi(\Omega_2^\Omega\times\omega+\Omega_2^{\psi(\Omega_2^\Omega\times\omega)})</math>
* <math>0,1,2,1,0,1,2=\psi(\Omega_2^\Omega\times\omega+\Omega_2^\Omega)</math>
* <math>0,1,2,1,0,1,2,0,1,2=\psi(\Omega_2^\Omega\times\omega+\Omega_2^\Omega\times2)</math>
* <math>0,1,2,1,0,1,2,0,1,2,1=\psi(\Omega_2^\Omega\times\omega\times2)</math>
* <math>0,1,2,1,0,1,2,1=\psi(\Omega_2^\Omega\times\omega^2)</math>
* <math>0,1,2,1,1=\psi(\Omega_2^\Omega\times\omega^\omega)</math>
* <math>0,1,2,1,1,2=\psi(\Omega_2^\Omega\times\psi(0))</math>
* <math>0,1,2,1,1,2,=\psi(\Omega_2^\Omega\times\psi(0))</math>
* <math>0,1,2,1,1,2,0,1,2,0,1,2,1,1,2=\psi(\Omega_2^\Omega\times\psi(0)\times2)</math>
* <math>0,1,2,1,1,2,0,1,2,1=\psi(\Omega_2^\Omega\times\psi(0)\times\omega)</math>
* <math>0,1,2,1,1,2,0,1,2,1,0,1,2,1,1,2=\psi(\Omega_2^\Omega\times\psi(0)^2)</math>
* <math>0,1,2,1,1,2,0,1,2,1,1=\psi(\Omega_2^\Omega\times\psi(0)^\omega)</math>
* <math>0,1,2,1,1,2,1=\psi(\Omega_2^\Omega\times\psi(\omega))</math>
* <math>0,1,2,1,1,2,1,1,2=\psi(\Omega_2^\Omega\times\psi(\psi(0)))</math>
* <math>0,1,2,1,1,2,1,2=\psi(\Omega_2^\Omega\times\psi(\Omega))</math>
* <math>0,1,2,1,1,2,1,2,1,1,2,1,2=\psi(\Omega_2^\Omega\times\psi(\Omega\times\psi(\Omega)))</math>
* <math>0,1,2,1,1,2,1,2,1,2=\psi(\Omega_2^\Omega\times\psi(\Omega^2))</math>
* <math>0,1,2,1,1,2,2=\psi(\Omega_2^\Omega\times\psi(\Omega^\omega))</math>
* <math>0,1,2,1,1,2,3=\psi(\Omega_2^\Omega\times\psi(\Omega^\Omega))</math>
* <math>0,1,2,1,1,2,3,1,2,3=\psi(\Omega_2^\Omega\times\psi(\Omega_2^\Omega))</math>
* <math>0,1,2,1,1,2,3,2=\psi(\Omega_2^\Omega\times\psi(\Omega_2^\Omega\times\omega))</math>
* <math>0,1,2,1,1,2,3,2,1,2,3,2=\psi(\Omega_2^\Omega\times\psi(\Omega_2^\Omega\times\omega^2))</math>
* <math>0,1,2,1,1,2,3,2,2=\psi(\Omega_2^\Omega\times\psi(\Omega_2^\Omega\times\omega^\omega))</math>
* <math>0,1,2,1,1,2,3,2,2,3=\psi(\Omega_2^\Omega\times\psi(\Omega_2^\Omega\times\psi(0)))</math>
* <math>0,1,2,1,1,2,3,2,2,3,4,3=\psi(\Omega_2^\Omega\times\psi(\Omega_2^\Omega\times\psi(\Omega_2^\Omega)))</math>
* <math>0,1,2,1,2=\psi(\Omega_2^\Omega\times\Omega)</math>

=== Part 11 ===
* <math>0,1,2,1,2,0,1=\psi(\Omega_2^\Omega\times\Omega)\times\omega</math>
* <math>0,1,2,1,2,0,1,0,1,1,2=\psi(\Omega_2^\Omega\times\Omega)\times\psi(0)</math>
* <math>0,1,2,1,2,0,1,0,1,1,2,3,2,3=\psi(\Omega_2^\Omega\times\Omega)^2</math>
* <math>0,1,2,1,2,0,1,0,1,1,2,3,2,3,0,1,1,2=\psi(\Omega_2^\Omega\times\Omega+1)</math>
* <math>0,1,2,1,2,0,1,0,1,1,2,3,2,3,0,1,1,2,1,2=\psi(\Omega_2^\Omega\times\Omega+\Omega)</math>
* <math>0,1,2,1,2,0,1,0,1,1,2,3,2,3,0,1,1,2,2=\psi(\Omega_2^\Omega\times\Omega+\Omega^\omega)</math>
* <math>0,1,2,1,2,0,1,0,1,1,2,3,2,3,0,1,1,2,3,2,3=\psi(\Omega_2^\Omega\times\Omega+\Omega^{\psi(\Omega_2^\Omega\times\Omega)})</math>
* <math>0,1,2,1,2,0,1,0,1,1,2,3,2,3,1=\psi(\Omega_2^\Omega\times\Omega+\Omega^{\psi(\Omega_2^\Omega\times\Omega)}\times\omega)</math>
* <math>0,1,2,1,2,0,1,0,1,1,2,3,2,3,1,1,2=\psi(\Omega_2^\Omega\times\Omega+\Omega^{\psi(\Omega_2^\Omega\times\Omega)}\times\psi(0))</math>
* <math>0,1,2,1,2,0,1,0,1,1,2,3,2,3,1,2=\psi(\Omega_2^\Omega\times\Omega+\Omega^{\psi(\Omega_2^\Omega\times\Omega)+1})</math>
* <math>0,1,2,1,2,0,1,0,1,2=\psi(\Omega_2^\Omega\times\Omega+\Omega^\Omega)</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,0,1,2=\psi(\Omega_2^\Omega\times\Omega+\Omega^\Omega\times2)</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,1=\psi(\Omega_2^\Omega\times\Omega+\Omega^\Omega\times\omega)</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,1,0,1,1=\psi(\Omega_2^\Omega\times\Omega+\Omega^\Omega\times\omega^2)</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,1,0,1,2=\psi(\Omega_2^\Omega\times\Omega+\Omega^{\Omega+1})</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,1,1=\psi(\Omega_2^\Omega\times\Omega+\Omega^{\Omega+\omega})</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,1,1,1=\psi(\Omega_2^\Omega\times\Omega+\Omega^{\Omega^\omega})</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,1,2=\psi(\Omega_2^\Omega\times\Omega+\psi_1(0))</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,1,2,0,1,1,2,1=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\omega))</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,1,2,0,1,2=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega))</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,1,2,1=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega\times\omega))</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,1,2,1,1,2=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\psi_1(0)))</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,1,2,1,2=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2))</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,1,2,1,2,1,2=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^2))</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,2=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega))</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,2=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega))</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,2,0,1,0,1,2,0,1,2=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega)\times2)</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,2,0,1,1=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega)\times\omega)</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,2,0,1,1,0,1,1,2,3,2,3=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega)\times\psi(\Omega_2^\Omega\times\Omega))</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,2,0,1,1,0,1,2=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega)\times\Omega)</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,2,0,1,1,0,1,2,0,1,2=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega)^2)</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,2,0,1,1,1=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega)^\omega)</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,2,0,1,1,2=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega+1))</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,2,0,1,1,2,0,1,2=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega+\Omega))</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,2,0,1,1,2,0,1,2,0,1,2=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)))</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,2,0,1,1,2,1=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)\times\omega))</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,2,0,1,1,2,1,2=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega+\Omega_2))</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,2,0,1,1,2,1,2,1,1,2,1,2=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega+\Omega_2\times2))</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,2,0,1,1,2,1,2,1,2=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega+\Omega_2^2))</math>
* <math>0,1,2,1,2,0,1,0,1,2,0,1,2,0,1,2=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega\times2))</math>
* <math>0,1,2,1,2,0,1,0,1,2,1=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega\times\omega))</math>
* <math>0,1,2,1,2,0,1,0,1,2,1,1,2=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega\times\psi(0)))</math>
* <math>0,1,2,1,2,0,1,0,1,2,1,1,2,1,2=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega\times\psi(\Omega)))</math>
* <math>0,1,2,1,2,0,1,0,1,2,1,1,2,3,1,2,3=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega\times\psi(\Omega_2^\Omega)))</math>
* <math>0,1,2,1,2,0,1,0,1,2,1,2=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega\times\Omega))</math>

=== Part 12 ===
* <math>0,1,2,1,2,0,1,1=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega)\times\omega)</math>
* <math>0,1,2,1,2,0,1,1,2=\psi(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega+1))</math>
* <math>0,1,2,1,2,0,1,1,2,1,2=\psi(\Omega_2^\Omega\times\Omega+\Omega_2)</math>
* <math>0,1,2,1,2,0,1,2=\psi(\Omega_2^\Omega\times\Omega+\Omega_2^\Omega)</math>
* <math>0,1,2,1,2,0,1,2,0,1,2,1=\psi(\Omega_2^\Omega\times\Omega+\Omega_2^\Omega\times\omega)</math>
* <math>0,1,2,1,2,0,1,2,0,1,2,1,1,2=\psi(\Omega_2^\Omega\times\Omega+\Omega_2^\Omega\times\psi(0))</math>
* <math>0,1,2,1,2,0,1,2,0,1,2,1,1,2,1,2=\psi(\Omega_2^\Omega\times\Omega+\Omega_2^\Omega\times\psi(\Omega))</math>
* <math>0,1,2,1,2,0,1,2,0,1,2,1,1,2,3,2,3=\psi(\Omega_2^\Omega\times\Omega+\Omega_2^\Omega\times\psi(\Omega_2^\Omega\times\Omega))</math>
* <math>0,1,2,1,2,0,1,2,0,1,2,1,2=\psi(\Omega_2^\Omega\times\Omega\times 2)</math>
* <math>0,1,2,1,2,0,1,2,0,1,2,1,2,0,1,2,0,1,2,1,2=\psi(\Omega_2^\Omega\times\Omega\times3)</math>
* <math>0,1,2,1,2,0,1,2,1=\psi(\Omega_2^\Omega\times\Omega\times\omega)</math>
* <math>0,1,2,1,2,0,1,2,1,0,1,2,1=\psi(\Omega_2^\Omega\times\Omega\times\omega^2)</math>
* <math>0,1,2,1,2,0,1,2,1,0,1,2,1,2=\psi(\Omega_2^\Omega\times\Omega^2)</math>
* <math>0,1,2,1,2,0,1,2,1,1=\psi(\Omega_2^\Omega\times\Omega^\omega)</math>
* <math>0,1,2,1,2,0,1,2,1,1,0,1,2,1,2=\psi(\Omega_2^\Omega\times\Omega^\Omega)</math>
* <math>0,1,2,1,2,0,1,2,1,1,2=\psi(\Omega_2^\Omega\times\psi_1(0))</math>
* <math>0,1,2,1,2,0,1,2,1,1,2,0,1,2,0,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(0)+\Omega_2^\Omega\times\Omega)</math>
* <math>0,1,2,1,2,0,1,2,1,1,2,0,1,2,0,1,2,1,2,0,1,2,1,1,2=\psi(\Omega_2^\Omega\times\psi_1(0)\times2)</math>
* <math>0,1,2,1,2,0,1,2,1,1,2,0,1,2,1=\psi(\Omega_2^\Omega\times\psi_1(0)\times\omega)</math>
* <math>0,1,2,1,2,0,1,2,1,1,2,0,1,2,1,0,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(0)\times\Omega)</math>
* <math>0,1,2,1,2,0,1,2,1,1,2,0,1,2,1,0,1,2,1,2,0,1,2,1,1,2=\psi(\Omega_2^\Omega\times\psi_1(0)^2)</math>
* <math>0,1,2,1,2,0,1,2,1,1,2,0,1,2,1,1=\psi(\Omega_2^\Omega\times\psi_1(0)^\omega)</math>
* <math>0,1,2,1,2,0,1,2,1,1,2,0,1,2,1,1,2=\psi(\Omega_2^\Omega\times\psi_1(1))</math>
* <math>0,1,2,1,2,0,1,2,1,1,2,0,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega))</math>
* <math>0,1,2,1,2,0,1,2,1,1,2,1=\psi(\Omega_2^\Omega\times\psi_1(\Omega\times\omega))</math>
* <math>0,1,2,1,2,0,1,2,1,1,2,1,1=\psi(\Omega_2^\Omega\times\psi_1(\Omega^\omega))</math>
* <math>0,1,2,1,2,0,1,2,1,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2))</math>
* <math>0,1,2,1,2,0,1,2,1,1,2,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^2))</math>
* <math>0,1,2,1,2,0,1,2,1,1,2,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\omega))</math>
* <math>0,1,2,1,2,0,1,2,1,1,2,3=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^{\psi(\Omega^\Omega)}))</math>
* <math>0,1,2,1,2,0,1,2,1,1,2,3,2,3=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^{\psi(\Omega_2^\Omega\times\Omega)}))</math>
* <math>0,1,2,1,2,0,1,2,1,2=\psi(\Omega_2^{\Omega}\times\psi_1(\Omega_2^\Omega))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,0,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\Omega))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,0,1,2,1,2,0,1,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\Omega+1))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,0,1,2,1,2,0,1,1,2,0,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\Omega+\Omega))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,0,1,2,1,2,0,1,1,2,0,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega\times\Omega)))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,0,1,2,1,2,0,1,1,2,1=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\Omega+\psi_1(\Omega_2^\Omega\times\Omega)\times\omega))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,0,1,2,1,2,0,1,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\Omega+\Omega_2))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,0,1,2,1,2,0,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\Omega+\Omega_2^\Omega))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,0,1,2,1,2,0,1,2,0,1,2,1=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\Omega+\Omega_2^\Omega\times\omega))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,0,1,2,1,2,0,1,2,0,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\Omega\times2))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,0,1,2,1,2,0,1,2,1=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\Omega\times\omega))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,0,1,2,1,2,0,1,2,1,0,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\Omega^2))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,0,1,2,1,2,0,1,2,1,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\psi_1(0)))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,0,1,2,1,2,0,1,2,1,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2)))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,0,1,2,1,2,0,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,1=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega))\times\omega)</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+1))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,1,2,0,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\Omega)))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,1,2,0,1,2,1,2,0,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega))))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,1,2,1=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega))\times\omega))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,1,2,1,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+1)))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\Omega_2)</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,1,2,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\Omega_2\times2)</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\Omega_2^\Omega)</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,2,0,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\Omega_2^\Omega\times2)</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,2,0,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\Omega_2^\Omega\times\Omega)</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,2,0,1,2,1,2,0,1,2,0,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\Omega_2^\Omega\times\Omega\times2)</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,2,0,1,2,1,2,0,1,2,1=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\Omega_2^\Omega\times\Omega\times\omega)</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,2,0,1,2,1,2,0,1,2,1,0,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\Omega_2^\Omega\times\Omega^2)</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,2,0,1,2,1,2,0,1,2,1,1=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\Omega_2^\Omega\times\Omega^\omega)</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,2,0,1,2,1,2,0,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)\times2)</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,2,1=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)\times\omega)</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,2,1,0,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)\times\Omega)</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,2,1,0,1,2,1,2,0,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)^2)</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,2,1,1=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)^\omega)</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,2,1,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+1))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,2,1,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+\Omega_2))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,2,1,1,2,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+\Omega_2^2))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times2))</math>
* <math>0,1,2,1,2,0,1,2,1,2,0,1,2,1,2,0,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times3))</math>
* <math>0,1,2,1,2,1=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times\omega))</math>
* <math>0,1,2,1,2,1,1=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times\omega^2))</math>
* <math>0,1,2,1,2,1,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times\psi(0)))</math>
* <math>0,1,2,1,2,1,2=\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times\Omega))</math>
* <math>0,1,2,1,2,2=\psi(\Omega_2^{\Omega+1})</math>

=== Part 13 ===
* <math>0,1,2,1,2,2,1,2=\psi(\Omega_2^{\Omega+1}\times\Omega)</math>
* <math>0,1,2,1,2,2,1,2,0,1,2,1,2,2,1,2=\psi(\Omega_2^{\Omega+1}\times\psi_1(\Omega_2^{\Omega+1}))</math>
* <math>0,1,2,1,2,2,1,2,1=\psi(\Omega_2^{\Omega+1}\times\psi_1(\Omega_2^{\Omega+1}\times\omega))</math>
* <math>0,1,2,1,2,2,1,2,1,2=\psi(\Omega_2^{\Omega+1}\times\psi_1(\Omega_2^{\Omega+1}\times\Omega))</math>
* <math>0,1,2,1,2,2,1,2,1,2,2=\psi(\Omega_2^{\Omega+2})</math>
* <math>0,1,2,1,2,2,1,2,1,2,2,1,2,1,2,2=\psi(\Omega_2^{\Omega+3})</math>
* <math>0,1,2,1,2,2,1,2,2=\psi(\Omega_2^{\Omega+\omega})</math>
* <math>0,1,2,1,2,2,1,2,2,1,2,1,2,2,1,2,2=\psi(\Omega_2^{\Omega+\omega\times2})</math>
* <math>0,1,2,1,2,2,1,2,2,1,2,2=\psi(\Omega_2^{\Omega+\omega^2})</math>
* <math>0,1,2,1,2,2,2=\psi(\Omega_2^{\Omega+\omega^\omega})</math>
* <math>0,1,2,1,2,2,3=\psi(\Omega_2^{\Omega+\psi(0)})</math>
* <math>0,1,2,1,2,2,3,4,2,3,4=\psi(\Omega_2^{\Omega+\psi(\Omega_2)})</math>
* <math>0,1,2,1,2,2,3,4,2,3,4,2,3,4=\psi(\Omega_2^{\Omega+\psi(\Omega_2^\Omega)})</math>
* <math>0,1,2,1,2,2,3,4,2,3,4,3,4=\psi(\Omega_2^{\Omega+\psi(\Omega_2^\Omega\times\Omega)})</math>
* <math>0,1,2,1,2,3=\psi(\Omega_2^{\Omega\times2})</math>
* <math>0,1,2,1,2,3,0,1,0,1,2=\psi(\Omega_2^{\Omega\times2}+\Omega^\Omega)</math>
* <math>0,1,2,1,2,3,0,1,0,1,2,0,1,2=\psi(\Omega_2^{\Omega\times2}+\psi_1(\Omega_2^\Omega))</math>
* <math>0,1,2,1,2,3,0,1,0,1,2,1=\psi(\Omega_2^{\Omega\times2}+\psi_1(\Omega_2^\Omega\times\omega))</math>
* <math>0,1,2,1,2,3,0,1,0,1,2,1,2=\psi(\Omega_2^{\Omega\times2}+\psi_1(\Omega_2^{\Omega+1}))</math>
* <math>0,1,2,1,2,3,0,1,0,1,2,1,2,1,2=\psi(\Omega_2^{\Omega\times2}+\psi_1(\Omega_2^{\Omega+2}))</math>
* <math>0,1,2,1,2,3,0,1,0,1,2,1,2,2=\psi(\Omega_2^{\Omega\times2}+\psi_1(\Omega_2^{\Omega+\omega}))</math>
* <math>0,1,2,1,2,3,0,1,0,1,2,1,2,3=\psi(\Omega_2^{\Omega\times2}+\psi_1(\Omega_2^{\Omega\times2}))</math>
* <math>0,1,2,1,2,3,0,1,1=\psi(\Omega_2^{\Omega\times2}+\psi_1(\Omega_2^{\Omega\times2})\times\omega)</math>
* <math>0,1,2,1,2,3,0,1,1,2=\psi(\Omega_2^{\Omega\times2}+\psi_1(\Omega_2^{\Omega\times2}+1))</math>
* <math>0,1,2,1,2,3,0,1,1,2,1,2=\psi(\Omega_2^{\Omega\times2}+\Omega_2)</math>
* <math>0,1,2,1,2,3,0,1,2=\psi(\Omega_2^{\Omega\times2}+\Omega_2^\Omega)</math>
* <math>0,1,2,1,2,3,0,1,2,0,1,2=\psi(\Omega_2^{\Omega\times2}+\Omega_2^\Omega\times2)</math>
* <math>0,1,2,1,2,3,0,1,2,0,1,2,1=\psi(\Omega_2^{\Omega\times2}+\Omega_2^\Omega\times\omega)</math>
* <math>0,1,2,1,2,3,0,1,2,0,1,2,1,2=\psi(\Omega_2^{\Omega\times2}+\Omega_2^\Omega\times\Omega)</math>
* <math>0,1,2,1,2,3,0,1,2,0,1,2,1,2,0,1,2,1=\psi(\Omega_2^{\Omega\times2}+\Omega_2^\Omega\times\Omega\times\omega)</math>
* <math>0,1,2,1,2,3,0,1,2,0,1,2,1,2,0,1,2,1,0,1,2,1,2=\psi(\Omega_2^{\Omega\times2}+\Omega_2^\Omega\times\Omega^2)</math>
* <math>0,1,2,1,2,3,0,1,2,0,1,2,1,2,0,1,2,1,1=\psi(\Omega_2^{\Omega\times2}+\Omega_2^\Omega\times\Omega^\omega)</math>
* <math>0,1,2,1,2,3,0,1,2,0,1,2,1,2,0,1,2,1,1,2=\psi(\Omega_2^{\Omega\times2}+\Omega_2^\Omega\times\psi_1(0))</math>
* <math>0,1,2,1,2,3,0,1,2,0,1,2,1,2,0,1,2,1,2=\psi(\Omega_2^{\Omega\times2}+\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega))</math>
* <math>0,1,2,1,2,3,0,1,2,0,1,2,1,2,1=\psi(\Omega_2^{\Omega\times2}+\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times\omega))</math>
* <math>0,1,2,1,2,3,0,1,2,0,1,2,1,2,1,2=\psi(\Omega_2^{\Omega\times2}+\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times\Omega))</math>
* <math>0,1,2,1,2,3,0,1,2,0,1,2,1,2,1,2,1=\psi(\Omega_2^{\Omega\times2}+\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times\omega)))</math>
* <math>0,1,2,1,2,3,0,1,2,0,1,2,1,2,2=\psi(\Omega_2^{\Omega\times2}+\Omega_2^\Omega\times\psi_1(\Omega_2^{\Omega+1}))</math>
* <math>0,1,2,1,2,3,0,1,2,0,1,2,1,2,3=\psi(\Omega_2^{\Omega\times2}+\Omega_2^\Omega\times\psi_1(\Omega_2^{\Omega\times2}))</math>
* <math>0,1,2,1,2,3,0,1,2,0,1,2,1,2,3,0,1,2=\psi(\Omega_2^{\Omega\times2}+\Omega_2^\Omega\times\psi_1(\Omega_2^{\Omega\times2})+\Omega^\Omega)</math>
* <math>0,1,2,1,2,3,0,1,2,1=\psi(\Omega_2^{\Omega\times2}+\Omega_2^\Omega\times\psi_1(\Omega_2^{\Omega\times2})\times\omega)</math>
* <math>0,1,2,1,2,3,0,1,2,1,0,1,2,1,2,3=\psi(\Omega_2^{\Omega\times2}+\Omega_2^\Omega\times\psi_1(\Omega_2^{\Omega\times2})^2)</math>
* <math>0,1,2,1,2,3,0,1,2,1,1,2=\psi(\Omega_2^{\Omega\times2}+\Omega_2^\Omega\times\psi_1(\Omega_2^{\Omega\times2}+1))</math>
* <math>0,1,2,1,2,3,0,1,2,1,1,2,1,2=\psi(\Omega_2^{\Omega\times2}+\Omega_2^\Omega\times\psi_1(\Omega_2^{\Omega\times2}+\Omega_2))</math>
* <math>0,1,2,1,2,3,0,1,2,1,1,2,2=\psi(\Omega_2^{\Omega\times2}+\Omega_2^\Omega\times\psi_1(\Omega_2^{\Omega\times2}+\Omega_2^\omega))</math>
* <math>0,1,2,1,2,3,0,1,2,1,2=\psi(\Omega_2^{\Omega\times2}+\Omega_2^\Omega\times\psi_1(\Omega_2^{\Omega\times2}+\Omega_2^\Omega))</math>
* <math>0,1,2,1,2,3,0,1,2,1,2,1,2=\psi(\Omega_2^{\Omega\times2}+\Omega_2^\Omega\times\psi_1(\Omega_2^{\Omega\times2}+\Omega_2^\Omega\times\psi_1(\Omega_2^{\Omega\times2}+\Omega_2^\Omega)))</math>
* <math>0,1,2,1,2,3,0,1,2,1,2,2=\psi(\Omega_2^{\Omega\times2}+\Omega_2^{\Omega+1})</math>
* <math>0,1,2,1,2,3,0,1,2,1,2,2=\psi(\Omega_2^{\Omega\times2}+\Omega_2^{\Omega+1})</math>
* <math>0,1,2,1,2,3,0,1,2,1,2,2,0,1,2,1,2,2=\psi(\Omega_2^{\Omega\times2}+\Omega_2^{\Omega+1}\times2)</math>
* <math>0,1,2,1,2,3,0,1,2,1,2,2,1,2,1,2,2=\psi(\Omega_2^{\Omega\times2}+\Omega_2^{\Omega+2})</math>
* <math>0,1,2,1,2,3,0,1,2,1,2,2,1,2,2=\psi(\Omega_2^{\Omega\times2}+\Omega_2^{\Omega+\omega})</math>
* <math>0,1,2,1,2,3,0,1,2,1,2,3=\psi(\Omega_2^{\Omega\times2}\times2)</math>

=== Part 14 ===
* <math>0,1,2,1,2,3,1=\psi(\Omega_2^{\Omega\times2}\times\omega)</math>
* <math>0,1,2,1,2,3,1,2=\psi(\Omega_2^{\Omega\times2}\times\Omega)</math>
* <math>0,1,2,1,2,3,1,2,0,1,2,1,2,3,1,2=\psi(\Omega_2^{\Omega\times2}\times\psi_1(\Omega_2^{\Omega\times2}))</math>
* <math>0,1,2,1,2,3,1,2,1,2=\psi(\Omega_2^{\Omega\times2}\times\psi_1(\Omega_2^{\Omega\times2}\times\Omega))</math>
* <math>0,1,2,1,2,3,1,2,1,2,2=\psi(\Omega_2^{\Omega\times2+1})</math>
* <math>0,1,2,1,2,3,1,2,1,2,3=\psi(\Omega_2^{\Omega\times3})</math>
* <math>0,1,2,1,2,3,1,2,2=\psi(\Omega_2^{\Omega\times\omega})</math>
* <math>0,1,2,1,2,3,1,2,2,1,2,2,3=\psi(\Omega_2^{\Omega\times\psi(0)})</math>
* <math>0,1,2,1,2,3,1,2,2,1,2,3=\psi(\Omega_2^{\Omega^2})</math>
* <math>0,1,2,1,2,3,1,2,2,3=\psi(\Omega_2^{\psi_1(0)})</math>
* <math>0,1,2,1,2,3,1,2,2,3,2,3=\psi(\Omega_2^{\psi_1(\Omega_2)})</math>
* <math>0,1,2,1,2,3,1,2,3=\psi(\Omega_2^{\psi_1(\Omega_2^\Omega)})</math>
* <math>0,1,2,1,2,3,1,2,3,1,2,1,2,2=\psi(\Omega_2^{\psi_1(\Omega_2^\Omega)+1})</math>
* <math>0,1,2,1,2,3,1,2,3,1,2,1,2,3=\psi(\Omega_2^{\psi_1(\Omega_2^\Omega)+\Omega})</math>
* <math>0,1,2,1,2,3,1,2,3,1,2,1,2,3,1,2,2,3=\psi(\Omega_2^{\psi_1(\Omega_2^\Omega)+\psi_1(0)})</math>
* <math>0,1,2,1,2,3,1,2,3,1,2,1,2,3,1,2,3=\psi(\Omega_2^{\psi_1(\Omega_2^\Omega)\times2})</math>
* <math>0,1,2,1,2,3,1,2,3,1,2,2=\psi(\Omega_2^{\psi_1(\Omega_2^\Omega)\times\omega})</math>
* <math>0,1,2,1,2,3,1,2,3,1,2,2,3=\psi(\Omega_2^{\psi_1(\Omega_2^\Omega+1)})</math>
* <math>0,1,2,1,2,3,1,2,3,1,2,2,3,1,2,3,1,2,3=\psi(\Omega_2^{\psi_1(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega))})</math>
* <math>0,1,2,1,2,3,1,2,3,1,2,2,3,2,3=\psi(\Omega_2^{\psi_1(\Omega_2^\Omega+\Omega_2)})</math>
* <math>0,1,2,1,2,3,1,2,3,1,2,3=\psi(\Omega_2^{\psi_1(\Omega_2^\Omega\times2)})</math>
* <math>0,1,2,1,2,3,2=\psi(\Omega_2^{\psi_1(\Omega_2^\Omega\times\omega)})</math>
* <math>0,1,2,1,2,3,2,3=\psi(\Omega_2^{\psi_1(\Omega_2^\Omega\times\Omega)})</math>
* <math>0,1,2,1,2,3,2,3,2,3,3=\psi(\Omega_2^{\psi_1(\Omega_2^{\Omega+1})})</math>
* <math>0,1,2,1,2,3,2,3,4=\psi(\Omega_2^{\psi_1(\Omega_2^{\Omega\times2})})</math>
* <math>0,1,2,1,2,3,2,3,4,2,3,4=\psi(\Omega_2^{\psi_1(\Omega_2^{\psi_1(\Omega_2^\Omega)})})</math>
* <math>0,1,2,2=\psi(\Omega_2^{\Omega_2})</math>
* <math>0,1,2,2,0,1=\psi(\Omega_2^{\Omega_2})\times\omega</math>
* <math>0,1,2,2,0,1,0,1,1,2,3,3=\psi(\Omega_2^{\Omega_2})^2</math>
* <math>0,1,2,2,0,1,0,1,1,2,3,3,0,1,1=\psi(\Omega_2^{\Omega_2})^\omega</math>
* <math>0,1,2,2,0,1,0,1,1,2,3,3,0,1,1,2=\psi(\Omega_2^{\Omega_2}+1)</math>
* <math>0,1,2,2,0,1,0,1,1,2,3,3,0,1,1,2,1,1,2=\psi(\Omega_2^{\Omega_2}+\psi(\Omega_2^{\Omega_2}+1))</math>
* <math>0,1,2,2,0,1,0,1,1,2,3,3,0,1,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\Omega)</math>
* <math>0,1,2,2,0,1,0,1,1,2,3,3,0,1,1,2,2=\psi(\Omega_2^{\Omega_2}+\Omega)</math>
* <math>0,1,2,2,0,1,0,1,1,2,3,3,0,1,1,2,2=\psi(\Omega_2^{\Omega_2}+\Omega^\omega)</math>
* <math>0,1,2,2,0,1,0,1,1,2,3,3,0,1,1,2,3,3=\psi(\Omega_2^{\Omega_2}+\Omega^{\psi(\Omega_2^{\Omega_2})})</math>
* <math>0,1,2,2,0,1,0,1,1,2,3,3,0,1,1,2,3,3,0,1,1,2=\psi(\Omega_2^{\Omega_2}+\Omega^{\psi(\Omega_2^{\Omega_2})}+1)</math>
* <math>0,1,2,2,0,1,0,1,1,2,3,3,1=\psi(\Omega_2^{\Omega_2}+\Omega^{\psi(\Omega_2^{\Omega_2})}\times\omega)</math>
* <math>0,1,2,2,0,1,0,1,1,2,3,3,1,2=\psi(\Omega_2^{\Omega_2}+\Omega^{\psi(\Omega_2^{\Omega_2})+1})</math>
* <math>0,1,2,2,0,1,0,1,2=\psi(\Omega_2^{\Omega_2}+\Omega^{\Omega})</math>
* <math>0,1,2,2,0,1,0,1,2,0,1,0,1,2=\psi(\Omega_2^{\Omega_2}+\Omega^\Omega\times2)</math>
* <math>0,1,2,2,0,1,0,1,2,0,1,1=\psi(\Omega_2^{\Omega_2}+\Omega^\Omega\times\omega)</math>
* <math>0,1,2,2,0,1,0,1,2,0,1,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(0))</math>
* <math>0,1,2,2,0,1,0,1,2,0,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega))</math>
* <math>0,1,2,2,0,1,0,1,2,0,1,2,0,1,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega)\times\omega)</math>
* <math>0,1,2,2,0,1,0,1,2,0,1,2,0,1,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega+1))</math>
* <math>0,1,2,2,0,1,0,1,2,0,1,2,0,1,1,2,0,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega+\Omega))</math>
* <math>0,1,2,2,0,1,0,1,2,0,1,2,0,1,1,2,0,1,2,0,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)))</math>
* <math>0,1,2,2,0,1,0,1,2,0,1,2,0,1,1,2,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)\times\omega))</math>
* <math>0,1,2,2,0,1,0,1,2,0,1,2,0,1,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega+\Omega_2))</math>
* <math>0,1,2,2,0,1,0,1,2,0,1,2,0,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times2))</math>
* <math>0,1,2,2,0,1,0,1,2,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\omega))</math>
* <math>0,1,2,2,0,1,0,1,2,1,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi(0)))</math>
* <math>0,1,2,2,0,1,0,1,2,1,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi(\Omega)))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\Omega))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\Omega)\times\omega)</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\Omega+1))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\Omega+\Omega_2))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\Omega+\Omega_2^\Omega))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,0,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\Omega+\Omega_2^\Omega\times2))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\Omega\times\omega))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\Omega^2))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(0)))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2)))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+1))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\Omega_2))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\Omega_2^\Omega))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,0,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\Omega_2^\Omega\times2))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\Omega_2^\Omega\times\Omega))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,0,1,2,1,2,0,1,2,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\Omega_2^\Omega\times\Omega\times\omega))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,0,1,2,1,2,0,1,2,1,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\Omega_2^\Omega\times\Omega^2))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,0,1,2,1,2,0,1,2,1,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\Omega_2^\Omega\times\psi_1(0)))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,0,1,2,1,2,0,1,2,1,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\Omega_2^\Omega\times\psi_1(\Omega_2)))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,0,1,2,1,2,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)\times2))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)\times\omega))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1,0,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)\times\omega+\Omega_2^\Omega))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)\times\Omega))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1,0,1,2,1,2,0,1,2,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)\times\Omega\times\omega))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1,0,1,2,1,2,0,1,2,1,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)\times\Omega^2))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1,0,1,2,1,2,0,1,2,1,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)\times\Omega^\omega))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1,0,1,2,1,2,0,1,2,1,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)\times\psi_1(0)))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1,0,1,2,1,2,0,1,2,1,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)\times\psi_1(\Omega_2)))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1,0,1,2,1,2,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)^2))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)^\omega))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+1)))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1,1,2,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+\Omega)))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1,1,2,0,1,2,1,2,0,1,2,1,1,2,1,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+\psi_1(0))))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1,1,2,0,1,2,1,2,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega))))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1,1,2,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)\times\omega)))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1,1,2,1,0,1,2,1,2,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)^2)))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1,1,2,1,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)^\omega)))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1,1,2,1,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega+1))))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1,1,2,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+\Omega_2^2)))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times2)))</math>

=== Part 15 ===
* <math>0,1,2,2,0,1,0,1,2,1,2,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times\omega)))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times\Omega))))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega+1}))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,2,1,2,1,2,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega+2}))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,2,1,2,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega+\omega}))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,2,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega+\omega^\omega}))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,2,3=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega+\psi(0)}))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,3=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega\times2}))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,3,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega\times2}\times\Omega))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,3,1,2,1,2,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega\times2+1}))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,3,1,2,1,2,3=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega\times3}))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,3,1,2,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega\times\omega}))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,3,1,2,2,3=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\psi_1(0)}))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,3,1,2,3=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\psi_1(\Omega_2^\Omega)}))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,3,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\psi_1(\Omega_2^\Omega\times\omega)}))</math>
* <math>0,1,2,2,0,1,0,1,2,1,2,3,2,3=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\psi_1(\Omega_2^\Omega\times\Omega)}))</math>
* <math>0,1,2,2,0,1,0,1,2,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2}))</math>
* <math>0,1,2,2,0,1,0,1,2,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2}))</math>
* <math>0,1,2,2,0,1,0,1,2,2,0,1,0,1,2,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times2)</math>
* <math>0,1,2,2,0,1,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\omega)</math>
* <math>0,1,2,2,0,1,1,0,1,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\omega^2)</math>
* <math>0,1,2,2,0,1,1,0,1,1,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\omega^\omega)</math>
* <math>0,1,2,2,0,1,1,0,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\Omega)</math>
* <math>0,1,2,2,0,1,1,0,1,2,0,1,0,1,2,2,0,1,1,0,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\omega\times2)</math>
* <math>0,1,2,2,0,1,1,0,1,2,0,1,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\Omega\times\omega)</math>
* <math>0,1,2,2,0,1,1,0,1,2,0,1,1,0,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\Omega^2)</math>
* <math>0,1,2,2,0,1,1,0,1,2,0,1,1,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\Omega^\omega)</math>
* <math>0,1,2,2,0,1,1,0,1,2,0,1,1,1,0,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\Omega^\Omega)</math>
* <math>0,1,2,2,0,1,1,0,1,2,0,1,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(0))</math>
* <math>0,1,2,2,0,1,1,0,1,2,0,1,1,2,0,1,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(1))</math>
* <math>0,1,2,2,0,1,1,0,1,2,0,1,1,2,0,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,0,1,1,2,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega\times\omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,0,1,1,2,1,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\psi_1(0)))</math>
* <math>0,1,2,2,0,1,1,0,1,2,0,1,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2))</math>
* <math>0,1,2,2,0,1,1,0,1,2,0,1,1,2,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,0,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\Omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,0,1,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\Omega+1))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,0,1,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\Omega+\Omega_2))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,0,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\Omega+\Omega_2^\Omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,0,1,2,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\Omega\times\omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,0,1,2,1,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\psi_1(0)))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,0,1,2,1,2,0,1,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+1))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,0,1,2,1,2,0,1,1,2,0,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\Omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,0,1,2,1,2,0,1,1,2,0,1,2,0,1,1,2,1,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(0)))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,0,1,2,1,2,0,1,1,2,0,1,2,0,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega)))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,0,1,2,1,2,0,1,1,2,0,1,2,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\omega)))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,0,1,2,1,2,0,1,1,2,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\Omega)))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,0,1,2,1,2,0,1,1,2,0,1,2,1,2,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega))))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,0,1,2,1,2,0,1,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\Omega_2))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,0,1,2,1,2,0,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\Omega_2^\Omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,0,1,2,1,2,0,1,2,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)+\Omega_2^\Omega\times\Omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,0,1,2,1,2,0,1,2,0,1,2,1,2,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)\times2))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)\times\omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1,0,1,2,1,2,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)^2))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+1)))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+\Omega_2)))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,0,1,2,1,2,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times2)))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times\omega)))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times\Omega)))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^{\Omega+1}))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,2,1,2,1,2,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^{\Omega+2}))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,2,1,2,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^{\Omega+\omega}))</math>

=== Part 16 ===
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\psi_1(\Omega_2^{\Omega\times2}))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})^2)</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,1,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})^2\times\omega)</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,1,1,0,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})^2\times\Omega)</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,1,1,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})^2\times\psi_1(\Omega_2^\Omega\times\Omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,1,1,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})^2\times\psi_1(\Omega_2^\Omega\times\Omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,1,1,0,1,2,1,2,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})^2\times\psi_1(\Omega_2^{\Omega+1}))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,1,1,0,1,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})^3)</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,1,1,1=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})^\omega)</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,1,2=\psi(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2}+1))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2=\psi(\Omega_2^{\Omega_2}+\Omega_2^\Omega)</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,0,1,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}+\Omega_2^\Omega\times\psi_1(\Omega_2^{\Omega_2}))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1=\psi(\Omega_2^{\Omega_2}+\Omega_2^\Omega\times\psi_1(\Omega_2^{\Omega_2})\times\omega)</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\Omega_2^\Omega\times\psi_1(\Omega_2^{\Omega_2})\times\Omega)</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2,0,1,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}+\Omega_2^\Omega\times\psi_1(\Omega_2^{\Omega_2})^2)</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2,1,1,2=\psi(\Omega_2^{\Omega_2}+\Omega_2^\Omega\times\psi_1(\Omega_2^{\Omega_2}+1))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\Omega_2^\Omega\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^\Omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\Omega_2^\Omega\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^\Omega\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^\Omega)))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2,2=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\Omega+1})</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2,3=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\Omega\times2})</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2,3,1,2,2,3=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(0)})</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2,3,1,2,3=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^\Omega)})</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2,3,2,3=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^\Omega\times\Omega)})</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2,3,2,3,4=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega\times2})})</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})})</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2,3,3,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times2)</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2,3,3,0,1,1,1,0,1,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\psi_1(\Omega_2^{\Omega_2}))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2,3,3,0,1,1,1,0,1,2,1,2,3,3,0,1,2=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^\Omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2,3,3,0,1,1,1,0,1,2,1,2,3,3,0,1,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2,3,3,0,1,1,2=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}+1))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2,3,3,0,1,1,2,0,1,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}+\psi_1(\Omega_2^{\Omega_2})))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2,3,3,0,1,1,2,0,1,2,1,2,3,3,0,1,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}+\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})})))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2,3,3,0,1,1,2,1,2=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}+\Omega_2))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2,3,3,0,1,2=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}+\Omega_2^\Omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2,3,3,0,1,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times2))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,1=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,1,2=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\Omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,1,2,1,2,2=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})+1})</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,1,2,1,2,3=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})+\Omega})</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,1,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})\times2})</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,1,2,2=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})\times\omega})</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,1,2,2,1,2,3=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})\times\Omega})</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,1,2,2,1,2,3,2,3,4,4=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})^2})</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,1,2,2,1,2,3,2,3,4,4,1,2,2,3=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2}+1)})</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,1,2,2,1,2,3,2,3,4,4,1,2,3=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2}+\Omega_2^\Omega)})</math>
* <math>0,1,2,2,0,1,1,0,1,2,1,2,3,3,1,2,2,1,2,3,2,3,4,4,1,2,3,2,3,4,4=\psi(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})})})</math>
* <math>0,1,2,2,0,1,1,0,1,2,2=\psi(\Omega_2^{\Omega_2}\times2)</math>

=== Part 17 ===
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,0,1,2=\psi(\Omega_2^{\Omega_2}\times2+\Omega^\Omega)</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,0,1,2,0,1,2=\psi(\Omega_2^{\Omega_2}\times2+\psi_1(\Omega_2^\Omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}\times2+\psi_1(\Omega_2^\Omega\times\Omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,0,1,2,1,2,2=\psi(\Omega_2^{\Omega_2}\times2+\psi_1(\Omega_2^{\Omega+1}))</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,0,1,2,1,2,3=\psi(\Omega_2^{\Omega_2}\times2+\psi_1(\Omega_2^{\Omega\times2}))</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,0,1,2,2=\psi(\Omega_2^{\Omega_2}\times2+\psi_1(\Omega_2^{\Omega_2}))</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,0,1,2,2,0,1,1=\psi(\Omega_2^{\Omega_2}\times2+\psi_1(\Omega_2^{\Omega_2})\times\omega)</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,0,1,2,2,0,1,1,0,1,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}\times2+\psi_1(\Omega_2^{\Omega_2})^2)</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,1,2=\psi(\Omega_2^{\Omega_2}\times2+\psi_1(\Omega_2^{\Omega_2}+1))</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2=\psi(\Omega_2^{\Omega_2}\times2+\psi_1(\Omega_2^{\Omega_2}+\Omega_2^\Omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,0,1,2,2,0,1,1,0,1,2,1,2,3,3,0,1,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}\times2+\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}))</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,0,1,2,2,0,1,1,0,1,2,1,2,3,3,1=\psi(\Omega_2^{\Omega_2}\times2+\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,0,1,2,2,0,1,1,0,1,2,1,2,3,3,1,2,2=\psi(\Omega_2^{\Omega_2}\times2+\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})\times\omega}))</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,0,1,2,2,0,1,1,0,1,2,2=\psi(\Omega_2^{\Omega_2}\times2+\psi_1(\Omega_2^{\Omega_2}\times2))</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,1=\psi(\Omega_2^{\Omega_2}\times2+\psi_1(\Omega_2^{\Omega_2}\times2)\times\omega)</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,1,0,1,2=\psi(\Omega_2^{\Omega_2}\times2+\psi_1(\Omega_2^{\Omega_2}\times2)\times\Omega)</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,1,0,1,2,1=\psi(\Omega_2^{\Omega_2}\times2+\psi_1(\Omega_2^{\Omega_2}\times2)\times\psi_1(\Omega_2^\Omega\times\omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,1,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}\times2+\psi_1(\Omega_2^{\Omega_2}\times2)\times\psi_1(\Omega_2^\Omega\times\Omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,1,0,1,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}\times2+\psi_1(\Omega_2^{\Omega_2}\times2)\times\psi_1(\Omega_2^{\Omega_2}))</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,1,0,1,2,1,2,3,3,1,2,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}\times2+\psi_1(\Omega_2^{\Omega_2}\times2)^2)</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,1,0,1,2,1,2,3,3,1,2,2,1,2,3,3,0,1,1,2=\psi(\Omega_2^{\Omega_2}\times2+\psi_1(\Omega_2^{\Omega_2}\times2+1))</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,1,0,1,2,1,2,3,3,1,2,2,1,2,3,3,0,1,2=\psi(\Omega_2^{\Omega_2}\times2+\Omega_2^\Omega)</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,1,0,1,2,1,2,3,3,1,2,2,1,2,3,3,0,1,2,1,2,3,3,1,2,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}\times2+\Omega_2^{\psi_1(\Omega_2^{\Omega_2}\times2)})</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,1,0,1,2,1,2,3,3,1,2,2,1,2,3,3,1=\psi(\Omega_2^{\Omega_2}\times2+\Omega_2^{\psi_1(\Omega_2^{\Omega_2}\times2)}\times\psi(\Omega_2^{\Omega_2}\times2+\Omega_2^{\psi_1(\Omega_2^{\Omega_2}\times2)}\times\omega))</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,1,0,1,2,1,2,3,3,1,2,2,1,2,3,3,1,2,1,2,2=\psi(\Omega_2^{\Omega_2}\times2+\Omega_2^{\psi_1(\Omega_2^{\Omega_2}\times2)+1})</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,1,0,1,2,1,2,3,3,1,2,2,1,2,3,3,1,2,2=\psi(\Omega_2^{\Omega_2}\times2+\Omega_2^{\psi_1(\Omega_2^{\Omega_2}\times2)\times\omega})</math>
* <math>0,1,2,2,0,1,1,0,1,2,2,0,1,1,0,1,2,2=\psi(\Omega_2^{\Omega_2}\times3)</math>
* <math>0,1,2,2,0,1,1,1=\psi(\Omega_2^{\Omega_2}\times\omega)</math>

=== Part 18 ===
* <math>0,1,2,2,0,1,1,1=\psi(\Omega_2^{\Omega_2}\times\omega)</math>
* <math>0,1,2,2,0,1,1,1,0,1,1,1=\psi(\Omega_2^{\Omega_2}\times\omega^2)</math>
* <math>0,1,2,2,0,1,1,1,0,1,2=\psi(\Omega_2^{\Omega_2}\times\Omega)</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,0,1,1,2=\psi(\Omega_2^{\Omega_2}\times\psi_1(0))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,0,1,2=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^\Omega))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^\Omega\times\omega))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^\Omega\times\Omega))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,0,1,2=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^\Omega\times\Omega+\Omega_2^\Omega))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,0,1,2,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^\Omega\times\Omega\times2))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,1,2=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times\Omega)))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,2=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega+1}))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega\times2}))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,0,1,1,2=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+1))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,0,1,2=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^\Omega)))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,0,1,2,0,1,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,0,1,2,1=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2})\times\omega))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,0,1,2,1,1,2=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\psi_1(\Omega_2^{\Omega_2}+1)))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,0,1,2,1,1,2,1,2=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,0,1,2,1,2=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^\Omega))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,0,1,2,1,2,0,1,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^\Omega\times\psi_1(\Omega_2^{\Omega_2})))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,0,1,2,1,2,1,2=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^\Omega\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^\Omega)))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,0,1,2,1,2,2=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\Omega+1}))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,0,1,2,1,2,3=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\Omega\times2}))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,0,1,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,0,1,2,1,2,3,3,0,1,1,2=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}+1))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,0,1,2,1,2,3,3,0,1,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times2))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,1=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\omega))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,1,1,2=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\psi(0)))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,1,2=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\Omega))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,1,2,0,1,2,1,2,3,3,0,1,2,1,2,3,3,1,2=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\Omega\times2))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,1,2,0,1,2,1,2,3,3,1=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\Omega\times\omega))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,1,2,0,1,2,1,2,3,3,1,2=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\psi_1(\Omega_2^\Omega)))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,1,2,1=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\psi_1(\Omega_2^\Omega\times\omega)))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,1,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\psi_1(\Omega_2^{\Omega_2})))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,1,2,1,2,3,3,0,1,2,1,2,3,3,1=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\psi_1(\Omega_2^{\Omega_2})\times\omega))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,1,2,1,2,3,3,0,1,2,1,2,3,3,1,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})})))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,1,2,1,2,3,3,1,2=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}\times\Omega)))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,1,2,2=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})+1}))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,1,2,2,1,2,3,2,3,4,4=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})\times2}))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,1,2,2,1,2,3,3=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}\times2))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,1,2,3,3,1,2,2,2=\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}\times\omega))</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,2=\psi(\Omega_2^{\Omega_2+1})</math>
* <math>0,1,2,2,0,1,1,1,0,1,2,2,0,1,1,1=\psi(\Omega_2^{\Omega_2+\omega})</math>
* <math>0,1,2,2,0,1,1,1,1=\psi(\Omega_2^{\Omega_2+\omega^2})</math>
* <math>0,1,2,2,0,1,1,1,1,1=\psi(\Omega_2^{\Omega_2\times\omega})</math>
* <math>0,1,2,2,0,1,1,1,1,1,0,1,2,2=\psi(\Omega_2^{\Omega_2^2})</math>
* <math>0,1,2,2,0,1,1,2=\psi(\psi_2(0))</math>

=== Part 19 ===
* <math>0,1,2,2,0,1,1,2=\psi(\psi_2(0))</math>
* <math>0,1,2,2,0,1,1,2,0,1,0,1,2,2=\psi(\psi_2(0)+\psi_1(\Omega_2^{\Omega_2}))</math>
* <math>0,1,2,2,0,1,1,2,0,1,0,1,2,2,0,1,1,2=\psi(\psi_2(0)\times2)</math>
* <math>0,1,2,2,0,1,1,2,0,1,1=\psi(\psi_2(0)\times\omega)</math>
* <math>0,1,2,2,0,1,1,2,0,1,1,0,1,2,2=\psi(\psi_2(0)\times\Omega_2)</math>
* <math>0,1,2,2,0,1,1,2,0,1,1,0,1,2,2,0,1,1,2=\psi(\psi_2(0)^2)</math>
* <math>0,1,2,2,0,1,1,2,0,1,1,2=\psi(\psi_2(1))</math>
* <math>0,1,2,2,0,1,1,2,0,1,2,2=\psi(\psi_2(\Omega_2))</math>
* <math>0,1,2,2,0,1,1,2,1=\psi(\psi_2(\Omega_2)\times\omega)</math>
* <math>0,1,2,2,0,1,1,2,1,1,2=\psi(\psi_2(\Omega_2+1))</math>
* <math>0,1,2,2,0,1,1,2,1,2=\psi(\Omega_3)</math>
* <math>0,1,2,2,0,1,2=\psi(\Omega_3^\Omega)</math>
* <math>0,1,2,2,0,1,2,0,1,0,1,2,2,0,1,2=\psi(\Omega_3^\Omega+\psi_1(\Omega_3^\Omega))</math>
* <math>0,1,2,2,0,1,2,0,1,1=\psi(\Omega_3^\Omega+\psi_1(\Omega_3^\Omega)\times\omega)</math>
* <math>0,1,2,2,0,1,2,0,1,1,0,1,2,1,2,3,3,0,1,1,2=\psi(\Omega_3^\Omega+\psi_1(\Omega_3^\Omega+1))</math>
* <math>0,1,2,2,0,1,2,0,1,1,0,1,2,1,2,3,3,0,1,1,2,1,2=\psi(\Omega_3^\Omega+\Omega_2)</math>
* <math>0,1,2,2,0,1,2,0,1,1,0,1,2,2=\psi(\Omega_3^\Omega+\Omega_2^{\Omega_2})</math>
* <math>0,1,2,2,0,1,2,0,1,1,0,1,2,2,0,1,1,2=\psi(\Omega_3^\Omega+\psi_2(0))</math>
* <math>0,1,2,2,0,1,2,0,1,1,0,1,2,2,0,1,2=\psi(\Omega_3^\Omega+\psi_2(\Omega_3^\Omega))</math>
* <math>0,1,2,2,0,1,2,0,1,1,1=\psi(\Omega_3^\Omega+\psi_2(\Omega_3^\Omega)\times\omega)</math>
* <math>0,1,2,2,0,1,2,0,1,1,2=\psi(\Omega_3^\Omega+\psi_2(\Omega_3^\Omega+1))</math>
* <math>0,1,2,2,0,1,2,0,1,1,2,1,2=\psi(\Omega_3^\Omega+\Omega_3)</math>
* <math>0,1,2,2,0,1,2,0,1,2=\psi(\Omega_3^\Omega\times2)</math>
* <math>0,1,2,2,0,1,2,0,1,2,1=\psi(\Omega_3^\Omega\times\omega)</math>
* <math>0,1,2,2,0,1,2,0,1,2,1,2=\psi(\Omega_3^\Omega\times\Omega)</math>
* <math>0,1,2,2,0,1,2,0,1,2,1,2,1,2=\psi(\Omega_3^\Omega\times\psi_1(\Omega_2^\Omega\times\Omega))</math>
* <math>0,1,2,2,0,1,2,0,1,2,1,2,2=\psi(\Omega_3^\Omega\times\psi_1(\Omega_2^{\Omega+1}))</math>
* <math>0,1,2,2,0,1,2,0,1,2,1,2,3,3=\psi(\Omega_3^\Omega\times\psi_1(\Omega_2^{\Omega_2}))</math>
* <math>0,1,2,2,0,1,2,0,1,2,1,2,3,3,1,2,3=\psi(\Omega_3^\Omega\times\psi_1(\Omega_3^{\Omega_\Omega}))</math>
* <math>0,1,2,2,0,1,2,0,1,2,2=\psi(\Omega_3^\Omega\times\Omega_2)</math>
* <math>0,1,2,2,0,1,2,1=\psi(\Omega_3^\Omega\times\Omega_2\times\omega)</math>
* <math>0,1,2,2,0,1,2,1,1,2=\psi(\Omega_3^\Omega\times\psi_2(0))</math>
* <math>0,1,2,2,0,1,2,1,1,2,0,1,2,2=\psi(\Omega_3^\Omega\times\psi_2(\Omega_2))</math>
* <math>0,1,2,2,0,1,2,1,1,2,1=\psi(\Omega_3^\Omega\times\psi_2(\Omega_2\times\omega))</math>
* <math>0,1,2,2,0,1,2,1,1,2,1,2=\psi(\Omega_3^\Omega\times\psi_2(\Omega_3))</math>
* <math>0,1,2,2,0,1,2,1,2=\psi(\Omega_3^\Omega\times\psi_2(\Omega_3^\Omega))</math>
* <math>0,1,2,2,0,1,2,1,2,0,1,2,1,2=\psi(\Omega_3^\Omega\times\psi_2(\Omega_3^\Omega\times2))</math>
* <math>0,1,2,2,0,1,2,1,2,2=\psi(\Omega_3^{\Omega+1})</math>
* <math>0,1,2,2,0,1,2,1,2,3,1,2,2,3=\psi(\Omega_3^{\psi_2(0)})</math>
* <math>0,1,2,2,0,1,2,1,2,3,3=\psi(\Omega_3^{\psi_2(\Omega_2^{\Omega_2})})</math>
* <math>0,1,2,2,0,1,2,2=\psi(\Omega_3^{\Omega_2})</math>
* <math>0,1,2,2,0,1,2,2=\psi(\Omega_3^{\Omega_2})</math>
* <math>0,1,2,2,1=\psi(\Omega_3^{\Omega_2}\times\omega)</math>
* <math>0,1,2,2,1,2=\psi(\Omega_3^{\Omega_2}\times\Omega)</math>
* <math>0,1,2,2,1,2,0,1,2,2,1,1,2=\psi(\Omega_3^{\Omega_2}\times\psi_1(0))</math>
* <math>0,1,2,2,1,2,0,1,2,2,1,2=\psi(\Omega_3^{\Omega_2}\times\psi_1(\Omega_2^\Omega))</math>
* <math>0,1,2,2,1,2,1,2,2=\psi(\Omega_3^{\Omega_2}\times\psi_1(\Omega_2^{\Omega+1}))</math>
* <math>0,1,2,2,1,2,1,2,3,3=\psi(\Omega_3^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}))</math>
* <math>0,1,2,2,1,2,1,2,3,3,1,2,3=\psi(\Omega_3^{\Omega_2}\times\psi_1(\Omega_3^{\Omega}))</math>
* <math>0,1,2,2,1,2,1,2,3,3,1,2,3,3=\psi(\Omega_3^{\Omega_2}\times\psi_1(\Omega_3^{\Omega_2}))</math>
* <math>0,1,2,2,1,2,1,2,3,3,2=\psi(\Omega_3^{\Omega_2}\times\psi_1(\Omega_3^{\Omega_2}\times\omega))</math>
* <math>0,1,2,2,1,2,2=\psi(\Omega_3^{\Omega_2}\times\Omega_2)</math>
* <math>0,1,2,2,1,2,2,0,1,2,2=\psi(\Omega_3^{\Omega_2}\times\Omega_2+\Omega_3^{\Omega_2})</math>
* <math>0,1,2,2,1,2,2,0,1,2,2,0,1,2,2,1,2,2=\psi(\Omega_3^{\Omega_2}\times\Omega_2\times2)</math>
* <math>0,1,2,2,1,2,2,0,1,2,2,1=\psi(\Omega_3^{\Omega_2}\times\Omega_2\times\omega)</math>
* <math>0,1,2,2,1,2,2,0,1,2,2,1,1,2=\psi(\Omega_3^{\Omega_2}\times\psi_2(0))</math>
* <math>0,1,2,2,1,2,2,0,1,2,2,1,2=\psi(\Omega_3^{\Omega_2}\times\psi_2(\Omega_3^\Omega))</math>
* <math>0,1,2,2,1,2,2,0,1,2,2,1,2,2=\psi(\Omega_3^{\Omega_2}\times\psi_2(\Omega_3^{\Omega_2}))</math>
* <math>0,1,2,2,1,2,2,1=\psi(\Omega_3^{\Omega_2}\times\psi_2(\Omega_3^{\Omega_2}\times\Omega))</math>
* <math>0,1,2,2,1,2,2,1,2,2=\psi(\Omega_3^{\Omega_2}\times\psi_2(\Omega_3^{\Omega_2}\times\Omega_2))</math>
* <math>0,1,2,2,1,2,2,2=\psi(\Omega_3^{\Omega_2+1})</math>
* <math>0,1,2,2,2=\psi(\Omega_3^{\Omega_3})</math>
* <math>0,1,2,2,3=\psi(\Omega_\omega)=\mathrm{BO}</math>

=== Part 20 ===
* <math>0,1,2,2,3,0,1,0,1,2=\psi(\Omega_\omega+\Omega^\Omega)</math>
* <math>0,1,2,2,3,0,1,0,1,2,0,1,1,2=\psi(\Omega_\omega+\psi_1(0))</math>
* <math>0,1,2,2,3,0,1,0,1,2,2=\psi(\Omega_\omega+\psi_1(\Omega_2^{\Omega_2}))</math>
* <math>0,1,2,2,3,0,1,0,1,2,2,3=\psi(\Omega_\omega+\psi_1(\Omega_\omega))</math>
* <math>0,1,2,2,3,0,1,1=\psi(\Omega_\omega+\psi_1(\Omega_\omega)\times\omega)</math>
* <math>0,1,2,2,3,0,1,1,0,1,2=\psi(\Omega_\omega+\psi_1(\Omega_\omega)\times\Omega)</math>
* <math>0,1,2,2,3,0,1,1,0,1,2,0,1,1,2=\psi(\Omega_\omega+\psi_1(\Omega_\omega)\times\psi_1(0))</math>
* <math>0,1,2,2,3,0,1,1,0,1,2,0,1,2=\psi(\Omega_\omega+\psi_1(\Omega_\omega)\times\psi_1(\Omega_2^\Omega))</math>
* <math>0,1,2,2,3,0,1,1,0,1,2,1,2=\psi(\Omega_\omega+\psi_1(\Omega_\omega)\times\psi_1(\Omega_2^\Omega\times\Omega))</math>
* <math>0,1,2,2,3,0,1,1,0,1,2,1,2,2=\psi(\Omega_\omega+\psi_1(\Omega_\omega)\times\psi_1(\Omega_2^{\Omega+1}))</math>
* <math>0,1,2,2,3,0,1,1,0,1,2,1,2,3,3,4=\psi(\Omega_\omega+\psi_1(\Omega_\omega)^2)</math>
* <math>0,1,2,2,3,0,1,1,0,1,2,1,2,3,3,4,0,1,1,2=\psi(\Omega_\omega+\psi_1(\Omega_\omega+1))</math>
* <math>0,1,2,2,3,0,1,1,0,1,2,1,2,3,3,4,0,1,1,2,1,2=\psi(\Omega_\omega+\Omega_2)</math>
* <math>0,1,2,2,3,0,1,1,0,1,2,1,2,3,3,4,0,1,2=\psi(\Omega_\omega+\Omega_2^\Omega)</math>
* <math>0,1,2,2,3,0,1,1,0,1,2,1,2,3,3,4,0,1,2,0,1,2=\psi(\Omega_\omega+\Omega_2^\Omega\times2)</math>
* <math>0,1,2,2,3,0,1,1,0,1,2,1,2,3,3,4,0,1,2,0,1,2,1,2,3,3,4=\psi(\Omega_\omega+\Omega_2^\Omega\times\psi(\Omega_\omega))</math>
* <math>0,1,2,2,3,0,1,1,0,1,2,1,2,3,3,4,0,1,2,1=\psi(\Omega_\omega+\Omega_2^\Omega\times\psi(\Omega_\omega)\times\omega)</math>
* <math>0,1,2,2,3,0,1,1,0,1,2,1,2,3,3,4,0,1,2,1,1,2=\psi(\Omega_\omega+\Omega_2^\Omega\times\psi(\Omega_\omega+1))</math>
* <math>0,1,2,2,3,0,1,1,0,1,2,1,2,3,3,4,0,1,2,1,2=\psi(\Omega_\omega+\Omega_2^\Omega\times\psi(\Omega_\omega+\Omega_2^\Omega))</math>
* <math>0,1,2,2,3,0,1,1,0,1,2,1,2,3,3,4,0,1,2,1,2,0,1,2,1,2,3,3,4=\psi(\Omega_\omega+\Omega_2^\Omega\times\psi(\Omega_\omega+\Omega_2^\Omega\times\psi_1(\Omega_\omega)))</math>
* <math>0,1,2,2,3,0,1,1,0,1,2,1,2,3,3,4,0,1,2,1,2,2=\psi(\Omega_\omega+\Omega_2^{\Omega+1})</math>
* <math>0,1,2,2,3,0,1,1,0,1,2,1,2,3,3,4,0,1,2,1,2,3,1,2,2,3=\psi(\Omega_\omega+\Omega_2^{\psi_1(0)})</math>
* <math>0,1,2,2,3,0,1,1,0,1,2,1,2,3,3,4,0,1,2,1,2,3,3,4=\psi(\Omega_\omega+\Omega_2^{\psi_1(\Omega_\omega)})</math>
* <math>0,1,2,2,3,0,1,1,0,1,2,1,2,3,3,4,1=\psi(\Omega_\omega+\Omega_2^{\psi_1(\Omega_\omega)}\times\omega)</math>
* <math>0,1,2,2,3,0,1,1,0,1,2,2=\psi(\Omega_\omega+\Omega_2^{\Omega_2})</math>
* <math>0,1,2,2,3,0,1,1,0,1,2,2,0,1,1,2=\psi(\Omega_\omega+\psi_2(0))</math>
* <math>0,1,2,2,3,0,1,1,0,1,2,2,0,1,1,2,1,2=\psi(\Omega_\omega+\psi_2(\Omega_2))</math>
* <math>0,1,2,2,3,0,1,1,0,1,2,2,3=\psi(\Omega_\omega+\psi_2(\Omega_\omega))</math>
* <math>0,1,2,2,3,0,1,1,1=\psi(\Omega_\omega+\psi_2(\Omega_\omega)\times\omega)</math>
* <math>0,1,2,2,3,0,1,1,2=\psi(\Omega_\omega\times2)</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,0,1,2,2,3=\psi(\Omega_\omega\times2+\psi_1(\Omega_\omega))</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,0,1,2,2,3,0,1,1,2=\psi(\Omega_\omega\times2+\psi_1(\Omega_\omega\times2))</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,1=\psi(\Omega_\omega\times2+\psi_1(\Omega_\omega\times2)\times\omega)</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,1,0,1,2,2=\psi(\Omega_\omega\times2+\psi_1(\Omega_\omega\times2)\times\Omega_2)</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,1,0,1,2,2,3=\psi(\Omega_\omega\times2+\psi_2(\Omega_\omega))</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,1,0,1,2,2,3,0,1,1,2=\psi(\Omega_\omega\times2+\psi_2(\Omega_\omega\times2))</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,1,0,1,2,2,3,0,1,1,2,0,1,1=\psi(\Omega_\omega\times2+\psi_2(\Omega_\omega\times2)+\psi_1(\Omega_\omega\times2+\psi_2(\Omega_\omega\times2))\times\omega)</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,1,0,1,2,2,3,0,1,1,2=\psi(\Omega_\omega\times2+\psi_2(\Omega_\omega\times2))</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,1,2=\psi(\Omega_\omega\times3)</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,2=\psi(\Omega_\omega\times\Omega)</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,2,0,1,0,1,2,2,3,0,1,1,0,1,2=\psi(\Omega_\omega\times\Omega+\psi_1(\Omega_\omega)\times\Omega)</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,2,0,1,0,1,2,2,3,0,1,1,0,1,2,1,2,3,3,4=\psi(\Omega_\omega\times\Omega+\psi_1(\Omega_\omega)^2)</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,2,0,1,0,1,2,2,3,0,1,1,0,1,2,1,2,3,3,4,0,1,1,2,1,2=\psi(\Omega_\omega\times\Omega+\psi_1(\Omega_\omega+\Omega_2))</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,2,0,1,0,1,2,2,3,0,1,1,0,1,2,2,3=\psi(\Omega_\omega\times\Omega+\psi_1(\Omega_\omega+\psi_2(\Omega_\omega)))</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,2,0,1,0,1,2,2,3,0,1,1,2=\psi(\Omega_\omega\times\Omega+\psi_1(\Omega_\omega\times2))</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,2,0,1,0,1,2,2,3,0,1,1,2,0,1,2=\psi(\Omega_\omega\times\Omega+\psi_1(\Omega_\omega\times\Omega))</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,2,0,1,1=\psi(\Omega_\omega\times\Omega+\psi_1(\Omega_\omega\times\Omega)\times\omega)</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,2,0,1,1,0,1,2,2=\psi(\Omega_\omega\times\Omega+\Omega_2)</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,2,0,1,1,0,1,2,2,3=\psi(\Omega_\omega\times\Omega+\psi_2(\Omega_\omega))</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,2,0,1,1,2=\psi(\Omega_\omega\times\Omega+\Omega_\omega)</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,2,0,1,1,2,1=\psi(\Omega_\omega\times\Omega\times\omega)</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,2,0,1,1,2,1,0,1,2=\psi(\Omega_\omega\times\Omega^2)</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,2,0,1,1,2,1,1,2=\psi(\Omega_\omega\times\psi_1(0))</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,2,0,1,2=\psi(\Omega_\omega\times\psi_1(\Omega_2^\Omega))</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,2,1=\psi(\Omega_\omega\times\psi_1(\Omega_2^\Omega\times\omega))</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,2,1,2,3,3,4=\psi(\Omega_\omega\times\psi_1(\Omega_\omega))</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,2,2=\psi(\Omega_\omega\times\Omega_2)</math>
* <math>0,1,2,2,3,0,1,1,2,0,1,2,2,3=\psi(\Omega_\omega^2)</math>
* <math>0,1,2,2,3,0,1,1,2,1=\psi(\Omega_\omega^2\times\omega)</math>
* <math>0,1,2,2,3,0,1,1,2,1,0,1,2,2,3=\psi(\Omega_\omega^3)</math>
* <math>0,1,2,2,3,0,1,1,2,1,1,2=\psi(\psi_\omega(0))</math>
* <math>0,1,2,2,3,0,1,1,2,1,1,2,0,1,1,2,0,1,2,2,3,0,1,1,2,1,1,2=\psi(\psi_\omega(0)\times2)</math>
* <math>0,1,2,2,3,0,1,1,2,1,1,2,0,1,1,2,1,1,2=\psi(\psi_\omega(1))</math>
* <math>0,1,2,2,3,0,1,1,2,1,2=\psi(\Omega_{\omega+1})</math>
* <math>0,1,2,2,3,0,1,1,2,2=\psi(\Omega_{\omega+1}^\omega)</math>
* <math>0,1,2,2,3,0,1,2=\psi(\Omega_{\omega+1}^\Omega)</math>
* <math>0,1,2,2,3,0,1,2,0,1,0,1,2,2,3,0,1,2=\psi(\Omega_{\omega+1}^\Omega+\psi_1(\Omega_{\omega+1}^\Omega))</math>
* <math>0,1,2,2,3,0,1,2,0,1,1=\psi(\Omega_{\omega+1}^\Omega+\psi_1(\Omega_{\omega+1}^\Omega)\times\omega)</math>
* <math>0,1,2,2,3,0,1,2,0,1,1,2=\psi(\Omega_{\omega+1}^\Omega+\Omega_\omega)</math>
* <math>0,1,2,2,3,0,1,2,0,1,1,2,0,1,2,2,3,0,1,2=\psi(\Omega_{\omega+1}^\Omega\times2)</math>
* <math>0,1,2,2,3,0,1,2,0,1,1,2,1=\psi(\Omega_{\omega+1}^\Omega\times\omega)</math>
* <math>0,1,2,2,3,0,1,2,0,1,1,2,1,0,1,2,2,3=\psi(\Omega_{\omega+1}^{\Omega}\times\Omega_\omega)</math>
* <math>0,1,2,2,3,0,1,2,0,1,1,2,1,0,1,2,2,3,0,1,1,2,1,1,2=\psi(\Omega_{\omega+1}^{\Omega}\times\psi_\omega(0))</math>
* <math>0,1,2,2,3,0,1,2,0,1,1,2,1,0,1,2,2,3,0,1,2=\psi(\Omega_{\omega+1}^{\Omega}\times\psi_\omega(\Omega_{\omega+1}^\Omega))</math>
* <math>0,1,2,2,3,0,1,2,0,1,1,2,1,1=\psi(\Omega_{\omega+1}^{\Omega}\times\psi_\omega(\Omega_{\omega+1}^\Omega)^\omega)</math>
* <math>0,1,2,2,3,0,1,2,0,1,1,2,1,2=\psi(\Omega_{\omega+1}^{\Omega}\times\psi_\omega(\Omega_{\omega+1}^\Omega+\Omega_{\omega+1}))</math>
* <math>0,1,2,2,3,0,1,2,0,1,2=\psi(\Omega_{\omega+1}^{\Omega}\times\psi_\omega(\Omega_{\omega+1}^\Omega\times2))</math>
* <math>0,1,2,2,3,0,1,2,0,1,2,2,3=\psi(\Omega_{\omega+1}^{\Omega}\times\psi_\omega(\Omega_{\omega+1}^\Omega\times\Omega_\omega))</math>
* <math>0,1,2,2,3,0,1,2,1=\psi(\Omega_{\omega+1}^{\Omega}\times\psi_\omega(\Omega_{\omega+1}^\Omega\times\Omega_\omega\times\omega))</math>
* <math>0,1,2,2,3,0,1,2,1,1,2=\psi(\Omega_{\omega+1}^{\Omega}\times\psi_\omega(\Omega_{\omega+1}^\Omega\times\psi_\omega(0)))</math>
* <math>0,1,2,2,3,0,1,2,1,1,2,1,2=\psi(\Omega_{\omega+1}^{\Omega}\times\psi_\omega(\Omega_{\omega+1}^\Omega\times\psi_\omega(\Omega_{\omega+1})))</math>
* <math>0,1,2,2,3,0,1,2,1,2=\psi(\Omega_{\omega+1}^{\Omega}\times\psi_\omega(\Omega_{\omega+1}^\Omega\times\psi_\omega(\Omega_{\omega+1}^\Omega)))</math>
* <math>0,1,2,2,3,0,1,2,1,2,2=\psi(\Omega_{\omega+1}^{\Omega+1})</math>
* <math>0,1,2,2,3,0,1,2,1,2,3,1,2,2,3=\psi(\Omega_{\omega+1}^{\psi_1(0)})</math>
* <math>0,1,2,2,3,0,1,2,1,2,3,3,4=\psi(\Omega_{\omega+1}^{\psi_1(\Omega_\omega)})</math>
* <math>0,1,2,2,3,0,1,2,2=\psi(\Omega_{\omega+1}^{\Omega_2})</math>
* <math>0,1,2,2,3,0,1,2,2,3=\psi(\Omega_{\omega+1}^{\Omega_\omega})</math>
* <math>0,1,2,2,3,1=\psi(\Omega_{\omega+1}^{\Omega_\omega}\times\omega)</math>
* <math>0,1,2,2,3,1,2=\psi(\Omega_{\omega+1}^{\Omega_\omega}\times\Omega)</math>
* <math>0,1,2,2,3,1,2,2=\psi(\Omega_{\omega+1}^{\Omega_\omega}\times\Omega_2)</math>
* <math>0,1,2,2,3,1,2,2,3=\psi(\Omega_{\omega+1}^{\Omega_\omega}\times\Omega_\omega)</math>
* <math>0,1,2,2,3,1,2,2,3,2=\psi(\Omega_{\omega+1}^{\Omega_\omega+1})</math>
* <math>0,1,2,2,3,1,2,3=\psi(\Omega_{\omega+1}^{\Omega_\omega+\Omega})</math>
* <math>0,1,2,2,3,1,2,3,1,2,3=\psi(\Omega_{\omega+1}^{\Omega_\omega+\psi_1(\Omega_2^\Omega)})</math>
* <math>0,1,2,2,3,1,2,3,2,3=\psi(\Omega_{\omega+1}^{\Omega_\omega+\psi_1(\Omega_2^\Omega\times\Omega)})</math>
* <math>0,1,2,2,3,1,2,3,2,3,4,4,5=\psi(\Omega_{\omega+1}^{\Omega_\omega+\psi_1(\Omega_\omega)})</math>
* <math>0,1,2,2,3,1,2,3,3=\psi(\Omega_{\omega+1}^{\Omega_\omega+\Omega_2})</math>
* <math>0,1,2,2,3,1,2,3,3,4=\psi(\Omega_{\omega+1}^{\Omega_\omega\times2})</math>
* <math>0,1,2,2,3,2=\psi(\Omega_{\omega+1}^{\Omega_{\omega+1}})</math>
* <math>0,1,2,2,3,2,2=\psi(\Omega_{\omega+2}^{\Omega_{\omega+2}})</math>
* <math>0,1,2,2,3,2,2,3=\psi(\Omega_{\omega\times2})</math>
* <math>0,1,2,2,3,2,3=\psi(\Omega_{\omega^2})</math>
* <math>0,1,2,2,3,4=\psi(\Omega_{\psi(\Omega^\Omega)})</math>
* <math>0,1,2,2,3,4,4,5=\psi(\Omega_{\psi(\Omega_\omega)})</math>
* <math>0,1,2,3=\psi(\Omega_{\Omega})</math>

=== Part 21 ===
* <math>0,1,2,3,0,1,0,1,2,3=\psi(\Omega_\Omega+\psi_1(\Omega_\Omega))</math>
* <math>0,1,2,3,0,1,1=\psi(\Omega_\Omega+\psi_1(\Omega_\Omega)\times\omega)</math>
* <math>0,1,2,3,0,1,1,0,1,2,3=\psi(\Omega_\Omega+\psi_2(\Omega_\Omega))</math>
* <math>0,1,2,3,0,1,1,2=\psi(\Omega_\Omega+\Omega_\omega)</math>
* <math>0,1,2,3,0,1,1,2,1,1,2=\psi(\Omega_\Omega+\Omega_{\omega\times2})</math>
* <math>0,1,2,3,0,1,2=\psi(\Omega_\Omega\times2)</math>
* <math>0,1,2,3,0,1,2,0,1,1=\psi(\Omega_\Omega\times2+\psi_1(\Omega_\Omega\times2)\times\omega)</math>
* <math>0,1,2,3,0,1,2,0,1,2=\psi(\Omega_\Omega\times3)</math>
* <math>0,1,2,3,0,1,2,0,1,2,1,2=\psi(\Omega_\Omega\times\Omega)</math>
* <math>0,1,2,3,0,1,2,0,1,2,2=\psi(\Omega_\Omega\times\Omega_2)</math>
* <math>0,1,2,3,0,1,2,0,1,2,3=\psi(\Omega_\Omega^2)</math>
* <math>0,1,2,3,0,1,2,0,1,2,3,0,1,2=\psi(\Omega_\Omega^2+\Omega_\Omega)</math>
* <math>0,1,2,3,0,1,2,1=\psi(\Omega_\Omega^2\times\omega)</math>
* <math>0,1,2,3,0,1,2,1,0,1,2,0,1,2,3=\psi(\Omega_\Omega^2\times\omega+\Omega_\Omega^2)</math>
* <math>0,1,2,3,0,1,2,1,0,1,2,0,1,2,3,0,1,2,1=\psi(\Omega_\Omega^2\times\omega\times2)</math>
* <math>0,1,2,3,0,1,2,1,0,1,2,1=\psi(\Omega_\Omega^2\times\omega^2)</math>
* <math>0,1,2,3,0,1,2,1,0,1,2,3=\psi(\Omega_\Omega^3)</math>
* <math>0,1,2,3,0,1,2,1,0,1,2,3,0,1,2,1=\psi(\Omega_\Omega^3\times\omega)</math>
* <math>0,1,2,3,0,1,2,1,1=\psi(\Omega_\Omega^\omega)</math>
* <math>0,1,2,3,0,1,2,1,1,0,1,2,1=\psi(\Omega_\Omega^\omega\times\omega)</math>
* <math>0,1,2,3,0,1,2,1,1,0,1,2,1,1=\psi(\Omega_\Omega^{\omega\times2})</math>
* <math>0,1,2,3,0,1,2,1,1,0,1,2,3=\psi(\Omega_\Omega^{\Omega_\Omega})</math>
* <math>0,1,2,3,0,1,2,1,1,2=\psi(\psi_{\Omega_{\Omega+1}}(0))</math>
* <math>0,1,2,3,0,1,2,1,2=\psi(\Omega_{\Omega+1}^{\Omega})</math>
* <math>0,1,2,3,0,1,2,1,2,0,1,2=\psi(\Omega_{\Omega+1}^{\Omega}+\Omega_\Omega)</math>
* <math>0,1,2,3,0,1,2,1,2,0,1,2,1=\psi(\Omega_{\Omega+1}^{\Omega}+\psi_{\Omega_{\Omega+1}}(\Omega_{\Omega+1}^{\Omega})\times\omega)</math>
* <math>0,1,2,3,0,1,2,1,2,0,1,2,1,1,2=\psi(\Omega_{\Omega+1}^{\Omega}+\psi_{\Omega_{\Omega+1}}(\Omega_{\Omega+1}^{\Omega}+1))</math>
* <math>0,1,2,3,0,1,2,1,2,0,1,2,1,1,2,1,2=\psi(\Omega_{\Omega+1}^{\Omega}+\Omega_{\Omega+1})</math>
* <math>0,1,2,3,0,1,2,1,2,0,1,2,1,2=\psi(\Omega_{\Omega+1}^{\Omega}\times2)</math>
* <math>0,1,2,3,0,1,2,1,2,0,1,2,3=\psi(\Omega_{\Omega+1}^{\Omega}\times\Omega_\Omega)</math>
* <math>0,1,2,3,0,1,2,1,2,1=\psi(\Omega_{\Omega+1}^{\Omega}\times\Omega_\Omega\times\omega)</math>
* <math>0,1,2,3,0,1,2,1,2,1,1,2=\psi(\Omega_{\Omega+1}^{\Omega}\times\psi_{\Omega_{\Omega+1}}(0))</math>
* <math>0,1,2,3,0,1,2,1,2,1,2=\psi(\Omega_{\Omega+1}^{\Omega}\times\psi_{\Omega_{\Omega+1}}(\Omega_{\Omega+1}^{\Omega}))</math>
* <math>0,1,2,3,0,1,2,1,2,1,2,0,1,2,1,2,1=\psi(\Omega_{\Omega+1}^{\Omega}\times\psi_{\Omega_{\Omega+1}}(\Omega_{\Omega+1}^{\Omega})\times\omega)</math>
* <math>0,1,2,3,0,1,2,1,2,1,2,0,1,2,1,2,1,1,2=\psi(\Omega_{\Omega+1}^{\Omega}\times\psi_{\Omega_{\Omega+1}}(\Omega_{\Omega+1}^{\Omega}+1))</math>
* <math>0,1,2,3,0,1,2,1,2,1,2,0,1,2,1,2,1,1,2,1,2=\psi(\Omega_{\Omega+1}^{\Omega}\times\psi_{\Omega_{\Omega+1}}(\Omega_{\Omega+1}^{\Omega}+\Omega_{\Omega+1}))</math>
* <math>0,1,2,3,0,1,2,1,2,1,2,0,1,2,1,2,1,2=\psi(\Omega_{\Omega+1}^{\Omega}\times\psi_{\Omega_{\Omega+1}}(\Omega_{\Omega+1}^{\Omega}\times2))</math>
* <math>0,1,2,3,0,1,2,1,2,1,2,0,1,2,3=\psi(\Omega_{\Omega+1}^{\Omega}\times\psi_{\Omega_{\Omega+1}}(\Omega_{\Omega+1}^{\Omega}\times\Omega_\Omega))</math>
* <math>0,1,2,3,0,1,2,1,2,2=\psi(\Omega_{\Omega+1}^{\Omega+1})</math>
* <math>0,1,2,3,0,1,2,1,2,3=\psi(\Omega_{\Omega+1}^{\Omega\times2})</math>
* <math>0,1,2,3,0,1,2,2=\psi(\Omega_{\Omega+1}^{\Omega_2})</math>
* <math>0,1,2,3,0,1,2,2,3=\psi(\Omega_{\Omega+1}^{\Omega_\omega})</math>
* <math>0,1,2,3,0,1,2,3=\psi(\Omega_{\Omega+1}^{\Omega_\Omega})</math>
* <math>0,1,2,3,0,1,2,3,0,1,0,1,2,3,0,1,2,3=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}+\psi_1(\Omega_{\Omega+1}^{\Omega_\Omega}))</math>
* <math>0,1,2,3,0,1,2,3,0,1,2=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}+\Omega_{\Omega})</math>
* <math>0,1,2,3,0,1,2,3,0,1,2,3=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times2)</math>
* <math>0,1,2,3,1=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\omega)</math>
* <math>0,1,2,3,1,2=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\Omega)</math>
* <math>0,1,2,3,1,2,0,1,2,3=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\Omega+\Omega_{\Omega+1}^{\Omega_\Omega})</math>
* <math>0,1,2,3,1,2,0,1,2,3,1,1,2,0,1,2,3,1,2=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\psi_1(\Omega))</math>
* <math>0,1,2,3,1,2,0,1,2,3,1,2=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\psi_1(\Omega_2^\Omega))</math>
* <math>0,1,2,3,1,2,1,2=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\psi_1(\Omega_2^\Omega\times\Omega))</math>
* <math>0,1,2,3,1,2,1,2,2=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\psi_1(\Omega_2^{\Omega+1}))</math>
* <math>0,1,2,3,1,2,1,2,3,3,4=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\psi_1(\Omega_\omega))</math>
* <math>0,1,2,3,1,2,1,2,3,4=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\psi_1(\Omega_\Omega))</math>
* <math>0,1,2,3,1,2,1,2,3,4,1,2,3=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\psi_1(\Omega_\Omega\times2))</math>
* <math>0,1,2,3,1,2,1,2,3,4,1,2,3,4=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\psi_1(\Omega_{\Omega+1}^{\Omega_\Omega}))</math>

=== Part 22 ===
* <math>0,1,2,3,1,2,2=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\Omega_2)</math>
* <math>0,1,2,3,1,2,2,1,2,2=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\psi_2(\Omega_{3}^{\Omega_2}\times\Omega_2))</math>
* <math>0,1,2,3,1,2,2,1,2,2,2=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\psi_2(\Omega_{3}^{\Omega_2+1}))</math>
* <math>0,1,2,3,1,2,2,1,2,3,4=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\psi_2(\Omega_{\Omega}))</math>
* <math>0,1,2,3,1,2,2,1,2,3,4,1,2,3,4=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\psi_2(\Omega_{\Omega+1}^{\Omega_\Omega}))</math>
* <math>0,1,2,3,1,2,2,2=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\Omega_3)</math>
* <math>0,1,2,3,1,2,2,3=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\Omega_\omega)</math>
* <math>0,1,2,3,1,2,3=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\Omega_\Omega)</math>
* <math>0,1,2,3,1,2,3,0,1,2=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\Omega_\Omega+\Omega_\Omega)</math>
* <math>0,1,2,3,1,2,3,0,1,2,3=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\Omega_\Omega+\Omega_{\Omega+1}^{\Omega_\Omega})</math>
* <math>0,1,2,3,1,2,3,0,1,2,3,0,1,2,3,1,2,3=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\Omega_\Omega\times2)</math>
* <math>0,1,2,3,1,2,3,0,1,2,3,1,1,2=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\psi_{\Omega_{\Omega+1}}(0))</math>
* <math>0,1,2,3,1,2,3,0,1,2,3,1,2=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\psi_{\Omega_{\Omega+1}}(\Omega_{\Omega+1}^\Omega))</math>
* <math>0,1,2,3,1,2,3,0,1,2,3,1,2,2=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\psi_{\Omega_{\Omega+1}}(\Omega_{\Omega+1}^{\Omega_2}))</math>
* <math>0,1,2,3,1,2,3,0,1,2,3,1,2,2,3=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\psi_{\Omega_{\Omega+1}}(\Omega_{\Omega+1}^{\Omega_\omega}))</math>
* <math>0,1,2,3,1,2,3,0,1,2,3,1,2,3=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\psi_{\Omega_{\Omega+1}}(\Omega_{\Omega+1}^{\Omega_\Omega}))</math>
* <math>0,1,2,3,1,2,3,1=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\psi_{\Omega_{\Omega+1}}(\Omega_{\Omega+1}^{\Omega_\Omega}\times\omega))</math>
* <math>0,1,2,3,1,2,3,1,2=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\psi_{\Omega_{\Omega+1}}(\Omega_{\Omega+1}^{\Omega_\Omega}\times\Omega))</math>
* <math>0,1,2,3,1,2,3,1,2,3=\psi(\Omega_{\Omega+1}^{\Omega_\Omega}\times\psi_{\Omega_{\Omega+1}}(\Omega_{\Omega+1}^{\Omega_\Omega}\times\Omega_\Omega))</math>
* <math>0,1,2,3,1,2,3,2=\psi(\Omega_{\Omega+1}^{\Omega_\Omega+1})</math>
* <math>0,1,2,3,1,2,3,2,3=\psi(\Omega_{\Omega+1}^{\Omega_\Omega+\Omega})</math>
* <math>0,1,2,3,1,2,3,2,3,3=\psi(\Omega_{\Omega+1}^{\Omega_\Omega+\Omega_2})</math>
* <math>0,1,2,3,1,2,3,3=\psi(\Omega_{\Omega+1}^{\Omega_\Omega+\Omega_2})</math>
* <math>0,1,2,3,1,2,3,3,4=\psi(\Omega_{\Omega+1}^{\Omega_\Omega+\Omega_\omega})</math>
* <math>0,1,2,3,1,2,3,4=\psi(\Omega_{\Omega+1}^{\Omega_\Omega\times2})</math>
* <math>0,1,2,3,1,2,3,4,1,2,3=\psi(\Omega_{\Omega+1}^{\Omega_\Omega\times3})</math>
* <math>0,1,2,3,1,2,3,4,1,2,3,2,2,3=\psi(\Omega_{\Omega+1}^{\psi_{\Omega_{\Omega+1}}(0)})</math>
* <math>0,1,2,3,2=\psi(\Omega_{\Omega+1}^{\Omega_{\Omega+1}})</math>
* <math>0,1,2,3,2,2=\psi(\Omega_{\Omega+2}^{\Omega_{\Omega+2}})</math>
* <math>0,1,2,3,2,2,3=\psi(\Omega_{\Omega+\omega})</math>
* <math>0,1,2,3,2,3=\psi(\Omega_{\Omega\times2})</math>
* <math>0,1,2,3,2,3,3=\psi(\Omega_{\Omega\times\omega})</math>
* <math>0,1,2,3,2,3,4=\psi(\Omega_{\Omega^2})</math>
* <math>0,1,2,3,2,3,4=\psi(\Omega_{\Omega^2})</math>
* <math>0,1,2,3,2,3,4,2,3=\psi(\Omega_{\Omega^2+\Omega})</math>
* <math>0,1,2,3,2,3,4,2,3,2,3,4=\psi(\Omega_{\Omega^2\times2})</math>
* <math>0,1,2,3,2,3,4,2,3,3=\psi(\Omega_{\Omega^2\times\omega})</math>
* <math>0,1,2,3,2,3,4,2,3,3,2,3,4=\psi(\Omega_{\Omega^3})</math>
* <math>0,1,2,3,2,3,4,2,3,3,4=\psi(\Omega_{\psi_1(0)})</math>
* <math>0,1,2,3,2,3,4,2,3,4=\psi(\Omega_{\psi_1(\Omega_2^\Omega)})</math>
* <math>0,1,2,3,2,3,4,3,4,4=\psi(\Omega_{\psi_1(\Omega_2^{\Omega+1})})</math>
* <math>0,1,2,3,2,3,4,4,5=\psi(\Omega_{\psi_1(\Omega_\omega)})</math>
* <math>0,1,2,3,2,3,4,5=\psi(\Omega_{\psi_1(\Omega_\Omega)})</math>
* <math>0,1,2,3,2,3,4,5,2,3,4,5=\psi(\Omega_{\psi_1(\Omega_{\Omega+1}^{\Omega_\Omega})})</math>
* <math>0,1,2,3,2,3,4,5,3,4=\psi(\Omega_{\psi_1(\Omega_{\Omega+1}^{\Omega_\Omega}\times\Omega)})</math>
* <math>0,1,2,3,2,3,4,5,3,4,5=\psi(\Omega_{\psi_1(\Omega_{\Omega+1}^{\Omega_\Omega}\times\Omega_\Omega)})</math>
* <math>0,1,2,3,2,3,4,5,4=\psi(\Omega_{\psi_1(\Omega_{\Omega+1}^{\Omega_{\Omega+1}})})</math>
* <math>0,1,2,3,2,3,4,5,4,5,6,7=\psi(\Omega_{\psi_1(\Omega_{\psi_1(\Omega_\Omega)})})</math>
* <math>0,1,2,3,3=\psi(\Omega_{\Omega_2})</math>
* <math>0,1,2,3,3,2,3=\psi(\Omega_{\Omega_2+1})</math>
* <math>0,1,2,3,3,2,3,2,3,4,5=\psi(\Omega_{\Omega_2+\psi_1(\Omega_\Omega)})</math>
* <math>0,1,2,3,3,2,3,2,3,4,5,5=\psi(\Omega_{\Omega_2+\psi_1(\Omega_{\Omega_2})})</math>
* <math>0,1,2,3,3,2,3,3=\psi(\Omega_{\Omega_2\times2})</math>
* <math>0,1,2,3,3,2,3,3,3=\psi(\Omega_{\Omega_2\times\omega})</math>
* <math>0,1,2,3,3,2,3,4=\psi(\Omega_{\Omega_2\times\Omega})</math>
* <math>0,1,2,3,3,2,3,4,4=\psi(\Omega_{\Omega_2^2})</math>
* <math>0,1,2,3,3,2,3,4,4,2,3,3,4=\psi(\Omega_{\psi_2(0)})</math>
* <math>0,1,2,3,3,2,3,4,4,5=\psi(\Omega_{\psi_2(\Omega_\omega)})</math>
* <math>0,1,2,3,3,2,3,4,5=\psi(\Omega_{\psi_2(\Omega_\Omega)})</math>
* <math>0,1,2,3,3,3=\psi(\Omega_{\Omega_3})</math>
* <math>0,1,2,3,3,4=\psi(\Omega_{\Omega_\omega})</math>
* <math>0,1,2,3,4=\psi(\Omega_{\Omega_\Omega})</math>
* <math>0,1,2,3,4,2,3,4,5,2,3,4,3,3,2,3,4,5,0,1,2,3,1,2,3,4,1,2,3,2,2,1,2,3,4,1,1,0,1,2,3,4,2,3,4,5,2,3,4,3,3,2,3,4,5=\psi(\Omega_{\Omega_\Omega^{\Omega_\Omega}}^{\Omega_{\Omega_\Omega^{\Omega_\Omega}}})</math>
* <math>0,1,2,3,4,5,\cdots=\psi(\psi_I(0))=\mathrm{EBO}</math>

[[分类:分析]]

FTO

2026-05-22T11:08:37Z

Baixie01000a7：/* 性质 */

'''FTO（First Transfinite Ordinal，第一个超限序数，即'''<math>\omega</math>'''）'''，是一个重要的[[序数]]。它被认为是具有“里程碑”意义的一个序数。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[Veblen 函数]]
|<math>\varphi(1)</math>
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(0)</math>
|-
|[[初等序列系统|PrSS]]
|<math>0,1</math>
|-
|[[BMS]]
|<math>\begin{pmatrix} 0 & 1 \end{pmatrix}</math>
|-
|[[长初等序列|LPrSS]]
|<math>1,2</math>
|-
|[[HPrSS]]
|<math>1,2</math>
|-
|[[0-Y]]
|<math>1,2</math>
|-
|[[Y序列|1-Y]]
|<math>1,2</math>
|-
|[[PSS Hydra]]
|<math>\psi^H_1(1)</math>
|-
|[[weak Veblen 函数]]
|<math>\varphi(1,0)</math>
|-
|[[BHM]]
|<math>\begin{pmatrix} 0 & 1 \end{pmatrix}</math>
|-
|[[BSM]]
|<math>\begin{pmatrix} 0&1 \end{pmatrix}</math>
|-
|[[NOCF]]
|<math>\psi(\Omega)</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(1)</math>
|}

=== 性质 ===
ω 是最小的[[序数#超限序数|超限序数]]，最小的非零[[序数#极限序数|极限序数]]，最小的不满足 <math>1+\alpha=\alpha+1</math> 的序数<math>\alpha</math>。

<math>\omega = |\omega| = \aleph_{0} </math>，详见[[基数]]。

[[证明论序数]]：<math>\rm Q</math>，<math>\rm KP^-</math>

极限在此处的记号：[[高德纳箭头]]，[[阿克曼函数]]，[[斯坦豪斯-莫泽表示法]]，[[下箭号表示法]]，[[Sudan 函数|苏丹函数]]，超运算

[[分类:序数]]

Googology 梗百科

2026-05-21T13:53:41Z

Baixie01000a7：/* 3.都在大群拉💩是吧？全都跑不了 */

本页面收录了一些中文 [[Googology|ggg]] 圈的梗。

== 一、聊天记录类 ==

=== 1.定义没有，牛B吹爆 ===
[[文件:12345B67.jpg|截图日期：2024年8月9日|缩略图]]
起因是 3184 说了句“来点小小的链节余项震撼”，后被 hypcos 回复“定义没有，牛B吹爆”

因为其过于经典而被广为流传。

后来还衍生出了多种版本，如“1234，5B67”和“□□□□，□□□□”，“分析没有，牛B吹爆”等

=== 2.XX给你打了 ===
出自于涵对 hypcos 的回复“坦克给你打了”。
[[文件:Tank.jpg|缩略图]]
其中“坦克”指的是 [[LVO]]，这个名词来源于文件《大数级别段位》（一个数字量级表）中的“掌控者坦克”。另一个较为出名的是“邢天战甲”，被用于指代 [[BO]]。

这个梗中的“坦克”可以被换成任意词，被用于调侃性地表达两个事物间的比较。

此外，受这段聊天记录影响，有一些人在讨论部分内容时也常常使用“我倾向于”表达自己的观点。

详细信息可以参考B站用户 3183丶4139 的[https://b23.tv/ULKDxxw 这期视频]。

=== 3.都在大群拉💩是吧？全都跑不了 ===

出自hypcos在2024年10月25日的发言。

当天00:09qwerty发送“。。。”，随后adm.油手就行复读“。。。”，随后多人复读。09:15后陆续出现“打断复读”、“打断打断复读”、“打断^ω 复读”、“ε(打断+1) 复读”、“2nd 复读”……

随后hypcos发言“都在大群拉💩是吧？全都跑不了”，并分别将real.油手就行，此人不存在等7人分别禁言1,2,4,8,16,32,1分钟。

该聊天记录衍生为“都在___拉_是吧？全都跑不了”与“QSSO+1”(Y序列的1,2,4,8,16,32,1)。

== 二、错字类 ==

=== 1.果糕 ===
果糕是馃槹的谐音版，馃槹是 emoji 表情😰按 UTF-8 编码后用 GBK 解码的结果。

具体可以见[https://2023largenumber.fandom.com/zh/wiki/%F0%9F%98%B0#articleComments/ 此处]。

=== 2.扽西 ===
最早是 PCF 的错字，将“分析”打成了扽西，后来逐渐演变成了一个梗，用于代指不严谨的分析。

=== 3.其他错字 ===
还有一些错字也比较经典，如“狄安娜”指电脑，“周记”指手机，“全业务额是”是“确实”，在此不一一列举。
[[文件:2025-08-11 狄安娜的考验.png|缩略图|疑似对外国友人有点高难度了（对中国人也是）]]
详细可以参考[https://docs.qq.com/sheet/DVnlZSENqbm1CU3FQ?u=7b7ca06006c34e6b84a6bbcc0ac26715&tab=000001 错字辞典]，它较为详细地记载了一些错字。

Loader 数

2026-05-15T17:43:47Z

Baixie01000a7：

'''Loader 数'''是 Ralph Loader 的 C 语言程序 '''Loader.c''' 的输出 <math>D^5(99)</math>，它在 2001 年的 [[Bignum Bakeoff]] 比赛（用不超过 512 字的代码生成尽可能大的有限整数）中获得第一名。

其中 D 函数的强度取决于 Huet-Coquand 构造演算（CoC）的证明论强度，其增长率达到了 <math>\mathrm {PTO}(\mathrm{Z}_\omega)</math>。迄今为止，它仍然是最强的可计算函数之一。

=== 定义 ===
Loader.c 的源代码<ref>https://github.com/rcls/busy</ref>如下：<syntaxhighlight lang="c" line="1">
#define R { return
#define P P (
#define L L (
#define T S (v, y, c,
#define C ),
#define X x)
#define F );}

int r, a;
P y, X
R y - ~y << x;
}
Z (X
R r = x % 2 ? 0 : 1 + Z (x / 2 F
L X
R x / 2 >> Z (x F
#define U = S(4,13,-4,
T t)
{
int
f = L t C
x = r;
R
f - 2 ?
f > 2 ?
f - v ? t - (f > v) * c : y :
P f, P T L X C
S (v+2, t U y C c, Z (X )))
:
A (T L X C
T Z (X ) F
}
A (y, X
R L y) - 1
? 5 << P y, X
: S (4, x, 4, Z (r) F
#define B (x /= 2) % 2 && (
D (X
{
int
f,
d,
c = 0,
t = 7,
u = 14;
while (x && D (x - 1 C B 1))
d = L L D (X ) C
f = L r C
x = L r C
c - r || (
L u) || L r) - f ||
B u = S (4, d, 4, r C
t = A (t, d) C
f / 2 & B c = P d, c C
t U t C
u U u) )
C
c && B
t = P
~u & 2 | B
u = 1 <此外，Loader 还给出了可读性更高的版本（我们使用中文注释）：<syntaxhighlight lang="c">
//Tree、INT、TREE、BitStream 都被定义为 int，只是为了区分用途。
//把宏 DESCEND 直接展开为变量 xx，用于 while 里的递归控制。
typedef int Tree;
typedef int INT;
typedef int TREE;
typedef int BitStream;
#define DESCEND xx

// 全局临时变量：
// lastRight —— 用于在解码配对结构时暂存“另一半”值；
// accumulate —— 累积所有推导结果（每个结果是(term, type, 剩余比特流, context) 四元组的配对编码）。
Tree lastRight, accumulate;

// —— 基础编码：二元配对函数 ——
// 将两个非负整数 yy, xx 编码为一个整数，保证一一对应（双射）。
// 公式：Pair(yy,xx) = (yy − ~yy) << xx = (2*yy + 1) << xx
// 这样低位的连续零数目即为 xx，高位奇数部分即为 2*yy+1，方便快速解码。
TREE Pair (TREE yy, TREE xx)
{
return yy - ~yy << xx;
}

// —— 解码：取配对的第二个分量 ——
// 从编码值 xx 中恢复出原始的第二个参数（移位次数）。
// 逻辑：若 xx 为奇数，则移位次数为 0；否则不断除以 2 并累加，直到遇到奇数。
// 计算结果同时写入 lastRight。
TREE Right (TREE xx)
{
return lastRight = xx % 2 ? 0 : 1 + Right (xx / 2);
}

// —— 解码：取配对的第一个分量 ——
// 先将编码右移 1 位（去除最低位信息），再右移 Right(xx) 位，得到原始的 yy。
// 上一次调用 Right 时已经把移位计数存入 lastRight，因此这里可直接使用。
TREE Left (TREE xx)
{
return xx / 2 >> Right (xx);
}

// —— 宏：提升（Lift） ——
// 将所有自由变量的 De Bruijn 索引统一 +1，维护绑定层级。
// 通过 Subst(vv=4, yy=13, context=-4, term=xx) 实现。
#define Lift(xx) Subst (4, 13, -4, xx)

// —— 归一化替换（Subst） ——
// 在 term 中，将索引 vv 的变量替换为术语 yy，并对索引 > vv 的变量减去 context。
// 同时对 λ 抽象 (aux=0)、Π 构造 (aux=1) 和函数应用 (aux=2) 等节点进行递归归一化。
// 参数说明：
// vv : 要替换的变量索引
// yy : 用来替换的术语（已规范化）
// context : 替换后，所有更大索引变量需减去的偏移
// term : 待处理的术语编码
TREE Subst (INT vv, TREE yy, INT context, TREE term)
{
Tree aux = Left (term), // 当前节点类型：0=λ，1=Π，2=应用，>2=变量/常量
xx = lastRight; // 当前节点主体或子配对

// 按节点类型分支处理
if (aux == 2) {
// 应用节点：先递归替换，再用 Apply 做 β-归约或重构
return Apply (
Subst (vv, yy, context, Left (xx)),
Subst (vv, yy, context, Right (xx))
);
}
else if (aux > 2) {
// 变量或常量：
// 若 aux == vv，则替换为 yy；否则若 aux>vv，就减去偏移 context
return aux == vv
? yy
: term - (aux > vv ? context : 0);
}
else {
// 抽象节点：aux==0 为 λ，aux==1 为 Π
// 构造新配对 (aux, (子项1', 子项2'))
// 对右子树的 yy 先做 Lift 以调整绑定深度
return Pair (
aux,
Pair (
Subst (vv, yy, context, Left (xx)),
Subst (vv+2, Lift(yy), context, Right (xx))
)
);
}
}

// —— 函数应用归一化（Apply） ——
// 若 yy 的操作码 Left(yy)==1（λ 抽象），则对其主体做一次 β-归约：Subst(4, xx, 4, body)。
// 否则重构应用节点 Pair(2, Pair(yy, xx))。
TREE Apply (TREE yy, TREE xx)
{
return Left (yy) == 1
? Subst (4, xx, 4, Right (lastRight))
: Pair (2, Pair (yy, xx));
}

// —— 比特流测试宏 ——
// 把 xx 当作待消费的比特流，每用一次 xx/=2，测试被除后最低位是否为 1。
#define MAYBE (xx /= 2) % 2 &&

// —— 主推导过程（Derive） ——
// 将整数 xx 视作一条比特流，按照 Curry–Howard 同构/类型规则生成所有可能的 λ 术语并归一化。
// 输出的(term, type, 剩余比特流, context) 四元组不断累加到全局 accumulate 中。
// 算法概览：
// 1. 递归调用 Derive(xx-1)，保证对所有小于 xx 的比特串也进行推导，确保单调增长。
// 2. 在 while 循环中，依次用 MAYBE 消费一位比特，决定是否执行对应规则：
// - APPLY (函数应用 β-归约)
// - 弱化 (Weaken，将新假设压入上下文，并提升当前项/类型)
// - Π 构造 / λ 引入
// - 变量引入 (VAR(0))
// 3. 每次规则应用后，把当前 term/type/剩余比特流/context 打包配对累积。
TREE Derive (BitStream xx)
{
Tree aux, auxTerm;
Tree context = 0, // 初始空上下文
term = 7, // STAR 常量：Pair(3,0)=7
type = 14; // BOX 常量：Pair(3,1)=14

// while 条件中先递归 Derive(xx-1)，再根据下一位比特决定是否进入循环体
while (DESCEND && Derive (xx - 1), MAYBE (1)) {

// 1) 从子推导中获取一个新项 auxTerm 及其类型 aux
auxTerm = Left (Left (Derive (xx)));
aux = Left (lastRight);
xx = Left (lastRight); // 更新剩余比特流

// 2) 若当前上下文与子推导上下文相等，则可以尝试 APPLY 或 Weaken
if (context == lastRight) {
// — APPLY：当类型符合 Π(aux, -) 时，对 term 执行函数应用
if (Left (type) == 1 && Left (lastRight) == aux && MAYBE (1)) {
type = Subst (4, auxTerm, 4, lastRight);
term = Apply (term, auxTerm);
}
// — 弱化：若 auxType 是 STAR/BOX，可引入新假设
else if ((aux / 2) && MAYBE (1)) {
context = Pair (auxTerm, context);
term = Lift (term);
type = Lift (type);
}
}

// 3) Π 构造或 λ 引入：当上下文非空时，可根据比特选择
if (context && MAYBE (1)) {
// LHS：若 type 不支持 Π 构造，则强制做 λ 引入，并相应先对 type 做 Π 构造
Tree isLambda = (~type & 2);
if (MAYBE (isLambda)) {
type = Pair (1, Pair (Left (context), type)); // Π(Left(context), type)
}
term = Pair (isLambda | 0, Pair (Left (context), term));
context = lastRight; // 弹出已用的上下文项
}

// 4) 变量引入：若 type 是 STAR/BOX，可引入 VAR(0)
if ((type / 2) && MAYBE (1)) {
context = Pair (term, context);
type = Lift (term);
term = Pair (4, 0); // VAR(0)
}
}

// 将当前四元组打包，并加到 accumulate
return accumulate = Pair (
Pair (term, Pair (type, Pair (xx, context))),
accumulate
);
}

// —— 主函数 ——
// 对初值 99 连续调用五次 Derive，以充分“填充” accumulate。
TREE main ()
{
return Derive (Derive (Derive (Derive (Derive (99)))));
}
</syntaxhighlight>{{默认排序:相关问题}}
[[分类:记号]]

Loader 数

2026-05-15T17:43:30Z

Baixie01000a7：

'''Loader 数'''是 Ralph Loader 的 C 语言程序 '''Loader.c''' 的输出 <math>D^5(99)</math>，它在 2001 年的 [[Bignum Bakeoff]] 比赛（用不超过 512 字的代码生成尽可能大的有限整数）中获得第一名。

其中 D 函数的强度取决于 Huet-Coquand 构造演算（CoC）的证明论强度，其增长率达到了 <math>{\mathrm PTO}(\mathrm{Z}_\omega)</math>。迄今为止，它仍然是最强的可计算函数之一。

=== 定义 ===
Loader.c 的源代码<ref>https://github.com/rcls/busy</ref>如下：<syntaxhighlight lang="c" line="1">
#define R { return
#define P P (
#define L L (
#define T S (v, y, c,
#define C ),
#define X x)
#define F );}

int r, a;
P y, X
R y - ~y << x;
}
Z (X
R r = x % 2 ? 0 : 1 + Z (x / 2 F
L X
R x / 2 >> Z (x F
#define U = S(4,13,-4,
T t)
{
int
f = L t C
x = r;
R
f - 2 ?
f > 2 ?
f - v ? t - (f > v) * c : y :
P f, P T L X C
S (v+2, t U y C c, Z (X )))
:
A (T L X C
T Z (X ) F
}
A (y, X
R L y) - 1
? 5 << P y, X
: S (4, x, 4, Z (r) F
#define B (x /= 2) % 2 && (
D (X
{
int
f,
d,
c = 0,
t = 7,
u = 14;
while (x && D (x - 1 C B 1))
d = L L D (X ) C
f = L r C
x = L r C
c - r || (
L u) || L r) - f ||
B u = S (4, d, 4, r C
t = A (t, d) C
f / 2 & B c = P d, c C
t U t C
u U u) )
C
c && B
t = P
~u & 2 | B
u = 1 <此外，Loader 还给出了可读性更高的版本（我们使用中文注释）：<syntaxhighlight lang="c">
//Tree、INT、TREE、BitStream 都被定义为 int，只是为了区分用途。
//把宏 DESCEND 直接展开为变量 xx，用于 while 里的递归控制。
typedef int Tree;
typedef int INT;
typedef int TREE;
typedef int BitStream;
#define DESCEND xx

// 全局临时变量：
// lastRight —— 用于在解码配对结构时暂存“另一半”值；
// accumulate —— 累积所有推导结果（每个结果是(term, type, 剩余比特流, context) 四元组的配对编码）。
Tree lastRight, accumulate;

// —— 基础编码：二元配对函数 ——
// 将两个非负整数 yy, xx 编码为一个整数，保证一一对应（双射）。
// 公式：Pair(yy,xx) = (yy − ~yy) << xx = (2*yy + 1) << xx
// 这样低位的连续零数目即为 xx，高位奇数部分即为 2*yy+1，方便快速解码。
TREE Pair (TREE yy, TREE xx)
{
return yy - ~yy << xx;
}

// —— 解码：取配对的第二个分量 ——
// 从编码值 xx 中恢复出原始的第二个参数（移位次数）。
// 逻辑：若 xx 为奇数，则移位次数为 0；否则不断除以 2 并累加，直到遇到奇数。
// 计算结果同时写入 lastRight。
TREE Right (TREE xx)
{
return lastRight = xx % 2 ? 0 : 1 + Right (xx / 2);
}

// —— 解码：取配对的第一个分量 ——
// 先将编码右移 1 位（去除最低位信息），再右移 Right(xx) 位，得到原始的 yy。
// 上一次调用 Right 时已经把移位计数存入 lastRight，因此这里可直接使用。
TREE Left (TREE xx)
{
return xx / 2 >> Right (xx);
}

// —— 宏：提升（Lift） ——
// 将所有自由变量的 De Bruijn 索引统一 +1，维护绑定层级。
// 通过 Subst(vv=4, yy=13, context=-4, term=xx) 实现。
#define Lift(xx) Subst (4, 13, -4, xx)

// —— 归一化替换（Subst） ——
// 在 term 中，将索引 vv 的变量替换为术语 yy，并对索引 > vv 的变量减去 context。
// 同时对 λ 抽象 (aux=0)、Π 构造 (aux=1) 和函数应用 (aux=2) 等节点进行递归归一化。
// 参数说明：
// vv : 要替换的变量索引
// yy : 用来替换的术语（已规范化）
// context : 替换后，所有更大索引变量需减去的偏移
// term : 待处理的术语编码
TREE Subst (INT vv, TREE yy, INT context, TREE term)
{
Tree aux = Left (term), // 当前节点类型：0=λ，1=Π，2=应用，>2=变量/常量
xx = lastRight; // 当前节点主体或子配对

// 按节点类型分支处理
if (aux == 2) {
// 应用节点：先递归替换，再用 Apply 做 β-归约或重构
return Apply (
Subst (vv, yy, context, Left (xx)),
Subst (vv, yy, context, Right (xx))
);
}
else if (aux > 2) {
// 变量或常量：
// 若 aux == vv，则替换为 yy；否则若 aux>vv，就减去偏移 context
return aux == vv
? yy
: term - (aux > vv ? context : 0);
}
else {
// 抽象节点：aux==0 为 λ，aux==1 为 Π
// 构造新配对 (aux, (子项1', 子项2'))
// 对右子树的 yy 先做 Lift 以调整绑定深度
return Pair (
aux,
Pair (
Subst (vv, yy, context, Left (xx)),
Subst (vv+2, Lift(yy), context, Right (xx))
)
);
}
}

// —— 函数应用归一化（Apply） ——
// 若 yy 的操作码 Left(yy)==1（λ 抽象），则对其主体做一次 β-归约：Subst(4, xx, 4, body)。
// 否则重构应用节点 Pair(2, Pair(yy, xx))。
TREE Apply (TREE yy, TREE xx)
{
return Left (yy) == 1
? Subst (4, xx, 4, Right (lastRight))
: Pair (2, Pair (yy, xx));
}

// —— 比特流测试宏 ——
// 把 xx 当作待消费的比特流，每用一次 xx/=2，测试被除后最低位是否为 1。
#define MAYBE (xx /= 2) % 2 &&

// —— 主推导过程（Derive） ——
// 将整数 xx 视作一条比特流，按照 Curry–Howard 同构/类型规则生成所有可能的 λ 术语并归一化。
// 输出的(term, type, 剩余比特流, context) 四元组不断累加到全局 accumulate 中。
// 算法概览：
// 1. 递归调用 Derive(xx-1)，保证对所有小于 xx 的比特串也进行推导，确保单调增长。
// 2. 在 while 循环中，依次用 MAYBE 消费一位比特，决定是否执行对应规则：
// - APPLY (函数应用 β-归约)
// - 弱化 (Weaken，将新假设压入上下文，并提升当前项/类型)
// - Π 构造 / λ 引入
// - 变量引入 (VAR(0))
// 3. 每次规则应用后，把当前 term/type/剩余比特流/context 打包配对累积。
TREE Derive (BitStream xx)
{
Tree aux, auxTerm;
Tree context = 0, // 初始空上下文
term = 7, // STAR 常量：Pair(3,0)=7
type = 14; // BOX 常量：Pair(3,1)=14

// while 条件中先递归 Derive(xx-1)，再根据下一位比特决定是否进入循环体
while (DESCEND && Derive (xx - 1), MAYBE (1)) {

// 1) 从子推导中获取一个新项 auxTerm 及其类型 aux
auxTerm = Left (Left (Derive (xx)));
aux = Left (lastRight);
xx = Left (lastRight); // 更新剩余比特流

// 2) 若当前上下文与子推导上下文相等，则可以尝试 APPLY 或 Weaken
if (context == lastRight) {
// — APPLY：当类型符合 Π(aux, -) 时，对 term 执行函数应用
if (Left (type) == 1 && Left (lastRight) == aux && MAYBE (1)) {
type = Subst (4, auxTerm, 4, lastRight);
term = Apply (term, auxTerm);
}
// — 弱化：若 auxType 是 STAR/BOX，可引入新假设
else if ((aux / 2) && MAYBE (1)) {
context = Pair (auxTerm, context);
term = Lift (term);
type = Lift (type);
}
}

// 3) Π 构造或 λ 引入：当上下文非空时，可根据比特选择
if (context && MAYBE (1)) {
// LHS：若 type 不支持 Π 构造，则强制做 λ 引入，并相应先对 type 做 Π 构造
Tree isLambda = (~type & 2);
if (MAYBE (isLambda)) {
type = Pair (1, Pair (Left (context), type)); // Π(Left(context), type)
}
term = Pair (isLambda | 0, Pair (Left (context), term));
context = lastRight; // 弹出已用的上下文项
}

// 4) 变量引入：若 type 是 STAR/BOX，可引入 VAR(0)
if ((type / 2) && MAYBE (1)) {
context = Pair (term, context);
type = Lift (term);
term = Pair (4, 0); // VAR(0)
}
}

// 将当前四元组打包，并加到 accumulate
return accumulate = Pair (
Pair (term, Pair (type, Pair (xx, context))),
accumulate
);
}

// —— 主函数 ——
// 对初值 99 连续调用五次 Derive，以充分“填充” accumulate。
TREE main ()
{
return Derive (Derive (Derive (Derive (Derive (99)))));
}
</syntaxhighlight>{{默认排序:相关问题}}
[[分类:记号]]

Goodstein函数

2026-05-15T17:20:47Z

Baixie01000a7：/* 枚举 */

'''古德斯坦函数(Goodstein Function)'''，是由鲁宾•古德斯坦(Reuben Goodstein)构造出的快速增长的函数。

== 定义 ==
首先需要定义数m的以n为底的遗传记法：

假设我们将一个非负整数m表示为n的幂次之和，然后将这些幂指数本身也表示为类似的幂次和，不断重复这一过程，直到所有的最高次指数都小于n。例如，我们可以将100写作<math>2^6+2^5+2^2</math>进一步可以写为<math>2^{2^2+2}+2^{2^2+1}+2^2</math>。这种表示方式称为m的以n为底的遗传记法。

Goodstein定义了一个数列<math>G_k(n)</math>：

对任意自然数n，都有<math>G_0(n)=n</math>

对任意自然数n,k，都有<math>G_{k+1}(n)</math>是把<math>G_k(n)</math>写成以k+2为底的遗传记法，随后把里面所有的k+2改成k+3，最后再把整个数减一所得到的数。

我们拿100作为例子：

<math>G_0(100) = 100 = 2^{2^2+2}+2^{2^2+1}+2^2</math>

<math>G_1(100) = 3^{3^3+3}+3^{3^3+1}+3^3-1 =3^{3^3+3}+3^{3^3+1}+3^2\times2+3\times2+2= 228767924549636</math>

<math>G_2(100) =4^{4^4+4}+4^{4^4+1}+4^2\times2+4\times2+1\approx3.486030062 \times 10^{156}</math>

……

这种快速增长的序列称为 Goodstein 序列。令人惊讶的是，对于 ''n'' 的所有值，<math>G_k(n)</math> 最终达到峰值、下降并返回零。这个事实被称为'''古德斯坦定理'''。更令人惊讶的是，可以证明古德斯坦定理无法用皮亚诺算术来证明。

我们定义古德斯坦函数<math>G(x)</math>等于古德斯坦序列<math>G_k(x)=0</math>时k的值。它的FGH增长率为<math>\varepsilon_0</math>.

== 例子 ==
我们以较小的x作为例子，来计算一下<math>G(x)</math>.为了更加清晰，我们不展示<math>G_k(n)</math> 的具体值，而是展示它的以k+2为底的遗传记法表示。读者可以自行计算取值。
{| class="wikitable mw-collapsible mw-collapsed" style="1"
|+x=1<div style="display:inline;opacity:0;height:0;">aaaaa</div>
!k
!<math>G_k(x)</math>以k+2为底的遗传记法表示
|-
|0
|1
|-
|1
|0
|}
因此G(1)=1.
{| class="wikitable mw-collapsible mw-collapsed"
|+x=2<div style="display:inline;opacity:0;height:0;">aaaaa</div>
!k
!<math>G_k(x)</math>以k+2为底的遗传记法表示
|-
|0
|2
|-
|1
|2
|-
|2
|1
|-
|3
|0
|}
因此G(2)=3.
{| class="wikitable mw-collapsible mw-collapsed"
|+x=3<div style="display:inline;opacity:0;height:0;">aaaaa</div>
!k
!<math>G_k(x)</math>以k+2为底的遗传记法表示
|-
|0
|2+1
|-
|1
|3
|-
|2
|3
|-
|3
|2
|-
|4
|1
|-
|5
|0
|}
因此G(3)=5.

从G(4)开始，古德斯坦函数将开始“起飞”
{| class="wikitable mw-collapsible mw-collapsed"
|+x=4<div style="display:inline;opacity:0;height:0;">aaaaa</div>
!k
!<math>G_k(x)</math>以k+2为底的遗传记法表示
|-
|0
|<math>2^2</math>
|-
|1
|<math>3^2\times2+3\times2+2</math>
|-
|2
|<math>4^2\times2+4\times2+1</math>
|-
|3
|<math>5^2\times2+5\times2</math>
|-
|4
|<math>6^2\times2+6+5</math>
|-
|9
|<math>11^2\times2+11</math>
|-
|10
|<math>12^2\times2+11</math>
|-
|21
|<math>23^2\times2</math>
|-
|22
|<math>24^2+24\times23+23</math>
|-
|45
|<math>47^2+47\times23</math>
|-
|46
|<math>48^2+48\times22+47</math>
|-
|93
|<math>95^2+95\times22</math>
|-
|189
|<math>191^2+191\times21</math>
|-
|381
|<math>383^2+383\times20</math>
|-
|402653181=<math>3\times2^{27}-3</math>
|<math>402653183^2</math>
|-
|402653182
|<math>402653184\times402653183+402653183</math>
|-
|<math>3\times2^{402653210}-3</math>
|<math>3\times2^{402653210}-1</math>
|-
|<math>3\times2^{402653210}-2</math>
|<math>3\times2^{402653210}-1</math>
|-
|<math>3\times2^{402653211}-3</math>
|0
|}
因此<math>G(4)=3\times2^{402653211}-3</math>

这里它展示了很清晰的“下降”过程。

我们有G(12)大于[[葛立恒数]]这个结论。

== 与 [[增长层级#哈代层级|HH]] 的关系 ==
定义<math>R^\omega_a(n)</math>为将n表示为以a为底的遗传记法，然后将所有的底数a全部替换为<math>\omega</math>所得到的序数。我们可以证明以下结论：

<math>G(n)=H_{R^\omega_2(n)}(3)-3</math>，其中<math>H_\alpha(n)</math>是 [[增长层级#哈代层级|Hardy 层级]]。

=== 证明 ===
以下叙述中总是考虑带乘法的[[康托范式]]和小于<math>\varepsilon_0</math>的序数，希腊字母表示序数，拉丁字母表示正整数。

先证一个引理：'''<math>H_{R^\omega_a(b+1)}(a)=H_{R^\omega_a(b)+1}(a)</math>，<math>a</math>是不小于3的正整数。'''

引理的证明：以下用<math>k</math>表示某个小于<math>a</math>的正整数。我们称一个序数<math>\alpha</math>是好的，如果它的康托范式中出现的所有正整数全都小于<math>a</math>。不难得出，<math>\alpha</math>是好的当且仅当它是某个<math>R^\omega_a(b)</math>的取值。

记<math>R^\omega_a(b+1)=\alpha</math>。将<math>H_\alpha(a)</math>进行多次取基本列，使下标为后继序数，得到<math>H_\beta(a)</math>。那么：

'''1) <math>\beta</math>是好的，不考虑正整数项。'''

由于<math>H_\beta(a)</math>的自变量为<math>a</math>，取基本列时得到的正整数不超过<math>a</math>。那么只要证明产生<math>\beta</math>时得到的<math>a</math>会在下一步被立即使用即可：

若<math>\alpha</math>是后继序数，则<math>\alpha=\beta</math>，显然是好的。

若<math>\alpha</math>是极限序数，设<math>\alpha=\alpha_0+\gamma\times{k}</math>：

# <math>\gamma=\omega</math>，则下一步得到<math>\alpha_0+\gamma\times{(k-1)}+a</math>，已经是后继了，故结论成立；
# <math>\gamma=\omega^{\delta+1}</math>，<math>\delta</math>是大于等于1的序数，则下一步得到<math>\alpha_0+\gamma\times{(k-1)}+\omega^\delta\times{a}</math>，下一步取<math>\omega^\delta\times{a}</math>的基本列，故结论成立；
# <math>\gamma=\omega^{\gamma_0+\omega\times{k}}</math>，则下一步得到<math>\alpha_0+\omega^{\gamma_0+\omega\times{(k-1)}+a}</math>，下一步取<math>\omega^{\cdots+a}</math>的基本列，故结论成立；
# <math>\gamma=\omega^{\gamma_0+\sigma\times{k}}</math>，<math>\sigma</math>是<math>\omega^2</math>的倍数，则此时等效于对<math>\sigma</math>取两次基本列的问题。由于<math>\sigma<\gamma</math>，使用序数的递降法知结论成立。

以上对于<math>\gamma=\omega^\sigma</math>中分别讨论了<math>\sigma=1</math>，<math>\sigma</math>为非1后继序数，<math>\sigma</math>为极限序数但不为<math>\omega^2</math>的倍数，<math>\sigma</math>为<math>\omega^2</math>的倍数的情况。综上，结论1)得证。

易得<math>g_{R^\omega_a(n)}(a)=n</math>，其中g是SGH。设<math>\beta=\theta+1</math>，则<math>\theta</math>是好的。所以，

由于增长层级在取基本列上规则相同，<math>g_\alpha(a)=g_\beta(a)</math>，

<math>g_{\theta+1}(a)=g_\beta(a)=g_\alpha(a)=b+1=g_{R^\omega_a(b)}(a)+1=g_{R^\omega_a(b)+1}(a)</math>，

<math>g_\theta(a)=g_{R^\omega_a(b)}(a)</math>。

由于<math>\theta</math>是好的，遗传记法是唯一的，故<math>\theta=R^\omega_a(b)</math>。从而<math>H_{R^\omega_a(b+1)}(a)=H_\alpha(a)=H_\beta(a)=H_{\theta+1}(a)=H_{R^\omega_a(b)+1}(a)</math>。引理得证。

'''原命题的证明''' 对于一般的自然数<math>k</math>，根据Goodstein序列的定义，有<math>R^\omega_{k+3}(G_{k+1}(n)+1)=R^\omega_{k+2}(G_k(n))</math>。于是，

<math>H_{R^\omega_{k+3}(G_{k+1}(n))}(k+4)=H_{R^\omega_{k+3}(G_{k+1}(n))+1}(k+3)</math>，

使用引理，

<math>=H_{R^\omega_{k+3}(G_{k+1}(n)+1)}(k+3)=H_{R^\omega_{k+2}(G_k(n))}(k+3)</math>。

于是，<math>H_{R^\omega_{k+2}(G_k(n))}(k+3)</math>是与<math>k</math>无关的常数。分别令<math>k=G(n)</math>，<math>k=0</math>，得到

<math>G(n)+3=H_0(G(n)+3)=H_{R^\omega_{G(n)+2}(0)}(G(n)+3)=H_{R^\omega_2(n)}(3)</math>，从而证明了

<math>G(n)=H_{R^\omega_2(n)}(3)-3</math>。

== 枚举 ==

有了刚刚的结论，我们可以快速地求出一些Goodstein函数的值。以下使用[[增长层级#快速增长层级|FGH]]，并且利用了结论<math>H_{\omega^\alpha}(n)=f_{\alpha}(n)</math>：

<math>G(0)=0</math>

<math>G(1)=1</math>

<math>G(2)=3</math>

<math>G(3)=5</math>

<math>G(4)=f_3(3)-3</math>

<math>G(5)=f_4(4)-3</math>

<math>G(6)=f_6(6)-3</math>

<math>G(7)=f_8(8)-3</math>

<math>G(8)=f_{\omega+1}(3)-3</math>

<math>G(9)=f_{\omega+1}(4)-3</math>

<math>G(10)=f_{\omega+1}(6)-3</math>

<math>G(11)=f_{\omega+1}(8)-3</math>

<math>G(12)=f_{\omega+1}(f_3(3))-3</math>

<math>G(13)=f_{\omega+1}(f_4(4))-3</math>

<math>G(14)=f_{\omega+1}(f_6(6))-3</math>

<math>G(15)=f_{\omega+1}(f_8(8))-3</math>

<math>G(16)=f_{\omega^3}(3)-3</math>

<math>G(17)=f_{\omega^4}(4)-3</math>

<math>G(18)=f_{\omega^6}(6)-3</math>

<math>G(19)=f_{\omega^8}(8)-3</math>

<math>G(20)=f_{\omega^\omega}(f_3(3))-3</math>

<math>\cdots</math>

一般地，我们有

<math>G(2\uparrow\uparrow{n})=f_{\omega\uparrow\uparrow(n-1)}(3)-3</math>。

据此可以得到，Goodstein函数的增长率为<math>\varepsilon_0</math>。

{{默认排序:相关问题}}
[[分类:记号]]

BMS

2026-05-15T11:12:15Z

Baixie01000a7：/* 争议 */

Bashicu 矩阵系统（Bashicu Matrix System，'''BMS'''）是一个[[序数记号]]。Bashicu Hyudora 在 2018 年给出了它的定义。

== 定义 ==

=== 原定义 ===
Bashicu 最初在他的未命名的 BASIC 编程语言改版上提交了 BMS 的定义。<ref name=":0"> Bashicu Hyudora (2015). [https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:BashicuHyudora/BASIC%E8%A8%80%E8%AA%9E%E3%81%AB%E3%82%88%E3%82%8B%E5%B7%A8%E5%A4%A7%E6%95%B0%E3%81%AE%E3%81%BE%E3%81%A8%E3%82%81#.E3.83.90.E3.82.B7.E3.82.AF.E8.A1.8C.E5.88.97.E6.95.B0.28Bashicu_matrix_number.29 Summary of large numbers in BASIC language] (BASIC言語による巨大数のまとめ). ''Googology Wiki''.</ref>BMS 的原定义是一个大数记号，理论的输出是一个大数。该程序并未设计为实际运行，原因在于语言修改的未定义性，同时也受限于内存与计算时间的现实约束，无法计算出这个大数的实际最终值。因此，Fish 编写了名为"Bashicu 矩阵计算器"的程序来演示预期的计算流程（该程序已得到 Bashicu 验证）。故 Bashicu 矩阵的正式定义可参考 Fish 程序的源代码。<ref>Kyodaisuu (2020). [https://github.com/kyodaisuu/basmat/blob/master/basmat.c basmat]. ''Gthub''.</ref>

=== 正式定义 ===
中文 googology 社区提到 BMS 默认是一个序数记号。以下是序数记号 BMS 的定义及说明：

首先是 BMS 合法式：BMS 的合法式是二维的自然数构成的序列，在外观上看是一个矩阵。如 <math>\begin{pmatrix} 0 & 1&2&1 \\ 0&1&1&1\\0&1&0&1 \end{pmatrix}</math> 就是一个 BMS 的合法式。在很多场合，这种二维的结构书写起来不是很方便，因此我们也常常把BMS从左到右、从上到下按列书写，每一列的不同行之间用逗号隔开，不同列之间用括号隔开。例如，上面的 BMS 也可以写成 <math>(0,0,0)(1,1,1)(2,1,0)(1,1,1)</math>。在很多情况下，除首列外，列末的 0 也可以省略不写，例如上面的 BMS 写为 <math>(0)(1,1,1)(2,1)(1,1,1)</math>。

理论上来说，只要是这样的式子就可以按照 BMS 的规则进行处理了。但实际操作过程中，我们还可以排除一些明显不标准的式子：

* 首列并非全 0
* 每一列并非不严格递减，即出现一列中下面的数大于上面的数
* 出现一个元素 a，它比它同行左边所有元素都大超过 1

在了解 BMS 的展开规则之前，需要先了解一些概念。

# 第一行元素的'''父项'''：对于位于第一行的元素 a，它的父项 b 是满足以下条件的项当中，位于最右边的项：1. 同样位于第一行且在 a 的左边；2. 小于 a。这里和 [[初等序列系统|PrSS]] 判定父项的规则是相同的。显然，0 没有父项。
# '''祖先项'''：一个元素自己，以及它的父项、父项的父项、父项的父项的父项……共同构成它的祖先项。
# 其余行元素的父项：对于不位于第一行的元素 c，它的父项 d 指满足以下条件的项当中，位于最右边的项：1. 与c位于同一行且在 c 的左边；2. 小于 c；3. d 正上方的项 e 是 c 正上方的项f的祖先项。0 没有父项。
# '''坏根'''：最后一列位于最下方的非零元素的父项所在列，称为坏根。如果最后一列所有元素为 0，则这个 BMS 表达式无坏根。值得一提的是，末列最靠下的非零元素记作 '''LNZ'''（Lowermost Non-Zero）
# '''好部'''、'''坏部'''：这两个概念与 PrSS 是相似的。位于坏根左边的所有列称为好部，记作 G，G 可以为空；从坏根到倒数第二列(包括坏根、倒数第二列)的部分称为坏部，记作B。
# '''阶差向量'''：在一个 n 行 BMS 中，我们把末列记为 <math>(\alpha_1,\alpha_2,\cdots,\alpha_n)</math>，把坏根列记为 <math>(\beta_1,\beta_2,\cdots,\beta_n)</math>，并且我们规定 <math>\alpha_{n+1}=0</math>。则阶差向量<math>\Delta=(\delta_1,\delta_2,\cdots,\delta_n)</math>按照这样的规则得到：<math>\delta_i = \begin{cases} \alpha_i-\beta_i, & \alpha_{i+1}\neq0 \\ 0, & \alpha_{i+1}=0 \end{cases}</math>。通俗的说，如果末列的第 <math>i+1</math> 项等于0，则 <math>\delta_i=0</math>，否则 <math>\delta_i</math> 等于末列第 i 行减去坏根列第 i 行。阶差向量记作 <math>\Delta</math>。
# <math>B_m</math>：<math>B_m</math>是 B 中每一列都加上 <math>\Delta</math> 的 m 倍所得到的新矩阵。但是有一点需要注意：如果 B 中某个元素 t 的祖先项不包含坏根中的元素，则在 <math>B_m</math> 对应位置的元素的值依然是 t，它不加 <math>\Delta</math>。

了解概念后，以下是 BMS 的展开规则：

# 空矩阵 = 0
# 如果表达式是非空矩阵 S，如果它没有坏根，那么 S 等于 S 去掉最后一列之后，剩余部分的后继。
# 否则，确定这个 BMS 表达式 S 的坏根、G、B、<math>\Delta</math>，S 的基本列第 n 项<math>S[n]=G\sim B\sim B_1 \sim B_2\sim B_3\sim\cdots\sim B_{n-1}</math>。其中 ~ 表示序列拼接。或者称 S 的展开式是 <math>G\sim B \underbrace{\sim B_1\sim B_2\sim \cdots}_{\omega}</math>。

BMS 的极限基本列是 <math>\{(0)(1),(0,0)(1,1),(0,0,0)(1,1,1),(0,0,0,0)(1,1,1,1),\cdots\}</math>，从这个基本列中元素开始取前驱或取基本列所能得到的表达式是 BMS 的标准式。

以下是 BMS 展开的一些实例：

例一：<math>(0,0,0)(1,1,1)(2,2,1)(3,2,0)(0,0,0)</math>

因为末列全都是 0，因此这个 BMS 没有坏根。根据规则 2，它是 <math>(0,0,0)(1,1,1)(2,2,1)(3,2,0)</math> 的后继。

例二：<math>(0,0,0)(1,1,1)(2,2,2)(3,3,3)(4,2,0)</math>

LNZ 是末列第二行的 2。首先确定末列第 1 行元素的祖先项，即标红的部分（末列本身不染色，下同）：<math>({\color{red}0},0,0)({\color{red}1},1,1)({\color{red}2},2,2)({\color{red}3},3,3)(4,2,0)</math>。因此末列第二行的 2 的父项只能在含有标红元素的这些列中选取。于是确定 LNZ 的父项为（标绿）：<math>({\color{red}0},0,0)({\color{red}1},{\color{green}1},1)({\color{red}2},2,2)({\color{red}3},3,3)(4,2,0)</math>。因此确定 <math>(1,1,1)</math> 是坏根。好部 G 是 <math>(0,0,0)</math>，坏部 B 是 <math>(1,1,1)(2,2,2)(3,3,3)</math>。计算出阶差向量 <math>\Delta=(3,0,0)</math>。检查 B 中是否存在祖先项不包含坏根中元素的项（当然，我们只需要检查 <math>\Delta</math> 非零的那些行），很幸运，没有。于是我们得到展开式是 <math>(0,0,0)(1,1,1)(2,2,2)(3,3,3)(4,1,1)(5,2,2)(6,3,3)(7,1,1)(8,2,2)(9,3,3)\cdots</math>

例三：<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)(4,2,0,0)(5,1,1,1)(6,2,2,1)(7,3,1,1)</math>

LNZ 是末列第四行的 1。首先确定末列第一行元素 7 的祖先项（标红）：<math>({\color{red}0},0,0,0)({\color{red}1},1,1,1)({\color{red}2},2,2,1)({\color{red}3},3,1,1)({\color{red}4},2,0,0)({\color{red}5},1,1,1)({\color{red}6},2,2,1)(7,3,1,1)</math>。在含有标红元素的列中寻找末列第二行元素 3 的祖先项（标绿）：<math>({\color{red}0},{\color{green}0},0,0)({\color{red}1},1,1,1)({\color{red}2},2,2,1)({\color{red}3},3,1,1)({\color{red}4},2,0,0)({\color{red}5},{\color{green}1},1,1)({\color{red}6},{\color{green}2},2,1)(7,3,1,1)</math>。在含有标绿元素的列中寻找末列第三行元素 1 的祖先项（标蓝）：<math>({\color{red}0},{\color{green}0},{\color{dodgerblue}0},0)({\color{red}1},1,1,1)({\color{red}2},2,2,1)({\color{red}3},3,1,1)({\color{red}4},2,0,0)({\color{red}5},{\color{green}1},1,1)({\color{red}6},{\color{green}2},2,1)(7,3,1,1)</math>。在含有标蓝元素的列中寻找 LNZ 的父项，即首列第四行的 0。于是得到坏根是 <math>(0,0,0,0)</math>，好部 G 是空矩阵，坏部 B 是 <math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)(4,2,0,0)(5,1,1,1)(6,2,2,1)</math>，计算阶差向量 <math>\Delta=(7,3,1,0)</math>。检查 B 中是否存在祖先项不包含坏根中元素的项（只检查 <math>\Delta</math> 非 0 的行）得到第五列第三行的 0 祖先项不经过坏根。于是我们得到展开式是

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)(4,2,{\color{red}0},0)(5,1,1,1)(6,2,2,1)(7,3,1,0)(8,4,2,1)(9,5,3,1)(10,6,2,1)(11,5,{\color{red}0},0)(12,4,2,1)(13,5,3,1)(14,6,2,0)(15,7,3,1)(16,8,4,1)(17,9,3,1)(18,8,{\color{red}0},0)(19,7,3,1)(20,8,4,1)\cdots</math>

展开 BMS 可以靠 [https://gyafun.jp/ln/basmat.cgi Bashicu Matrix Calculator] 或 [https://hypcos.github.io/notation-explorer/ Notation Explorer] 辅助。

=== 数学定义 ===
kotetian 给出 BMS 的数学定义，但是他给出的定义是大数记号版本的。以下是根据他的定义改写的序数记号版 BMS 的定义：

<math>\mathrm{Matrix:}{\boldsymbol S}={\boldsymbol S}_0{\boldsymbol S}_1\cdots{\boldsymbol S}_{X-1}</math>

<math>\mathrm{Vector:}~{\boldsymbol S}_x=(S_{x0},S_{x1},\cdots,S_{x(Y-1)})</math>

<math>\mathrm{parent~of}~{\boldsymbol S}_{xy}:~P_{y}(x)= \begin{cases} \max\{p|p<x\land {\boldsymbol S}_{py}<{\boldsymbol S}_{xy}\land \exists a(p=(P_{y-1})^a(x))\} & \text{if }y>0 \\ \max\{p|p<x\land {\boldsymbol S}_{py}<{\boldsymbol S}_{xy}\} & \text{if }y=0 \end{cases}</math>

<math>\mathrm{Lowermost~nonzero:}~t=\max\{y|{\boldsymbol S}_{(X-1)y}> 0\}</math>

<math>\mathrm{Bad~root:}~r = P_t(X-1)</math>

<math>\mathrm{Ascension~offset:}~\Delta_{y} = \begin{cases} {\boldsymbol S}_{(X-1)y}-{\boldsymbol S}_{ry} & \text{if }y < t \\ 0 & \text{if }y\geq t \end{cases}</math>

<math>\mathrm{Ascension~matrix:}~A_{xy}=\left\{\begin{array}{ll} 1 &(\mathrm{if}~ \exists a( r=(P_{y})^a(r+x)))\\ 0 &(\mathrm{otherwise}) \end{array}\right.</math>

<math>\mathrm{Good~part:}~{\boldsymbol G}={\boldsymbol S}_0{\boldsymbol S}_1\cdots{\boldsymbol S}_{r-1}</math>

<math>\mathrm{Bad~part:}~{\boldsymbol B}^{(a)}={\boldsymbol B}_0^{(a)}{\boldsymbol B}_1^{(a)}\cdots{\boldsymbol B}_{X-2-r}^{(a)}</math>

<math>{\boldsymbol B}_x^{(a)}=(B_{x0}^{(a)},B_{x1}^{(a)},\cdots,B_{x(Y-1)}^{(a)})</math>

<math>B_{xy}^{(a)}=S_{(r+x)y}+a\Delta_{y}A_{xy}</math>

<math>\varnothing=0</math>

<math>\boldsymbol{S} = \begin{cases} \boldsymbol{S}_0\boldsymbol{S}_1\boldsymbol{S}_2\cdots\boldsymbol{S}_{X-2}, & \text{if }\forall y,\boldsymbol{S}_{(X-1)y}=0 \\ \sup\{G,GB^{(0)},GB^{(0)}B^{(1)},GB^{(0)}B^{(1)}B^{(2)},\cdots\} & \text{otherwise} \end{cases}</math>

== 历史 ==
Bashicu 在2015年的时候给出了第一版 BMS 的定义，即 BM1。BM1 创建后的首个问题便是其是否必然终止。这一疑问直到 2016 年用户 KurohaKafka 在日本论坛 2ch.net 发表终止性证明才暂告段落。<ref>http://wc2014.2ch.net/test/read.cgi/math/1448211924/152-155n</ref>然而 Hyp cos 通过构造非终止序列推翻了该证明。<ref>Hyp cos (2016). [https://googology.fandom.com/wiki/Talk:Bashicu_matrix_system?oldid=118833#Something_wrong_happens Talk: Bashicu Matrix System, Something wrong happens]. ''Googology Wiki''.</ref>

为此，Bashicu 发布第二版（BM2），以 BASIC 语言重新实现算法。<ref name=":0" />2018年6月12日，他再次更新定义至 BM3，<ref>Kyodaisuu (2018). [https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:Kyodaisuu/%E3%83%90%E3%82%B7%E3%82%AF%E8%A1%8C%E5%88%97%E6%9C%80%E6%96%B0%E3%83%90%E3%83%BC%E3%82%B8%E3%83%A7%E3%83%B3 Bashiku Matrix Version 3] (バシク行列バージョン3). ''Googology Wiki''.</ref>但当月内 Alemagno12 便发现存在不终止的例证。<ref>Alemagno12 (2018). [https://googology.fandom.com/wiki/User_blog:Alemagno12/BM3_has_an_infinite_loop BM3 has an infinite loop]. ''Googology Wiki''.</ref>

2018 年 11 月 11 日，P進大好きbot 针对 PSS（即行数限制为 2 的 BMS）完成了终止性证明。<ref>P shin daisuki bot (P進大好きbot) (2018). [https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:P%E9%80%B2%E5%A4%A7%E5%A5%BD%E3%81%8Dbot/%E3%83%9A%E3%82%A2%E6%95%B0%E5%88%97%E3%81%AE%E5%81%9C%E6%AD%A2%E6%80%A7 Stopping property of pair sequences] (ペア数列の停止性). ''Googology Wiki''.</ref>

2018 年 8 月 28 日，Bubby3 确认 BM2 确实不会终止。<ref>Bubby3 (2018). [https://googology.fandom.com/wiki/User_blog:Bubby3/BM2_doesn%27t_terminate. BM2 doesn't terminate.]. ''Googology Wiki''.</ref>

Bashicu 最终修正官方定义推出 BM4，此为2018 年 9 月 1 日的最新版本。该版本最终在 2023 年 7 月 12 日被 Racheline（在 googology 社区中曾用名 Yto）证明停机。<ref>Rachel Hunter (2024). [https://arxiv.org/abs/2307.04606 Well-Orderedness of the Bashicu Matrix System]. ''arXiv''.</ref>

尽管 BM4 是最后官方修订版，但 googology 社区已衍生诸多非官方变体，如 BM2.2、BM2.5、BM2.6、BM3.1、BM3.1.1、BM3.2 及 PsiCubed2 版等。<ref>Ecl1psed276 (2018). [https://googology.fandom.com/wiki/User_blog:Ecl1psed276/A_list_of_all_BMS_versions_and_their_differences A list of all BMS versions and their differences]. ''Googology Wiki''.</ref>需注意的是，整数编号版本（1-4）均由 Bashicu 本人定义，其余版本均为他人修改。

由于 BMS 在三行之后出现提升效应造成分析上的极大困难，目前我们仍然在探索理想无提升 BMS（Idealized BMS，IBMS）的定义。[[BM3.3]]一度被认为是符合预期的 IBMS<ref>User blog:Rpakr/Bashicu Matrix Version 3.3 | Googology Wiki | Fandom</ref>，然而目前已经发现了 BM3.3 也具有提升。

=== 争议 ===
test_alpha0 声称 Yto(Racheline)剽窃了他的证明。据test_alpha0所说，他在2022年2月16日在googology wiki上发布了关于 BMS 停机证明的文章<ref>User blog:ReflectingOrdinal/A proof of termination of BMS | Googology Wiki | Fandom</ref>，并在 googology discord 社区回答了相关问题，Racheline 声称他的证明不严谨，但过了一段时间，Racheline在ArXiv上发了证明，框架与 test_alpha0 的证明完全一致。目前尚不清楚 Racheline 的回应。

== 强度分析 ==
主词条：[[BMS分析|BMS 分析]]，[[提升效应]]

BMS 的分析是一项浩大的工程，由于提升效应造成的困难。BMS的分析最初由Bubby3使用[[SAN]]进行，得出了<math>\text{lim(pDAN)}=(0,0,0)(1,1,1)(2,2,0)</math>，后来Yto接手了BMS的分析工作，使用[[稳定序数]]分析到了<math>(0,0,0)(1,1,1)(2,2,2)</math>。国内的YourCpper、bugit等人使用[[投影序数|投影]]进行BMS分析，达到了<math>(0,0,0,0)(1,1,1,1)(2,2,1,1)(3,0,0,0)</math>以上，但这些分析是错误的。后来FENG发现并修正了两人的分析错误，最终完成了BMS与向上投影的分析工作。

这里列举出一些关键节点：

<math>\varnothing=0</math>

<math>(0)=1</math>

<math>(0)(0)=2</math>

<math>(0)(1)=\omega</math>

<math>(0)(1)(1)=\omega^2</math>

<math>(0)(1)(2)=\omega^{\omega}</math>

<math>(0,0)(1,1)=\varepsilon_0</math>

<math>(0,0)(1,1)(1,1)=\varepsilon_1</math>

<math>(0,0)(1,1)(2,0)=\varepsilon_{\omega}</math>

<math>(0,0)(1,1)(2,1)=\zeta_0</math>

<math>(0,0)(1,1)(2,2)=\psi(\Omega_2)</math>

<math>(0,0,0)(1,1,1)=\psi(\Omega_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,1,0)=\psi(\Omega_{\omega}\times\Omega)</math>

<math>(0,0,0)(1,1,1)(2,1,0)(1,1,1)=\psi(\Omega_{\omega}^2)</math>

<math>(0,0,0)(1,1,1)(2,1,1)=\psi(\Omega_{\omega^2})</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)=\psi(I)</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,1)=\psi(I_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)=\psi(M_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,1)=\psi(K_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,2,0)=\psi(psd.\Pi_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,2,1)=\psi(\Pi_1(\lambda\alpha.(\Omega_{\alpha+2})-\Pi_1))</math>

<math>(0,0,0)(1,1,1)(2,2,1)(3,0,0)=\psi(\lambda\alpha.(\Omega_{\alpha+\omega})-\Pi_0)</math>

<math>(0,0,0)(1,1,1)(2,2,1)(3,2,1)=\psi(\Pi_1(\lambda\alpha.(I_{\alpha+1})-\Pi_1))</math>

<math>(0,0,0)(1,1,1)(2,2,1)(3,3,0)=\psi(\lambda\alpha.(\lambda\beta.\beta+1-\Pi_1[\alpha+1])-\Pi_1)</math>

<math>(0,0,0)(1,1,1)(2,2,2)=\psi(psd. \omega-\pi-\Pi_0)=\psi(\psi_\alpha(\alpha_{\omega}))</math>

<math>(0,0,0)(1,1,1)(2,2,2)(3,2,2)=\psi(\psi_\alpha(\alpha_{\omega^2}))</math>

<math>(0,0,0)(1,1,1)(2,2,2)(3,3,0)=\psi(\psi_\alpha(\psi_\beta(\varepsilon_{\alpha_{\beta+1}+1})))</math>

<math>(0,0,0)(1,1,1)(2,2,2)(3,3,3)=\psi(\beta_{\omega})</math>

<math>(0,0,0,0)(1,1,1,1)=\psi(\omega-\text{Projection})=\psi(\psi_S(\sigma S\times \omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,1,1,1)(3,1,0,0)(2,0,0,0)=\psi((1,0)-\text{Projection})=\psi(\psi_S(\sigma S\times S))</math>

<math>(0,0,0,0)(1,1,1,1)(2,1,1,1)(3,1,1,1)=\psi(\psi_S(\sigma S\times S\times\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,0,0)=\psi(\psi_S(\sigma S\times S\times\omega+S_2))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,1,1)=\psi(\psi_S(\sigma S\times S\times\omega+\psi_{S_3}(\sigma S\times S\times\omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,0)=\psi(\psi_S(\sigma S\times S\times\omega+S_\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)=\psi(\psi_S(\sigma S\times S\times\omega^2))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,2,0,0)(4,3,0,0)=\psi(\psi_S(\varepsilon_{\sigma S+1}))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,2,2,0)=\psi(\psi_S(\sigma S_\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,2,2,1)=\psi(\psi_S(\psi_{\sigma\sigma S}(\sigma S_{\sigma \sigma S+1}^2+1)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,0,0)=\psi(\psi_S(\psi_{\sigma\sigma S}(\sigma\sigma S_2)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)=\psi(\psi_S(\psi_{\sigma\sigma S}(S_{\sigma\sigma S_2+1}+\sigma S_{\sigma\sigma S+1}\times(S+1)+\sigma S\times S \times \omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,2,0)=\psi(\psi_S(\psi_{\sigma\sigma S}(S_{\sigma\sigma S_2+1}+\psi_{\sigma\sigma S_2}(S_{\sigma\sigma S_2+1}+1))))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,2,1)=\psi(\psi_S(\psi_{\sigma\sigma S}(S_{\sigma\sigma S_2+2}+1)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,0)=\psi(\psi_S(\psi_{\sigma\sigma S}(\sigma\sigma S_\omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,1)=\psi(\psi_S(\sigma\sigma S\times\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,1)(4,0,0,0)=\psi(\psi_S(\sigma\theta S\times\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,1)(4,4,4,0)=\psi(\psi_S(\psi_{\sigma\sigma\theta S}(\sigma\sigma\theta S_\omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,2)=\psi(\psi_X(\theta X\times\omega))</math>

<math>(0,0,0,0,0)(1,1,1,1,1)=\psi(\psi_H(H^{H^\omega}))</math>

<math>\text{Limit}=\psi(\psi_H(\varepsilon_{H+1}))</math>

<math>(0,0,0,0)(1,1,1,1)</math>被命名为 TSSO（Trio Sequence System Ordinal，三行序列系统序数），<math>(0,0,0,0,0)(1,1,1,1,1)</math>被命名为 QSSO（Quardo Sequence System Ordinal，四行序列系统序数）。BMS 的极限在中文 googology 社区被称为 SHO（Small Hydra Ordinal），但这一命名的起源不明（SHO 最早被用来指代 <math>\varepsilon_0</math>，后来不明不白的变成了 BMS 极限），也是非正式的，因此被部分人拒绝使用。也有人称 BMS 极限为 BMO。

== 来源 ==
{{默认排序:序数记号}}
[[分类:记号]]

LRO

2026-05-15T11:06:38Z

Baixie01000a7：/* 性质 */

LRO（Large Rathjen Ordinal），是一个重要的序数，指代 <math>\rm{psd.}\omega.\rm{ply}-\rm{stb}</math> 折叠后的结果，其真实大小目前尚没有明确结论，主流的观点是 LRO=[[TSSO]]。另一个更常用的版本叫做 pfec.LRO（简称 pLRO），忽略 [[Σ1稳定序数#Non-Gandy 现象|Non-Gandy 现象]]，其大小等于 BMS(0)(1,1,1)(2,2,2)，这个序数又称 SBO（Small Bashicu Ordinal）或 OBO（Omega Back Ordinal）。<ref>BashicuHyudora (2015). バシク行列の解析 [Analysis of the Bashicu matrix]. ''(EB/OL), Googology Wiki''. Available at: https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:BashicuHyudora/%E3%83%90%E3%82%B7%E3%82%AF%E8%A1%8C%E5%88%97%E3%81%AE%E8%A7%A3%E6%9E%90</ref>
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[稳定序数]]
|<math>\psi(\omega.\rm{ply}-\Pi_0)</math>
|-
|[[投影序数]]
|<math>\psi(\psi_\alpha(\alpha_\omega))</math>
|-
|[[UNOCF|Aarex's exUNOCF]]
|<math>\psi(C(1\{:\omega\}0))</math>
|-
|[[BMS]]
|<math>(0)(1,1,1)(2,2,2)</math>
|-
|[[0-Y]]
|<math>1,4,10</math>
|-
|[[Y序列|1-Y]]
|<math>1,2,4,8,15</math>
|-
|[[Ex-hydra]]
|<math>p1(p3(p6))</math>
|-
|[[Fake Fake Fake Zeta]]
|<math>\psi_\Zeta[\varepsilon_1](\rm{BO})</math>
|}

=== 性质 ===
[[证明论序数]]：<math>\Pi_2^1-\rm{CA}_0</math>，<math>\rm{KPnp}</math>（可能是 <math>\mathrm{KP}+\exist N \ \mathrm{admissibles-stable},N\in\omega</math> 的证明论序数<ref>HypCos (n.d.). TON vs. stability (remastered). ''(EB/OL), Googology Wiki''. Available at: https://googology.fandom.com/wiki/User:Hyp_cos/TON_vs._stability_(remastered)#Up_to_%CF%89_admissibles-stable</ref>）

极限在此处的记号：[[LMN]]，[[LON]]，non-recursive FGH，weak DLON，Lumi's LPSS，WDmEN，IUN，CCN，Sudden Hydra，[[Catching 函数|Catching Function]]，2-Proj，A Notation，1-Waiting Hydra

== 参考资料 ==
<references />
[[分类:序数]]

PPS

2026-05-09T14:06:36Z

Baixie01000a7：/* 改版+ PPS 4*/

'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。

PPS有着较为简单的定义，但分析它却极为复杂和困难。

2025年8月，PPS2被发现[[无穷降链]]。

2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。

2026年3月2日，PPS1的良序极限已被证实为<math>\zeta_0</math>。有关良序极限的一些解释，可以见[[用户:Phyrion/PPS|此处]]。

对PPS无穷降链的寻找可使用[https://github.com/hzyhhzy/AutoGuogaoMachine/tree/master 自动果糕机]进行辅助。

后续phyrion在25年圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。

前排提示：PPS的行为极其复杂，是标准的“果糕“记号

=== 定义 ===
以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。

PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）

极限表达式：0,1,2,3,4,5,......

记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x

展开：

1.如果末项是0，则它是后继序数

2.末项之前的部分保持不变

3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1

4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i>x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值

5.基本列[n]为展开到第y+n*L-1项
=== 分析 ===
另见[[PPS分析]]

PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。

=== 地府段 ===
PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。

==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====
[[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]
0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。

它们分别对应序数<math>\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}</math>

和<math>\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}</math>。

几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。

==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====
0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。

不过，它已经被发现了无穷降链，或许这就是第二地府分析困难的原因。

=== 良序极限 ===
PPS的良序极限为

0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9,

3,0,21,19,

3,0,0,3,0,28,18,9,

3,0,33,30,9,

3,0,0,3,0,41,29,18,9,

3,0,47,43,18,9,

3,0,0,3,0,56,42,29,18,9,

3,0,63,58,29,18,9,

3,0,0,3,0,73,57,42,29,18,9,

3,0,81,75,42,29,18,9,

3,0,0,3,0,92,74,57,42,29,18,9,

3,0,101,94,57,42,29,18,9,

3,0,0,3,0,113,93,74,57,42,29,18,9,

3,0,123,115,74,57,42,29,18,9,

3,0,0,3,0,136,114,93,74,57,42,29,18,9,

3,0,147,138,93,74,57,42,29,18,9,

3,0,0,3,0,161,137,114,93,74,57,42,29,18,9,

3,0,173,163,114,93,74,57,42,29,18,9......

它的大小已被确定为ζ_0。

其基本列为：

0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9,3,0,21,18,9,3,0,26=ε_ε_ε_ε_ε_ε_0

0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9,3,0,21,19,3,0,0,3,0,28,18,9,3,0,33,29,18,9,3,0,39=ε_ε_ε_ε_ε_ε_ε_0

0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9,3,0,21,19,3,0,0,3,0,28,18,9,3,0,33,30,9,3,0,0,3,0,41,29,18,9,3,0,47,42,29,18,9,3,0,54=ε_ε_ε_ε_ε_ε_ε_ε_0

0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9,3,0,21,19,3,0,0,3,0,28,18,9,3,0,33,30,9,3,0,0,3,0,41,29,18,9,3,0,47,43,18,9,3,0,0,3,0,56,42,29,18,9,3,0,63,57,42,29,18,9,3,0,71=ε_ε_ε_ε_ε_ε_ε_ε_ε_0

0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9,3,0,21,19,3,0,0,3,0,28,18,9,3,0,33,30,9,3,0,0,3,0,41,29,18,9,3,0,47,43,18,9,3,0,0,3,0,56,42,29,18,9,3,0,63,58,29,18,9,3,0,0,3,0,73,57,42,29,18,9,3,0,81,74,57,42,29,18,9,3,0,90=ε_ε_ε_ε_ε_ε_ε_ε_ε_ε_0

......

=== 改版 ===

==== PPM 1.2 ====
Parented Predecessor Matrix 1,2

极限表达式：(0)(1,1,1,1,1,...)

LNZ：末列的最大非零行序号

坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数

记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y

末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。

弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换

强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)

其他项展开：对任意的i>y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值

基本列[n]为展开到第y+nL-1项

==== PPM 2 ====
Parented Predecessor Matrix 2

极限表达式：(0)(1,1,1,1,1,...)

LNZ：末列的最大非零行序号

坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数

记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y

末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b，则比较[以这个项为首的判断序列]和[以坏根为首的判断序列]的字典序，如果前者大(只要存在一个)∨(坏根不在末项祖先链上∧这样的项存在)则弱展开，如果后者大∨这样的项不存在则强展开。

弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换

强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)

其他项展开：对任意的i>y-L+1，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值

基本列[n]为展开到第y+nL-1项

==== PPM 3 ====
Parented Predecessor Matrix 3

极限表达式：(0)(1,1,1,1,1,...)

LNZ：末列的最大非零行序号

坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数

记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y

末列展开：{

把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。

弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换

强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)

}

末列以右整数个复制单元长度的列展开：强展开时LNZ行元素的值每次复制时增加一个复制单元长度，其他同“其他项展开”

其他项展开：对任意的i>y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值

基本列[n]为展开到第y+nL-1项
==== PPS 4 ====
Parented Predecessor Sequence 4

极限表达式：0,1,2,3,....

坏根：列标是(末项的值)的项（首项的列标是1）；如果末项是0，则表示后继序数

记此时末项的列标减末项的值为L，坏根的值为b，末项的值为x、列标为y

末项展开：

> 如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么是弱展开，否则是强展开；
弱展开：将末项的值换成b；

> 强展开：在第b列和第x列(都不含)之间找到最右侧的值小于等于b的项，将末项的值换为这个项的列标；如果找不到，则等同弱展开

其他项展开：对任意的i>y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值

基本列[n]为展开到第y+nL-1项

{{默认排序:序数记号}}
[[分类:记号]]

iBLP

2026-05-07T11:56:21Z

Baixie01000a7：/* 分析 */

== 记号简介 ==
无限基本Laver图案(Infinite Basic Laver Pattern)是由test_alpha0的记号Basic Laver Pattern改造而来。IBLP目前尚不理想，还存在许多的坏图案。test_alpha0规定其极限表达式为(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,3,2)2(6,5,4)1，因为现在认为在该图案下方不存在坏图案，而其上方不远处就出现了很多坏图案。尽管如此，IBLP仍然被认为是目前最强的记号。本页面介绍的规则对应[https://hypcos.github.io/notation-explorer/ NE]上的DEN2。

== 定义 ==

=== 定义1 （IBLP） ===
一个IBLP是一个四元组<math>A=(n,(A_1,\dots,A_n),(l_1,\dots,l_n),(M_1,\dots,M_n))</math>，

其中：

<math>(1)n\in\N</math>。

<math>(2)</math>对每个<math>i\in\{1,\dots,n\}</math>，<math>A_i</math>是严格递增的非负整数序列，满足<math>\mathrm{len}(A_i)\geq2\text{且}\max(A_i)=i</math>。

<math>(3)</math>对每个<math>i\in\{1,\dots,n\}</math>，步长<math>l_i\in \N</math>。

<math>(4)</math>对每个<math>i\in\{1,\dots,n\}</math>，标记集合<math>M_i\subseteq A_i</math>

约定所有编号从 1 开始；<math>A_i[k]</math> 表示第 ''k'' 个元素，<math>A_i[-j]=A_i[\mathrm{len}(A_i)-j+1]</math>表示倒数第 ''j'' 个元素。

=== 定义2 （长行、中等行、短行） ===
行 <math>i</math> 称为长行若<math>\mathrm{len}(A_i)>2l_i</math>，称为中等行若<math>\mathrm{len}(A_i)=2l_i</math>，称为短行若 <math>\mathrm{len}(A_i)<2l_i</math>。

=== 定义3 （零图案、后继图案、极限图案） ===
若 ''n'' = 0，称 ''A'' 为零图案。若 <math>n>0\text{且}\mathrm{len}(A_n)=2\text{且}\min(A_n)=0</math>，称 ''A'' 为后继图案。否则称 ''A'' 为极限图案。

=== 定义4 （行比较键） ===
令<math>A_i=(A_1<a_2<\dots<a_m)\text{且}L=l_i</math>。定义保留序列

<math>K_i=\begin{cases}(a_1,a_2,\dots,a_m),&L\leq1;\\(a_1,a_{L+1},a_{L+2},\dots,a_m),&2\leq L\leq m;\\(a_1,a_2,\dots,a_m),&L\geq2\text{且}m<L.\end{cases}</math>

定义行键为<math>\overleftarrow{K_i}</math>（即<math>K_i
</math>逆序，从大到小）。

=== 定义5 （IBLP的大小比较） ===
给定两个 ''IBLP'' <math>A\text{、}B</math>，从 <math>i=1</math> 起逐行比较其

行键<math>\overleftarrow{K_i(A)}\text{与}\overleftarrow{K_i(B)}</math> 的字典序；第一处不同决定大小。若前<math>\min(n_a,n_b)</math>行都相等，则行数较小者更小。

=== 定义6 （一行的根<math>p(i)</math>） ===
对<math>i\in\{1,\dots,n\}</math>，定义<math>p(i)=A_i[-(l_i+1)]</math>.

=== 定义7 （传递序列<math>tr_i(j)</math>） ===
固定行 ''i''。若<math>j=A_i[k](1\leq k\leq\mathrm{len}(A_i))\text{且}k\geq l_i</math>，定义阈值 <math>\theta=A_i[k-l_i]</math>。令 <math>t_0=j</math>，并在<math>t_m>\theta\text{且}p(t_m)\text{有定义}</math>时令 <math>t_{m+1}=p(t_m)</math>。若存在最小 <math>m>0</math>使<math>t_m=\theta</math>，则定义<math>tr_i(j)=(t_0,t_1,\dots,t_m)</math>''，''否则称 <math>tr_i(j)</math> 无定义。若 <math>k\leq l_i</math>，亦称无定义。

=== 定义8 （部分函数<math>f_A</math>） ===
设 ''A'' 非零且有至少1行。令 <math>a_1=A_n[1]=\min(A_n)\text{，}L=l_n\text{，}p=p(n)=A_n[-(L+1)]</math>。定义部分函数 <math>f_A:\N\rightharpoonup\N</math>：

<math>(1)</math>若<math>x<a_1</math>，则<math>f_A(x)=x</math>；

<math>(2)</math>若<math>x=A_n[k]\text{且}x<p\text{且}k+L\leq\mathrm{len}(A_n)</math>，则<math>f_A(x)=A_n[k+L]</math>；

<math>(3)</math>若<math>x\geq p</math>，则<math>f_A(x)=x+n-p</math>；

<math>(4)</math>其余情形 <math>f_A(x)</math> 无定义。

=== 定义9 （copy 的行与步长） ===
设 ''A'' 行数为<math>n\geq1</math>，令 <math>p=p(n)</math>。若 copy 过程中出现 <math>f_A(x)</math> 无定义，则<math>copy(A)</math>无定义。否则定义 <math>A'=copy(A)</math> 行数为 <math>n'=2n-p</math>，满足：

<math>(1)</math>对<math>1\leq i\leq n-1\text{：}A_i'=A_i\text{，}l_i'=l_i\text{，}M_i'=M_i</math>；

<math>(2)</math>对每个<math>i\in\{1,\dots,n-p+1\}</math>，令源行<math>\sigma=p+i-1</math>，目标行<math>\tau=n-1+i</math>''i''，定义<math>A_\tau'=\mathrm{sort}(\{f_A(x)|x\in A_\sigma\})\text{，}l_\tau'=l_\sigma</math>，要求<math>\forall x\in A_\sigma\text{，}f_A(x)\text{有定义}</math>。

=== 定义10 （copy的标记过滤） ===
延续上一定义。对目标行<math>\tau</math>中元素<math>x\in A_\tau'</math>，令

<math>y\in A_\sigma</math>为其唯一来源（即 <math>f_A(y)=x</math>）。则 <math>x\in M_\tau'</math> 当且仅当：

<math>y\in M_\sigma</math>，并且满足下列之一：

* <math>tr_\sigma(y)</math>有定义且<math>tr_\sigma(y)[-2]\geq p</math>；
* 令<math>y_0</math>为<math>tr_\sigma(y)</math>中首次出现的<math><p</math>的元素（等价于“最大的
<math><p</math>的元素”）。要么<math>y_0<a_1</math>；要么存在 ''k'' 使<math>y_0=A_n[k]\text{且}k+L\leq\mathrm{len}(A_n)\text{且}A_n[k+L]\in M_n</math>，并且若 ''x'' 在 <math>A_\tau'</math>中的位置为 ''q''（从 1 开始），则当 <math>q+1-l_\sigma\geq1</math> 时需满足<math>A_\tau'[q+1-l_\sigma]\leq a_1.</math>

=== 定义11 （E(A,0)） ===
若 ''A'' 非零且 ''n ≥'' 1，则 ''E''(''A,'' 0) 为删除最后一行后的图案（行数变为 ''n −'' 1，其余行、步长、标记保持不变）。

=== 定义12 （''E''(''A, m'')的copy阶段 (''m≥1)''） ===
设A是极限图案。令<math>A^{(0)}=A</math>。若第一次<math>copy(A^{(0)})</math> 无定义，则称 ''A'' 为坏图案并定义<math>E(A,m)=E(A,0)</math>。否则定义

<math>A^{(1)}=copy(A^{(0)}),A^{(2)}=copy(A^{(1)}),\dots,A^{(m)}=copy(A^{(m-1)})</math>,

并令<math>B=E(A^{(m)},0)</math>

接下来对B做补全，初始行号 <math>r=n</math>（这里 ''n'' 为原始 ''A'' 的行数）。补全过程允许使用临时记录映射 <math>\rm Rec</math>（行号 <math>\mapsto</math> 有限序列），结束后丢弃。

=== 定义13 （标记补全） ===
固定当前行 ''r''。令<math>\mathcal{B}=\{b\in M_r|b\in A_r\}</math>并按升序枚举其元素<math>b_1<b_2<\dots<b_k</math>（该集合在本轮开始时冻结，新产生标记不加入本轮）。对每个 <math>b_i</math>依次：

<math>(1)</math>若 <math>tr_i(b_i)</math>无定义则跳过；

<math>(2)</math>令<math>t=tr_r(b_i)[-2]</math>。若<math>\mathrm{Rec}(t)</math>不存在或为空则跳过，否则记 <math>s=\mathrm{Rec}(t)</math>；

<math>(3)</math>若对所有<math>j=3,4,\dots,\mathrm{len}(tr_r(b_i))</math>都有<math>tr_r(b_i)[-j+1]+1\in A_{tr_r(b_i)[-j]}</math>，那么把s 及<math>b_i+1,b_i+2,\dots,b_i+\mathrm{len}(s)</math> 加入 <math>A_r</math>，并重新排序去重使

之严格递增。更新标记：''s'' 中元素不标记，<math>b_i+1,b_i+2,\dots,b_i+\mathrm{len}(s)</math> 全标

记，其余标记保留（按上述规则修正）。更新步长：<math>l_r=l_r+len(s)</math>。

=== 定义14 （原生补全） ===
固定当前行 ''r''。若<math>A_r</math>为长行，则原生补全不执行并返回 0。否则令<math>p_r=p(r)=A_r[-(l_r+1)]\text{，}a=A_r[-l_r]</math>.

构造序列 ''s''：令 <math>u_0=a</math>，并在<math>A_{u_m}[-2]</math> 存在且 <math>>p_r</math> 时令 <math>u_{m+1}=A_{u_m}[-2]</math>并把 <math>u_{m+1}</math> 追加到 ''s''，直至无法继续。令 <math>t=\mathrm{len}(s)</math>。若 <math>t=0</math> 返回 0；若<math>t>0</math>，令 <math>\mathrm{Rec}(r)=s</math> 并继续：

<math>(1)</math>在 ''r'' 后插入 ''t'' 行，使原本行号 <math>>r</math> 的行号整体加 ''t''；

<math>(2)</math> 仅对原本行号 <math>>r</math>的那些行，在其中把所有 <math>>r</math> 的元素加 ''t''，并同步

标记集合，步长不变；

<math>(3)</math>令旧行及旧步长为 <math>A_r^{old},l_r^{old}</math>。将旧行替换为 ''t'' + 1 行：

<math>A_{r+t}=\mathrm{sort}(A_r^{old}\cup s\cup\{r+1,r+2,\dots,r+t\})\text{，}l_{r+t}=l_r^{old}+t</math>.

标记规则：除s和r+t外均标记。

<math>(4)</math>对<math>i=t,t-1,\dots,1</math>，由<math>A_{r+i}</math>构造 <math>A_{r+i-1}</math>：删除元素<math>r+i</math>，并删除元素 <math>A_{r+i}[-l_{r+i}]</math>，去除<math>r+i-1</math> 的标记，并令 <math>l_{r+i-1}=l_{r+i}-1</math>。

<math>(5)</math>'''中等行例外：'''若<math>i=t</math> 且 ''<math>A_r^{old}</math>''为中等行，则在构造 <math>A_{r+i-1}</math> 时不删除 <math>A_{r+i}[-l_{r+i}]</math>且不减步长（令 <math>l_{r+i-1}=l_{r+i}</math>），但仍删除 <math>r+i</math> 并去除<math>r+i-1</math> 的标记。

原生补全返回t。

=== 定义15 （补全主循环(用于 ''E''(''A, m''))） ===
令初始<math>r=n</math>（''n'' 为原始 ''A'' 的行数）。当 ''r'' 不超过当前 ''B'' 的行数时循环：先对行 ''r'' 执行标记补全，再执行原生补全得到 ''t''，然后更新 <math>r=r+t+1</math>。当 ''r'' 越界时补全结束，丢弃 <math>\rm Rec</math>，所得 ''B'' 即为<math>E(A,m)</math>。

== 展开器 ==
iblp的展开器在[https://hypcos.github.io/notation-explorer/ NE]上可以找到，同时也可以使用如下Python代码直观地看到每个图案的行为。<syntaxhighlight lang="python3">
import bisect

def _clone_rows(rows):
return [row[:] for row in rows]

def _clone_mask(mask):
return [set(s) for s in mask]

def _find_index(sorted_row, val):
i = bisect.bisect_left(sorted_row, val)
if i < len(sorted_row) and sorted_row[i] == val:
return i
return None

def _shift_sorted_row_inplace(sorted_row, threshold, delta):
if delta == 0:
return
i = bisect.bisect_left(sorted_row, threshold)
for j in range(i, len(sorted_row)):
sorted_row[j] += delta

def _shift_mark_set(mark_set, threshold, delta):
if delta == 0 or not mark_set:
return mark_set
new = set()
for x in mark_set:
new.add(x + delta if x >= threshold else x)
return new

class ModifyUnpleasant(Exception):
pass

MSG_UNPLEASANT = (
"Something unpleasant happened. Please contact the author (E-mail: qwerasdfyh@126.com) "
"about the previous pattern so he can improve the rule design."
)

class BasicLaverPattern:
def __init__(self, rows, mask=None):
self.rows = _clone_rows(rows)
if mask is None:
self.mask = [set() for _ in self.rows]
else:
self.mask = _clone_mask(mask)
if self.mask:
self.mask[0] = set()
self._normalize_rows_inplace()

def _normalize_rows_inplace(self, start_row=1):
for r in range(max(1, start_row), len(self.rows)):
row = self.rows[r]
if row and row[-1] == r + 1:
row.pop()
self.mask[r].discard(r + 1)

def clone(self):
return BasicLaverPattern(self.rows, self.mask)

def is_zero(self):
return len(self.rows) == 1 and len(self.rows[0]) == 0

def is_successor(self):
if self.is_zero():
return False
last = self.rows[-1]
return len(last) == 2 and last[0] == 0

def draw(self):
if self.is_zero():
return
base_list = self.rows[0]
other_lists = self.rows[1:]
if not other_lists:
return
max_len = max((seq[-1] for seq in other_lists if seq), default=0) + 1
result = []
for i, seq in enumerate(other_lists, start=1):
line = [' '] * max_len
mset = self.mask[i]
for num in seq:
if 0 <= num < max_len:
line[num] = 'a' if num in mset else 'o'
if i <= len(base_list) and seq:
last_circle_index = seq[-1]
result.append(''.join(line[:last_circle_index + 1]) + f" {base_list[i-1]}")
for line in result:
print(line)

def to_string(self):
if self.is_zero():
return ""
base_list = self.rows[0]
out = []
for i in range(1, len(self.rows)):
seq = self.rows[i]
mset = self.mask[i]
parts = []
for x in reversed(seq):
parts.append(f"*{x}" if x in mset else str(x))
step = base_list[i - 1] if i - 1 < len(base_list) else 0
out.append("(" + ",".join(parts) + ")" + str(step))
return "".join(out)

def cut(self):
if self.is_zero():
return False
if len(self.rows) <= 1:
return False
if len(self.rows[0]) == 0:
self.rows = [[]]
self.mask = [set()]
return False
self.rows[0].pop()
self.rows.pop()
self.mask.pop()
if len(self.rows) == 1 and len(self.rows[0]) == 0:
self.mask = [set()]
self._normalize_rows_inplace()
return True

def _transmission_penultimate_and_terminal_checked(self, row_idx, n_value):
rows = self.rows
base = rows[0]
if n_value <= 0 or n_value >= len(rows):
return None
row = rows[row_idx]
l_m = base[row_idx - 1]
k = _find_index(row, n_value)
if k is None or k - l_m < 0:
return None
threshold = row[k - l_m]

cur = n_value
visited = {cur}
while True:
if cur <= 0 or cur >= len(rows):
return None
l_s = base[cur - 1]
if len(rows[cur]) < l_s + 1:
return None
nxt = rows[cur][-l_s - 1]
if nxt > threshold:
if nxt + 1 != cur + 1:
if _find_index(rows[cur], nxt + 1) is None:
return None
prev, cur = cur, nxt
if cur <= threshold:
return (prev, cur)
if cur in visited:
return None
visited.add(cur)

def _first_not_copied_in_transmission(self, orig_rows, orig_base, copied_set, row_idx, n_value):
row = orig_rows[row_idx]
l_m = orig_base[row_idx - 1]
k = _find_index(row, n_value)
if k is None or k - l_m < 0:
raise RuntimeError("Unpleasant.")
threshold = row[k - l_m]
cur = n_value
seq = [cur]
visited = {cur}
while True:
l_s = orig_base[cur - 1]
if len(orig_rows[cur]) < l_s + 1:
raise RuntimeError("Unpleasant.")
nxt = orig_rows[cur][-l_s - 1]
seq.append(nxt)
cur = nxt
if cur <= threshold:
break
if cur in visited:
raise RuntimeError("Unpleasant.")
visited.add(cur)
t = seq[-2]
terminal = seq[-1]
tprime = None
for x in seq:
if x not in copied_set:
tprime = x
break
return tprime, t, terminal

def _slice_right_block(self, row_idx, anchor, q):
row = self.rows[row_idx]
pos = _find_index(row, anchor)
if pos is None:
raise RuntimeError("Unpleasant.")
block = row[pos + 1: pos + 1 + q]
if len(block) != q:
raise RuntimeError("Unpleasant.")
return block

def _mark_completion_for_row(self, r, meta, native_done):
base = self.rows[0]
row0 = self.rows[r]
initial_marks = [x for x in row0 if x in self.mask[r]]
before = set(row0)
added_total = 0

for n in initial_marks:
if _find_index(self.rows[r], n) is None:
continue
if n <= 0 or n >= len(meta):
continue
info = meta[n]
if not info or not info.get("native_generated", False):
continue

tn = self._transmission_penultimate_and_terminal_checked(r, n)
if tn is None:
continue
t, n_terminal = tn
q = native_done.get(t, 0)
if q <= 0:
continue

target_row = t + q
left_block = self._slice_right_block(target_row, n_terminal, q)
right_block = list(range(n + 1, n + q + 1))

new_vals = set(left_block) | set(right_block)
truly_new = new_vals - before
if truly_new:
added_total += len(truly_new)
before |= truly_new

row_set = set(self.rows[r])
row_set.update(new_vals)
self.rows[r] = sorted(row_set)

self.mask[r].difference_update(left_block)
self.mask[r].update(right_block)

if added_total > 0:
base[r - 1] += (added_total // 2)

def _shift_values_ge(self, start_row_idx, threshold, delta):
for i in range(start_row_idx, len(self.rows)):
_shift_sorted_row_inplace(self.rows[i], threshold, delta)
self.mask[i] = _shift_mark_set(self.mask[i], threshold, delta)

def _native_completion_step(self, m, meta):
rows = self.rows
base = rows[0]
l = base[m - 1]
e = len(rows[m])

if e > 2 * l:
return False, 0

if l <= 0 or e < l:
return False, 0

s = [rows[m][-l]]
while True:
if s[-1] <= 0 or s[-1] >= len(rows):
return False, 0
if len(rows[s[-1]]) < 2:
return False, 0
s.append(rows[s[-1]][-2])
if len(rows[m]) < l + 1:
return False, 0
if s[-1] <= rows[m][-l - 1]:
break

k = len(s) - 1
if k == 1:
return False, 0
s.pop()
q = k - 1
if q <= 0:
return False, 0

marks_m_orig = set(self.mask[m])
self._shift_values_ge(m, m + 1, q)

if e == 2 * l:
c = rows[m][:]
else:
c = rows[m][:l - 1] + rows[m][l:]

ext = s[1:][::-1] + list(range(m + 1, m + q + 1))
rows[m].extend(ext)
rows[m].sort()
base[m - 1] += q

d = []
for i in range(q):
d_i = c + s[q - i:] + list(range(m + 1, m + i + 2))
d.append(sorted(d_i))

old_e = e + 1
base[:] = base[:m - 1] + list(range(old_e - l, old_e - l + q)) + base[m - 1:]
rows[:] = rows[:m] + d + rows[m:]
self.mask[:] = self.mask[:m] + [set() for _ in range(q)] + self.mask[m:]

meta_insert = [{"native_generated": True, "native_q": q} for _ in range(q)]
meta[:] = meta[:m] + meta_insert + meta[m:]

marks_to_propagate = {x + q if x >= m + 1 else x for x in marks_m_orig}
for row_idx in range(m, m + q + 1):
self.mask[row_idx].update(marks_to_propagate)
for j in range(1, q + 1):
self.mask[m + j].update(range(m, m + j))

self.mask[m + q].discard(m + 1 + q)
self._normalize_rows_inplace(start_row=m)
return True, q

def modify(self, copy_only=False, silent=False):
try:
orig_rows = _clone_rows(self.rows)
orig_mask = _clone_mask(self.mask)
orig_base = orig_rows[0][:]
orig_last_mask = set(orig_mask[-1]) if orig_mask else set()

rows = self.rows
base0 = rows[0]
n_before_cut = len(base0)
l_last = base0[n_before_cut - 1]
b = rows[-1][:]
b0 = b[0]
p_leftmost = b[0]

self.cut()
rows = self.rows
base0 = rows[0]

u = b[-l_last - 1]
v_copy = n_before_cut
base0.extend(orig_base[u - 1: v_copy])

b_map = {}
limit = len(b) - l_last
for i in range(limit):
key = b[i]
if key not in b_map:
b_map[key] = b[i + l_last]

def map_elem(x):
if x < b0:
return x
if x > u:
return x - u + n_before_cut
return b_map.get(x, -1)

copied_set = set(range(u, v_copy + 1))

for row_idx in range(u, v_copy + 1):
src_row = orig_rows[row_idx]
new_seq = []
for elem in src_row:
new_val = map_elem(elem)
if new_val == -1:
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
new_seq.append(new_val)
new_seq.sort()
rows.append(new_seq)

new_marks = set()
src_marks = orig_mask[row_idx]
if src_marks:
l_m = orig_base[row_idx - 1]
for marked_val in src_marks:
if _find_index(orig_rows[row_idx], marked_val) is None:
continue
tprime, t, _terminal = self._first_not_copied_in_transmission(
orig_rows, orig_base, copied_set, row_idx, marked_val
)
keep = False
if t in copied_set:
keep = True
else:
if tprime is not None and tprime < p_leftmost:
keep = True
elif tprime is not None:
u_img = b_map.get(tprime, None)
if u_img is not None and u_img in orig_last_mask:
mv_img = map_elem(marked_val)
if mv_img != -1:
pos_u = _find_index(new_seq, mv_img)
if pos_u is not None:
idx_check = pos_u - l_m + 1
if idx_check >= 0 and new_seq[idx_check] <= p_leftmost:
keep = True
if keep:
new_marks.add(map_elem(marked_val))
self.mask.append(new_marks)

if copy_only:
self._normalize_rows_inplace()
return self.clone()

meta = [None] * len(self.rows)
native_done = {}

m = n_before_cut
while True:
base0 = self.rows[0]
if m > len(base0):
break
self._mark_completion_for_row(m, meta, native_done)
did, q = self._native_completion_step(m, meta)
if did:
native_done[m] = q
m += q + 1
else:
m += 1

self._normalize_rows_inplace()
return self.clone()

except ModifyUnpleasant:
raise
except RuntimeError as e:
if str(e) == "Unpleasant.":
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
raise

initial_rows = [
[1, 1, 2, 2, 2],
[0, 1],
[0, 1, 2],
[0, 1, 2, 3],
[0, 1, 2, 3, 4],
[2, 3, 4, 5]
]
initial_mask = [set() for _ in initial_rows]
initial_mask[4] = {3}

def _encode_expr(pat: BasicLaverPattern):
base = pat.rows[0]
expr = []
for i in range(1, len(pat.rows)):
L = base[i - 1] if (i - 1) < len(base) else 0
vals_desc = list(reversed(pat.rows[i]))
mset = pat.mask[i]
row = [L] + [[v, (v in mset)] for v in vals_desc]
expr.append(row)
return expr

def _decode_expr(expr):
base = [row[0] for row in expr]
rows = [base]
mask = [set()]
for row in expr:
vals = [x[0] for x in row[1:]]
vals = sorted(set(vals))
rows.append(vals)
mask.append({x[0] for x in row[1:] if x[1]})
return BasicLaverPattern(rows, mask)

def _deepcopy_expr(expr):
return [[row[0]] + [[x[0], bool(x[1])] for x in row[1:]] for row in expr]

def _values(row):
return [row[0]] + [x[0] for x in row[1:]]

def _cut_expr(expr):
return _deepcopy_expr(expr[:-1])

def _pleasant_until(rows, t):
tv = _values(t)
L = t[0]
tcheck = tv[1 + L:]
if not tcheck:
return -1

tmax = tcheck[0]
tmin = tcheck[-1]
tset = set(tcheck)

for n, s in enumerate(rows):
scheck = _values(s)[1:]
i1 = -1
for idx, x in enumerate(scheck):
if x < tmax:
i1 = idx
break
i2 = -1
for idx in range(len(scheck) - 1, -1, -1):
if scheck[idx] > tmin:
i2 = idx
break

if i1 != -1 and i2 != -1 and i1 <= i2:
mid = scheck[i1:i2 + 1]
if any(x not in tset for x in mid):
return n
return -1

def _seq_from(expr, i, j):
row = expr[i]
val = row[j][0]
L = row[0]
threshold = row[j + L][0] if (j + L) < len(row) else 0

record = [[i + 1, j], [val]]
while val > threshold:
row = expr[val - 1]
idx = 1 + row[0]
record[-1].append(idx)
val = row[idx][0] if idx < len(row) else 0
record.append([val])

record.pop()
return record

def _apv(s_vals, t_vals):
L = t_vals[0]
t_last = t_vals[-1]
t_1 = t_vals[1]
t_1L = t_vals[1 + L] if (1 + L) < len(t_vals) else 0

out = []
for x in s_vals:
if x < t_last:
out.append(x)
elif x >= t_1L:
out.append(x - t_1L + t_1)
else:
k = -1
for idx in range(len(t_vals) - 1, -1, -1):
if t_vals[idx] == x:
k = idx
break
out.append(None if k == -1 else t_vals[k - L])
return out

def _ap(row_s, row_t):
svals = _values(row_s)[1:]
tvals = _values(row_t)
mapped = _apv(svals, tvals)
return [row_s[0]] + [[x, False] for x in mapped]

def _copy_block(raw, flag):
active = raw[-1]
expr = _cut_expr(raw)

begin = active[1 + active[0]][0]
end = (begin + flag) if (flag != -1) else (len(raw) + 1)
offset = len(raw) - begin

expr.extend([_ap(row, active) for row in raw[begin - 1:end - 1]])

active_min = active[-1][0]
begin_rowno = begin

for i in range(begin - 1, end - 1):
row = raw[i]
target_row = expr[i + offset]
for j in range(1, len(row)):
if not row[j][1]:
continue

seq = _seq_from(raw, i, j)

nomove = -1
for k, item in enumerate(seq):
if item[0] < begin_rowno:
nomove = k
break

if nomove == -1:
target_row[j][1] = True
continue

if seq[nomove][0] < active_min:
target_row[j][1] = True
continue

c = seq[nomove - 1][0] + offset
rowc = expr[c - 1]
b = rowc[seq[nomove - 1][1]][0]

idx_check = j + target_row[0] - 1
left_ok = (idx_check < len(target_row)) and (target_row[idx_check][0] <= active_min)
active_has_b_mark = any((x[0] == b and x[1]) for x in active[1:])

if left_ok and active_has_b_mark:
target_row[j][1] = True

return expr

def _comp_to(raw, r, already):
expr = _deepcopy_expr(raw)
for j in range(len(raw[r]) - 1, 0, -1):
if not raw[r][j][1]:
continue
n = raw[r][j][0]
seq = _seq_from(raw, r, j)
t = seq[-1][0]
T = already[t - 1] if (t - 1) < len(already) else None
if not T:
continue
q = len(T)
entries = (
[[x[0], bool(x[1])] for x in expr[r][1:]] +
[[x, False] for x in T] +
[[n + 1 + uu, True] for uu in range(q)]
)
entries.sort(key=lambda z: z[0], reverse=True)
expr[r] = [expr[r][0] + q] + entries
return expr

def _comp_from(raw, r, T):
q = len(T)

expr = [[row[0]] + [[x[0], bool(x[1])] for x in row[1:]] for row in raw[:r]]

if len(raw[r]) < raw[r][0] * 2 + 1:
lr = raw[r][0]
cr = raw[r][1:-raw[r][0]] + raw[r][1 + raw[r][0]:]
else:
lr = raw[r][0] + 1
cr = raw[r][1:]

need_len = r + q + 1
if len(expr) < need_len:
expr.extend([None] * (need_len - len(expr)))

for qq in range(q):
entries = (
[[x[0], bool(x[1])] for x in cr] +
[[x, False] for x in T[:1 + qq]] +
[[raw[r][1][0] + 1 + uu, False] for uu in range(qq)]
)
entries.sort(key=lambda z: z[0], reverse=True)
expr[r + qq] = [lr + qq] + entries

entries = (
[[x[0], bool(x[1])] for x in raw[r][1:]] +
[[x, False] for x in T] +
[[raw[r][1][0] + 1 + uu, False] for uu in range(q)]
)
entries.sort(key=lambda z: z[0], reverse=True)
expr[r + q] = [raw[r][0] + q] + entries

for qq in range(1, q + 1):
for uu in range(2, 1 + qq + 1):
expr[r + qq][uu][1] = True

threshold = raw[r][1][0]

def m(entry, idx):
if idx == 0:
return entry
vv = entry[0]
if vv <= threshold:
return [vv, bool(entry[1])]
return [vv + q, bool(entry[1])]

for row in raw[r + 1:]:
new_row = []
for idx, entry in enumerate(row):
new_row.append(m(entry, idx))
expr.append(new_row)

return expr

def _expand_pleasant_only(raw, FSterm, longer=False):
if FSterm < 0:
FSterm = 0

active = raw[-1]
L = active[0]
if (1 + L) >= len(active) or (active[1 + L][0] == 0):
return _cut_expr(raw)

begin = active[1 + L][0]
flag = _pleasant_until(raw[begin - 1:-1], active)
if flag != -1:
raise ModifyUnpleasant

expr = _deepcopy_expr(raw)
for _ in range(FSterm):
expr = _copy_block(expr, -1)

expr = _copy_block(expr, 1) if longer else _cut_expr(expr)

already = []
r = len(raw) - 1
while r < len(expr):
expr = _comp_to(expr, r, already)

if not (len(expr[r]) <= expr[r][0] * 2 + 1):
r += 1
continue

idx0 = expr[r][expr[r][0]][0]
T = [idx0]
bound = expr[r][expr[r][0] + 1][0]

while T[0] > bound:
rr = T[0] - 1
T.insert(0, expr[rr][2][0])

T = T[1:-1]
if len(T) < 1:
r += 1
continue

expr = _comp_from(expr, r, T)

while len(already) <= r:
already.append(None)
already[r] = T

r += len(T) + 1

return expr

def _expand_like_model(pattern: BasicLaverPattern, FSterm: int, longer: bool, silent: bool):
if pattern.is_zero():
return pattern.clone(), 0
if pattern.is_successor():
q = pattern.clone()
q.cut()
return q, 0

base0 = pattern.rows[0]
if not base0:
q = pattern.clone()
q.cut()
return q, 0

if FSterm <= 0:
q = pattern.clone()
q.cut()
return q, 0

try:
raw = _encode_expr(pattern)
res = _expand_pleasant_only(raw, FSterm=FSterm, longer=longer)
p2 = _decode_expr(res)
return p2.clone(), 1
except ModifyUnpleasant:
if not silent:
print(MSG_UNPLEASANT)
q = pattern.clone()
q.cut()
return q, 0

def _apply_special_one(pattern: BasicLaverPattern, silent=False):
if pattern.is_zero():
return pattern.clone(), 0
if pattern.is_successor():
p = pattern.clone()
p.cut()
return p, 0

p = pattern.clone()
try:
orig_rows = _clone_rows(p.rows)
orig_mask = _clone_mask(p.mask)
orig_base = orig_rows[0][:]
orig_last_mask = set(orig_mask[-1]) if orig_mask else set()

rows = p.rows
base0 = rows[0]
n_before_cut = len(base0)
if n_before_cut <= 0:
p2 = p.clone()
p2.cut()
return p2, 0

original_total_rows = len(rows)

l_last = base0[n_before_cut - 1]
b = rows[-1][:]
if not b:
p2 = p.clone()
p2.cut()
return p2, 0
b0 = b[0]
p_leftmost = b[0]

p.cut()
rows = p.rows
base0 = rows[0]

if l_last < 0 or len(b) < l_last + 1:
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
u = b[-l_last - 1]

if u - 1 < 0 or u - 1 >= len(orig_base):
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
base0.append(orig_base[u - 1])

b_map = {}
limit = len(b) - l_last
for i in range(limit):
key = b[i]
if key not in b_map:
b_map[key] = b[i + l_last]

def map_elem(x):
if x < b0:
return x
if x > u:
return x - u + n_before_cut
return b_map.get(x, -1)

copied_set = {u}

if u <= 0 or u >= len(orig_rows):
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant

src_row = orig_rows[u]
new_seq = []
for elem in src_row:
new_val = map_elem(elem)
if new_val == -1:
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
new_seq.append(new_val)
new_seq.sort()
rows.append(new_seq)

new_marks = set()
src_marks = orig_mask[u]
if src_marks:
l_m = orig_base[u - 1]
for marked_val in src_marks:
if _find_index(orig_rows[u], marked_val) is None:
continue
tprime, t, _terminal = p._first_not_copied_in_transmission(
orig_rows, orig_base, copied_set, u, marked_val
)
keep = False
if t in copied_set:
keep = True
else:
if tprime is not None and tprime < p_leftmost:
keep = True
elif tprime is not None:
u_img = b_map.get(tprime, None)
if u_img is not None and u_img in orig_last_mask:
mv_img = map_elem(marked_val)
if mv_img != -1:
pos_u = _find_index(new_seq, mv_img)
if pos_u is not None:
idx_check = pos_u - l_m + 1
if idx_check >= 0 and new_seq[idx_check] <= p_leftmost:
keep = True
if keep:
mv = map_elem(marked_val)
if mv != -1:
new_marks.add(mv)

p.mask.append(new_marks)
p._normalize_rows_inplace(start_row=len(p.rows) - 1)

meta = [None] * len(p.rows)
m = len(p.rows[0])
did, q = p._native_completion_step(m, meta)

if did and q > 0:
for _ in range(q):
p.cut()

while len(p.rows) > original_total_rows:
p.cut()

p._normalize_rows_inplace()
return p.clone(), 1

except ModifyUnpleasant:
q = pattern.clone()
q.cut()
return q, 0
except RuntimeError as e:
if str(e) == "Unpleasant.":
if not silent:
print(MSG_UNPLEASANT)
q = pattern.clone()
q.cut()
return q, 0
raise

def _apply_number(pattern, n, silent=False):
if pattern.is_zero():
return pattern.clone(), 0

if n == 0:
p = pattern.clone()
p.cut()
return p, 0

if pattern.is_successor():
p = pattern.clone()
p.cut()
return p, 0

if n == 1:
return _apply_special_one(pattern, silent=silent)

FSterm = n - 1
nxt, ok = _expand_like_model(pattern, FSterm=FSterm, longer=False, silent=silent)
if ok == 0:
return nxt, 0
return nxt, n

def reconstruct_pattern_list(op_numbers, silent=False):
pattern_list = [BasicLaverPattern(initial_rows, initial_mask)]
executed = []
for n in op_numbers:
cur = pattern_list[-1]
nxt, actual = _apply_number(cur, n, silent=silent)
executed.append(actual)
pattern_list.append(nxt)
return executed, pattern_list, None

def _cmp_lists(a, b):
la, lb = len(a), len(b)
m = la if la < lb else lb
for i in range(m):
if a[i] < b[i]:
return -1
if a[i] > b[i]:
return 1
if la < lb:
return -1
if la > lb:
return 1
return 0

def _row_key_for_compare(pat, row_idx):
base = pat.rows[0]
row = pat.rows[row_idx]
l = base[row_idx - 1] if row_idx - 1 < len(base) else 0
if l <= 1:
keep = row[:]
else:
if len(row) < l:
keep = row[:]
else:
keep = [row[0]] + row[l:]
keep = keep[::-1]
return keep

def compare_patterns(a, b):
ra = len(a.rows) - 1
rb = len(b.rows) - 1
m = ra if ra < rb else rb
for i in range(1, m + 1):
ka = _row_key_for_compare(a, i)
kb = _row_key_for_compare(b, i)
c = _cmp_lists(ka, kb)
if c != 0:
return c
if ra < rb:
return -1
if ra > rb:
return 1
return 0

def _is_prefix(seg, full):
if len(seg.rows) > len(full.rows):
return False
if seg.rows[0] != full.rows[0][:len(seg.rows[0])]:
return False
for i in range(1, len(seg.rows)):
if seg.rows[i] != full.rows[i]:
return False
return True

def _is_proper_prefix(seg, full):
return _is_prefix(seg, full) and (len(seg.rows) < len(full.rows))

def _pattern_equal(a: BasicLaverPattern, b: BasicLaverPattern):
return a.rows == b.rows and a.mask == b.mask

def _pattern_signature(p: BasicLaverPattern):
rows_sig = tuple(tuple(r) for r in p.rows)
mask_sig = tuple(tuple(sorted(s)) for s in p.mask)
return rows_sig, mask_sig

_EXPAND_COUNTS_CACHE = {}

def _expand_row_counts_from(start_pat: BasicLaverPattern, n: int):
if n < 0:
n = 0
key = (_pattern_signature(start_pat), n)
if key in _EXPAND_COUNTS_CACHE:
return _EXPAND_COUNTS_CACHE[key][:]

counts = [len(start_pat.rows)]
for k in range(1, n + 1):
res, _act = _apply_number(start_pat, k, silent=True)
counts.append(len(res.rows))

_EXPAND_COUNTS_CACHE[key] = counts[:]
return counts

def _simplify(op_numbers, pattern_list):
target = pattern_list[-1].clone()

s = op_numbers[:]
executed, pats, _ = reconstruct_pattern_list(s, silent=True)
s = executed
pattern_list = pats

i = len(s) - 1
while i >= 0:
if i >= len(s):
i = len(s) - 1
if i < 0:
break
if s[i] == 0:
i -= 1
continue

while True:
if i >= len(s):
break
n = s[i]

z = 0
j = i + 1
while j < len(s) and s[j] == 0:
z += 1
j += 1

candidate = None
need = None

if n == 1:
if z >= 1:
candidate = s[:i] + s[i + 1:]
else:
break
else:
start_pat = pattern_list[i]
counts = _expand_row_counts_from(start_pat, n)
need = counts[n] - counts[n - 1]
if need < 0:
need = 0

if z < need:
break

candidate = s[:]
candidate[i] = n - 1
if need > 0:
del candidate[i + 1: i + 1 + need]

cand_exec, cand_pats, _ = reconstruct_pattern_list(candidate, silent=True)
if not cand_pats or not _pattern_equal(cand_pats[-1], target):
break

s = cand_exec
pattern_list = cand_pats

if i >= len(s):
break
if s[i] == 0:
break

i = min(i, len(s) - 1)
i -= 1
while i >= 0 and s[i] == 0:
i -= 1

executed, pattern_list, _ = reconstruct_pattern_list(s, silent=True)
return executed, pattern_list

def _seq_str(nums):
return ",".join(str(x) for x in nums)

def _parse_o_string(s):
s = s.strip()
if s == "":
return BasicLaverPattern([[]], [set()]), None

pos = 0
rows_desc = []
steps = []
n = len(s)

while pos < n:
if s[pos] != "(":
return None, "error"
pos += 1
close = s.find(")", pos)
if close == -1:
return None, "error"
inside = s[pos:close].strip()
pos = close + 1

nums = []
if inside != "":
parts = inside.split(",")
for part in parts:
part = part.strip()
if part.startswith("*"):
part = part[1:].strip()
if part == "" or (not part.isdigit()):
return None, "error"
nums.append(int(part))

nums_asc = sorted(nums)
for i in range(1, len(nums_asc)):
if nums_asc[i] == nums_asc[i - 1]:
return None, "error"

if pos >= n or (not s[pos].isdigit()):
return None, "error"
j = pos
while j < n and s[j].isdigit():
j += 1
step = int(s[pos:j])
pos = j

rows_desc.append(nums_asc)
steps.append(step)

rows = [steps[:]] + rows_desc
mask = [set()] + [set() for _ in rows_desc]
return BasicLaverPattern(rows, mask), None

def _read_find_pattern(I):
initial = BasicLaverPattern(initial_rows, initial_mask)
C = initial.clone()

ops = []
pats = [C.clone()]

if compare_patterns(C, I) <= 0:
return C, ops, pats

MAX_OUTER = 50000
MAX_N = 20000
outer = 0

while outer < MAX_OUTER:
outer += 1

if compare_patterns(C, I) == 0:
return C, ops, pats

n = 0
while n <= MAX_N:
Cn, actual = _apply_number(C, n, silent=True)

if _is_proper_prefix(Cn, I):
n += 1
continue

if (compare_patterns(Cn, I) < 0) and (not _is_prefix(Cn, I)):
return C, ops, pats

if compare_patterns(Cn, I) >= 0:
if Cn.rows == C.rows and Cn.mask == C.mask:
return C, ops, pats
C = Cn
ops.append(actual)
pats.append(C.clone())
break

n += 1

else:
return C, ops, pats

return C, ops, pats

def main_program():
op_numbers = []
executed, pattern_list, _ = reconstruct_pattern_list(op_numbers, silent=True)
op_numbers = executed

while True:
cur = pattern_list[-1]
print("\nCurrent pattern:")
if cur.is_zero():
print("(empty)")
else:
cur.draw()

print(f"Operation sequence: {_seq_str(op_numbers)}")

if cur.is_zero():
pattern_type = "Zero"
elif cur.is_successor():
pattern_type = "Successor"
else:
pattern_type = "Limit"

msg = f"This is a {pattern_type} pattern."
msg += " Natural Number: Operation."
msg += " O: Output."
msg += " R: Read."
if len(pattern_list) > 1:
msg += " U: Undo."
msg += " S: Simplify."
msg += " I: Input operations."
print(msg)

user_input = input("Enter your operation: ").strip().upper()

if user_input.isdigit():
n_in = int(user_input)
nxt, actual = _apply_number(cur, n_in, silent=False)
pattern_list.append(nxt)
op_numbers.append(actual)
if actual == 0:
print("Applied cut operation.")
else:
print(f"Applied operation {actual}.")
continue

if user_input == 'O':
print(cur.to_string())
continue

if user_input == 'R':
raw = input("Input pattern string (from O): ").strip()
pat, err = _parse_o_string(raw)
if err:
print("error")
continue
found, ops, pats = _read_find_pattern(pat)
op_numbers = ops
pattern_list = pats
print(found.to_string())
continue

if user_input == 'U' and len(pattern_list) > 1:
op_numbers = op_numbers[:-1]
executed, pattern_list, _ = reconstruct_pattern_list(op_numbers, silent=True)
op_numbers = executed
print("Undo the last operation.")
continue

if user_input == 'S':
new_ops, new_patterns = _simplify(op_numbers, pattern_list)
if new_ops != op_numbers:
op_numbers = new_ops
pattern_list = new_patterns
print(f"Simplified operation sequence: {_seq_str(op_numbers)}")
else:
print("No further simplifications possible.")
continue

if user_input == 'I':
raw = input("Input the operation sequence (comma-separated natural numbers, e.g., 3,0,2,1): ").strip()
if raw == "":
parsed = []
else:
parts = [p.strip() for p in raw.split(",")]
if any(p == "" or (not p.isdigit()) for p in parts):
print("error")
continue
parsed = [int(p) for p in parts]
executed, pattern_list, _ = reconstruct_pattern_list(parsed, silent=True)
op_numbers = executed
continue

print("Invalid operation. Please try again.")

if __name__ == "__main__":
main_program()

</syntaxhighlight>

== 分析 ==
另见[[IBLP分析Part1]] [[IBLP分析Part2]] [[IBLP分析Part3]] [[IBLP分析Part4]]。

目前iBLP的分析已经到达(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,3,2)2(6,5)1，对应ω-Y极限。
{| class="wikitable"
|+
!ω-Y序列
!iBLP
|-
|1,2
|(1,0)1(2,1)1
|-
|1,2,4
|(1,0)1(2,1,0)1
|-
|1,2,4,8
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3
|-
|1,2,4,8,16
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4
|-
|1,3
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1
|-
|1,3,4,3
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1
|-
|1,3,7
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*9,*8,5,4,3,2,1,0)5
|-
|1,3,9
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*10,*9,*8,5,4,3,2,1,0)5
|-
|1,3,10
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,4)1
|-
|1,4
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,3,2)2
|-
|1,5
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,3,2)2(6,4,3,2)2
|-
|1,6
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,3,2)2(6,4,3,2)2(7,4,3,2)2
|-
|Limit
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,3,2)2(6,5)1
|}

{{默认排序:序数记号}}
[[分类:记号]]

序数超运算

2026-05-04T06:59:32Z

Baixie01000a7：

序数超运算是对序数使用[[超运算序列|超运算]]的尝试。它虽然是最直观、新人最容易想到的模式，但已经被长期的[[Googology]]实践所证明是低效、难以扩展的。

== 原定义 ==
首先，我们仿照[[高德纳箭头]]在自然数上的定义和[[序数#序数的运算|序数运算]]的定义，给出序数使用高德纳箭头的定义：

# <math>\alpha\uparrow^1\beta=\alpha^{\beta}</math>
# <math>\alpha\uparrow^c1=\alpha</math>
# <math>\alpha\uparrow^{c+1}(\beta+1)=\alpha\uparrow^c(\alpha\uparrow^{c+1}\beta)</math>
# <math>\alpha\uparrow^c\lambda=\sup\{\alpha\uparrow^c\beta|\beta<\lambda\}</math>

其中<math>\alpha,\beta</math>是任意序数，c是自然数，<math>\lambda</math>是非0极限序数。

这样一来，就有<math>\omega\uparrow^2(\omega+1)=\omega^{\omega\uparrow^2\omega}=\sup\{\omega^{\omega\uparrow^2n}|n<\omega\}=\sup\{\omega\uparrow^2n|n<\omega\}=\omega\uparrow^2\omega</math>.进一步，对任意<math>\beta\geq\omega</math>，都有<math>\omega\uparrow^2\beta=\omega\uparrow^2\omega</math>.再进一步，对任意的<math>c\geq2,\beta\geq\omega</math>,都有<math>\omega\uparrow^c\beta=\omega\uparrow^2\omega</math>.

这显然不是我们所期待的。

== 左结合法 ==
第一种试图解决问题的方案是左结合法。它借鉴了[[下箭号表示法|下箭头表示法]]，给出序数使用下箭头的定义：

# <math>\alpha\downarrow^1\beta=\alpha^{\beta}</math>
# <math>\alpha\downarrow^c1=\alpha</math>
# <math>\alpha\downarrow^{c+1}(\beta+1)=(\alpha\downarrow^{c+1}\beta)\downarrow\alpha</math>
# <math>\alpha\downarrow^c\lambda=\sup\{\alpha\downarrow^c\beta|\beta<\lambda\}</math>

其中<math>\alpha,\beta</math>是任意序数，c是自然数，<math>\lambda</math>是非0极限序数。

于是有：

<math>\omega\downarrow^22=\omega^\omega
</math>

<math>\omega\downarrow^23=\omega^{\omega^2}</math>

<math>\omega\downarrow^2\omega=\omega^{\omega^\omega}</math>

<math>(\omega\downarrow^2\omega)\downarrow^22=\omega^{\omega^{\omega^\omega}}</math>

<math>\omega\downarrow^33=\omega^{\omega^{\omega^{\omega^\omega}}}</math>

<math>\omega\downarrow^34=\omega^{\omega^{\omega^{\omega^{\omega^{\omega^\omega}}}}}</math>

<math>\omega\downarrow^3\omega=\varepsilon_0</math>

<math>(\omega\downarrow^3\omega)\downarrow^22=\varepsilon_0^{\varepsilon_0}</math>

<math>(\omega\downarrow^3\omega)\downarrow^2\omega=\varepsilon_0^{\varepsilon_0^\omega}</math>

<math>(\omega\downarrow^3\omega)\downarrow^32=\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}</math>

<math>(\omega\downarrow^3\omega)\downarrow^33=\varepsilon_0^{\varepsilon_0^{\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}}}</math>

<math>\omega\downarrow^43=\varepsilon_1</math>

<math>\omega\downarrow^44=\varepsilon_2</math>

<math>\omega\downarrow^4\omega=\varepsilon_\omega</math>

<math>(\omega\downarrow^4\omega)\downarrow^3\omega=\varepsilon_{\omega+1}</math>

<math>(\omega\downarrow^4\omega)\downarrow^42=\varepsilon_{\varepsilon_\omega}</math>

<math>(\omega\downarrow^4\omega)\downarrow^43=\varepsilon_{\varepsilon_\omega2}</math>

<math>\omega\downarrow^53=\varepsilon_{\varepsilon_\omega\omega}</math>

<math>\omega\downarrow^54=\varepsilon_{\varepsilon_{\varepsilon_\omega\omega}\omega}</math>

<math>\omega\downarrow^5\omega=\zeta_0</math>

<math>\omega\downarrow^6\omega=\zeta_\omega</math>

<math>\omega\downarrow^7\omega=\varphi(3,0)</math>

<math>\omega\downarrow^{1+2n}\omega=\varphi(n,0)</math>

把下箭头用到序数上，其极限为<math>\varphi(\omega,0)</math>，也符合箭头运算的强度。

但是，左结合的下箭头行为和高德纳箭头差异还是不小，而且两个箭头对应一个<math>\varphi(n,0)</math>还是不太符合我们的预期。

== 攀爬法 ==
第二种试图解决问题的方案是攀爬法。攀爬法提供了一种更强的推广。我们知道，<math>\varepsilon_1</math>的基本列是<math>\{\varepsilon_0+1,\omega^{\varepsilon_0+1},\omega^{\omega^{\varepsilon_0+1}},\omega^{\omega^{\omega^{\varepsilon_0+1}}},\cdots\}</math>，我们可以将其表示为<math>\{\omega^{\omega^{\omega^{\cdots}}}+1,\omega^{\omega^{\omega^{\cdots}}+1},\omega^{\omega^{\omega^{\cdots}+1}},\cdots\}</math>.在这里我们把<math>\omega</math>的指数塔固定在<math>\omega</math>。在这样的基本列中，+1像在指数塔攀爬一样，攀爬法也因此而得名。在基本列的尽头，+1攀爬到了指数塔的顶端，与原来在顶端的1相加变为2。因此我们得到<math>\varepsilon_1=\underbrace{\omega^{\omega^{\cdots^{2}}}}_{\omega+1 \text{ layers}}</math>.进一步的，按照攀爬法我们有<math>\varepsilon_{\omega}=\underbrace{\omega^{\omega^{\cdots^{\omega}}}}_{\omega+1 \text{ layers}}</math>,我们将其记为<math>\omega\uparrow\uparrow(\omega+1)=\varepsilon_{\omega}</math>.

进一步有：

<math>\omega\uparrow\uparrow(\omega+2)=\varepsilon_{\omega^{\omega}}</math>

<math>\omega\uparrow\uparrow(\omega\times2)=\varepsilon_{\varepsilon_0}</math>

<math>\omega\uparrow\uparrow(\omega^2)=\zeta_0</math>

<math>\omega\uparrow\uparrow(\omega^3)=\eta_0</math>

<math>\omega\uparrow\uparrow(\omega^{\omega})=\varphi(\omega,0)</math>

<math>\omega\uparrow\uparrow\omega\uparrow\uparrow\omega=\varphi(\varphi(1,0),0)</math>

<math>\omega\uparrow^34=\varphi(\varphi(\varphi(1,0),0),0)</math>

<math>\omega\uparrow^3\omega=\varphi(1,0,0)</math>

<math>\omega\uparrow^3(\omega+1)=\varphi(1,0,1)</math>

<math>\omega\uparrow^3(\omega^2)=\varphi(1,1,0)</math>

<math>\omega\uparrow^3\omega\uparrow^3\omega=\varphi(1,\varphi(1,0,0),0)</math>

<math>\omega\uparrow^44=\varphi(1,\varphi(1,\varphi(1,0,0),0),0)</math>

<math>\omega\uparrow^4\omega=\varphi(2,0,0)</math>

<math>\omega\uparrow^5\omega=\varphi(3,0,0)</math>

<math>\omega\uparrow^{\omega}\omega=\varphi(\omega,0,0)</math>

由此我们得到了攀爬法序数超运算的极限是<math>\varphi(\omega,0,0)</math>.

但是现在已经证明了，攀爬法是非良序的。因此这一做法得到的推广是不可靠的。

== +1法 ==
第三中试图解决问题的方案是+1法。

它基于一种特别朴素的想法，即：如果<math>\omega\uparrow^c\alpha=\alpha</math>,则修改其值为<math>\omega\uparrow^c(\alpha+1)</math>.显然，这一改变真正起到效果的是指数上的变化。当然，类似+1法，还可以用其他函数跳过不动点，例如+ω法，×2法，×ω法等，但不能达到下一个ε点。

关于+1法序数超运算，我们有：

例如：ω^^(ω+1)如果展开为ω^ω^^ω就会遇到不动点，因此触发上述的+1规则。

<math>\omega\uparrow\uparrow(\omega+1)=\omega^{\omega\uparrow\uparrow\omega+1}=\omega^{\varepsilon_0+1}</math>

然后，以此类推：

<math>\omega\uparrow\uparrow(\omega+2)=\omega^{\omega^{\varepsilon_0+1}}</math>

<math>\omega\uparrow\uparrow(\omega2)=\varepsilon_1</math>

<math>\omega\uparrow\uparrow(\omega3)=\varepsilon_2</math>

<math>\omega\uparrow\uparrow(\omega^2)=\varepsilon_{\omega}</math>

<math>\omega\uparrow^33=\omega\uparrow\uparrow\omega\uparrow\uparrow\omega=\varepsilon_{\varepsilon_0}</math>

<math>\omega\uparrow^3\omega=\zeta_0</math>

到ζ_0后，+1法的展开方式将会比较复杂，并产生一些奇特的基础序列。继续分析：

<math>\omega\uparrow^3(\omega+1)=\omega\uparrow\uparrow(\omega\uparrow^3\omega+1)
=\omega\uparrow(\omega\uparrow\uparrow(\omega\uparrow^3\omega)+1)
=\omega\uparrow(\omega\uparrow^3\omega+1)
=\omega^{\zeta_0+1}</math>

<math>\omega\uparrow\uparrow(\omega\uparrow^3\omega+\omega)=\varepsilon_{\zeta_0+1}</math>

<math>\omega\uparrow\uparrow(\omega\uparrow^3\omega*2)=\varepsilon_{\zeta_02}</math>

<math>\omega\uparrow^3(\omega+2)=\omega\uparrow\uparrow(\omega\uparrow^3(\omega+1))=\varepsilon_{\omega^{\zeta_0+1}}</math>

<math>\omega\uparrow^3(\omega+3)=\varepsilon_{\varepsilon_{\omega^{\zeta_0+1}}}</math>

<math>\omega\uparrow^3(\omega2)=\zeta_1</math>

<math>\omega\uparrow^43=\zeta_{\zeta_0}</math>

<math>\omega\uparrow^4\omega=\eta_0</math>

<math>\omega\uparrow^4(\omega+1)=\omega\uparrow^3(\omega\uparrow^4\omega+1)
=\omega\uparrow\omega\uparrow\uparrow\omega\uparrow^3(\omega\uparrow^4\omega+1)
=\omega\uparrow(\omega\uparrow^4\omega+1)
=\omega^{\eta_0+1}</math>

<math>\omega\uparrow^4(\omega+2)=\omega\uparrow^3(\omega\uparrow^4(\omega+1))=\zeta_{\omega^{\eta_0+1}}</math>

<math>\omega\uparrow^4(\omega2)=\eta_1</math>

<math>\omega\uparrow^5\omega=\varphi(4,0)</math>

<math>\omega\uparrow^{\omega}\omega=\varphi(\omega,0)</math>

于是我们得到其极限为<math>\varphi(\omega,0)</math>。它的优点是它和<math>\varphi</math>函数行为完全一致。但缺点也是这个。这导致了<math>\omega\uparrow\uparrow(\omega+1)=(\omega\uparrow\uparrow\omega)\times\omega</math>这种奇异的结果，某种意义上丢失了超运算自己的特性。因此可以说，+1法序数超运算被<math>\varphi</math>函数上位替代了。+1法序数超运算还可以继续拓展，在某些版本中，其增长率与类似的Veblen 函数及Feferman序数折叠函数类似，例如：

<math>\omega\{\omega\}(\omega2)=\varphi(\omega,1)</math>

<math>\omega\{\omega+1\}\omega=\varphi(\omega+1,0)</math>

<math>\omega\{\omega\uparrow\uparrow\omega\}\omega=\varphi(\varepsilon_0,0)</math>

<math>\omega\{\Omega\}3=\omega\{\omega\{\omega\}\omega\}\omega=\varphi(\varphi(\omega,0),0)</math>

<math>\omega\{\Omega\}\omega=\Gamma_0</math>

<math>\omega\{\Omega+1\}\omega=\varphi(1,1,0)</math>

<math>\omega\{\Omega2\}\omega=\varphi(2,0,0)</math>

<math>\omega\{\Omega^2\}\omega=\varphi(1,0,0,0)</math>

<math>\omega\{\Omega^\omega\}\omega=\psi(\Omega^{\Omega^\omega})</math>

<math>\omega\{\Omega^\Omega\}\omega=\psi(\Omega^{\Omega^\Omega})</math>

<math>\omega\{\Omega\uparrow\uparrow\omega\}\omega=\psi(\Omega_2)</math>

但如此的拓展达到同样序数的难度要明显大于一般的[[序数坍缩函数]]。有些版本引入了更为强大的结构，但已经失去了超运算的特性，其强度主要为引入的更高级序数结构，建议使用以更高级核心的序数记号替代之。

类似+1法的+ω法序数超运算由于整度较大，容易分析，方便进行拓展，有如下分析：[[+ω法序数超运算分析]]

== 总结 ==
到目前为止，序数超运算不是不良定义，就是不理想的。我们不建议在任何地方使用高于<math>\varepsilon_0</math>的序数超运算和更高级别的运算。如果要使用，必须仅仅将它作为形式上的符号，并且明确地说明其具体含义。事实上，我们完全可以使用[[Veblen 函数]]这样的更加强大且清晰的[[序数记号]]来替代它。
[[分类:记号]]
[[分类:入门]]
[[分类:序数超运算]]

Googology 梗百科

2026-05-01T14:40:19Z

Baixie01000a7：/* 3.都在大群拉💩是吧？全都跑不了 */

本页面收录了一些中文 [[Googology|ggg]] 圈的梗。

== 一、聊天记录类 ==

=== 1.定义没有，牛B吹爆 ===
[[文件:12345B67.jpg|截图日期：2024年8月9日|缩略图]]
起因是 3184 说了句“来点小小的链节余项震撼”，后被 hypcos 回复“定义没有，牛B吹爆”

因为其过于经典而被广为流传。

后来还衍生出了多种版本，如“1234，5B67”和“□□□□，□□□□”，“分析没有，牛B吹爆”等

=== 2.XX给你打了 ===
出自于涵对 hypcos 的回复“坦克给你打了”。
[[文件:Tank.jpg|缩略图]]
其中“坦克”指的是 [[LVO]]，这个名词来源于文件《大数级别段位》（一个数字量级表）中的“掌控者坦克”。另一个较为出名的是“邢天战甲”，被用于指代 [[BO]]。

这个梗中的“坦克”可以被换成任意词，被用于调侃性地表达两个事物间的比较。

此外，受这段聊天记录影响，有一些人在讨论部分内容时也常常使用“我倾向于”表达自己的观点。

详细信息可以参考B站用户 3183丶4139 的[https://b23.tv/ULKDxxw 这期视频]。

=== 3.都在大群拉💩是吧？全都跑不了 ===

出自hypcos在2024年10月25日的发言。

当天00:09qwerty发送“。。。”，随后adm.油手就行复读“。。。”，随后多人复读。09:15流光发送”打断复读“，随后出现“打断打断复读”，“打断^ω 复读”，“ε(打断+1) 复读”，“2nd 复读”……

随后hypcos发言“都在大群拉💩是吧？全都跑不了”，并分别将real.油手就行，此人不存在等7人分别禁言1,2,4,8,16,32,1分钟。

该聊天记录衍生为“都在___拉_是吧？全都跑不了”与“QSSO+1”(Y序列的1,2,4,8,16,32,1)。

== 二、错字类 ==

=== 1.果糕 ===
果糕是馃槹的谐音版，馃槹是 emoji 表情😰按 UTF-8 编码后用 GBK 解码的结果。

具体可以见[https://2023largenumber.fandom.com/zh/wiki/%F0%9F%98%B0#articleComments/ 此处]。

=== 2.扽西 ===
最早是 PCF 的错字，将“分析”打成了扽西，后来逐渐演变成了一个梗，用于代指不严谨的分析。

=== 3.其他错字 ===
还有一些错字也比较经典，如“狄安娜”指电脑，“周记”指手机，“全业务额是”是“确实”，在此不一一列举。
[[文件:2025-08-11 狄安娜的考验.png|缩略图|疑似对外国友人有点高难度了（对中国人也是）]]
详细可以参考[https://docs.qq.com/sheet/DVnlZSENqbm1CU3FQ?u=7b7ca06006c34e6b84a6bbcc0ac26715&tab=000001 错字辞典]，它较为详细地记载了一些错字。

Googology 梗百科

2026-05-01T14:39:45Z

Baixie01000a7：/* 一、聊天记录类 */

本页面收录了一些中文 [[Googology|ggg]] 圈的梗。

== 一、聊天记录类 ==

=== 1.定义没有，牛B吹爆 ===
[[文件:12345B67.jpg|截图日期：2024年8月9日|缩略图]]
起因是 3184 说了句“来点小小的链节余项震撼”，后被 hypcos 回复“定义没有，牛B吹爆”

因为其过于经典而被广为流传。

后来还衍生出了多种版本，如“1234，5B67”和“□□□□，□□□□”，“分析没有，牛B吹爆”等

=== 2.XX给你打了 ===
出自于涵对 hypcos 的回复“坦克给你打了”。
[[文件:Tank.jpg|缩略图]]
其中“坦克”指的是 [[LVO]]，这个名词来源于文件《大数级别段位》（一个数字量级表）中的“掌控者坦克”。另一个较为出名的是“邢天战甲”，被用于指代 [[BO]]。

这个梗中的“坦克”可以被换成任意词，被用于调侃性地表达两个事物间的比较。

此外，受这段聊天记录影响，有一些人在讨论部分内容时也常常使用“我倾向于”表达自己的观点。

详细信息可以参考B站用户 3183丶4139 的[https://b23.tv/ULKDxxw 这期视频]。

=== 3.都在大群拉💩是吧？全都跑不了 ===

出自hypcos在2024年10月25日的发言。

当天00:09qwerty发送“。。。”，随后adm.油手就行复读“。。。”，随后多人复读。09:15流光发送”打断复读“，随后出现“打断打断复读”，“打断^ω 复读”，“ε(打断+1) 复读”，“2nd 复读”……。

随后hypcos发言“都在大群拉💩是吧？全都跑不了”，并分别将real.油手就行，此人不存在等7人分别禁言1,2,4,8,16,32,1分钟。

该聊天记录衍生为“都在___拉_是吧？全都跑不了”与“QSSO+1”(Y序列的1,2,4,8,16,32,1)

== 二、错字类 ==

=== 1.果糕 ===
果糕是馃槹的谐音版，馃槹是 emoji 表情😰按 UTF-8 编码后用 GBK 解码的结果。

具体可以见[https://2023largenumber.fandom.com/zh/wiki/%F0%9F%98%B0#articleComments/ 此处]。

=== 2.扽西 ===
最早是 PCF 的错字，将“分析”打成了扽西，后来逐渐演变成了一个梗，用于代指不严谨的分析。

=== 3.其他错字 ===
还有一些错字也比较经典，如“狄安娜”指电脑，“周记”指手机，“全业务额是”是“确实”，在此不一一列举。
[[文件:2025-08-11 狄安娜的考验.png|缩略图|疑似对外国友人有点高难度了（对中国人也是）]]
详细可以参考[https://docs.qq.com/sheet/DVnlZSENqbm1CU3FQ?u=7b7ca06006c34e6b84a6bbcc0ac26715&tab=000001 错字辞典]，它较为详细地记载了一些错字。

文件:nigancuangaiwodehua.jpg

2026-05-01T14:38:40Z

Baixie01000a7：

文件:lashit.jpg

2026-05-01T14:34:28Z

Baixie01000a7：

BOCF

2026-05-01T12:43:03Z

Baixie01000a7：重定向页面至序数坍缩函数

#重定向 [[序数坍缩函数]]

IBLP分析

2026-04-30T16:33:43Z

Baixie01000a7：创建页面，内容为“== Part 1: 0~ψ(Ω_ω*Ω) == 主词条：IBLP分析Part1 == Part 2: ψ(Ω_ω*Ω)~SHO == 主词条：IBLP分析Part2 == Part 3: SHO~Y(1,3,4,3) == 主词条：IBLP分析Part3”

== Part 1: 0~ψ(Ω_ω*Ω) ==
主词条：[[IBLP分析Part1]]

== Part 2: ψ(Ω_ω*Ω)~[[SHO]] ==
主词条：[[IBLP分析Part2]]

== Part 3: SHO~Y(1,3,4,3) ==
主词条：[[IBLP分析Part3]]

IBLP分析Part4

2026-04-30T16:30:36Z

Baixie01000a7：

{| class="wikitable"
|Infinite Basic Laver Pattern
|ω-Y Sequence
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1
|1,3,4,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,3,2)1
|1,3,4,3,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12)1
|1,3,4,3,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12)1(14,3,2,1,0)3(15,*14,3,2,1,0)3(16,14,3)1(17,16,2,1,0)3(18,*17,16,3,2,1,0)4(19,*18,*17,16,14,3,2,1,0)5(20,*19,*18,*17,16,14,3,2,1,0)5(21,17,2,1,0)3(22,*21,17,3,2,1,0)4(23,*22,*21,17,14,3,2,1,0)5(24,*23,*22,*21,17,16,14,3,2,1,0)6(25,*22,*21,17,14,3,2,1,0)5(26,14,3)1
|1,3,4,3,4,2,5,9,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12)1(14,3,2,1,0)3(15,*14,3,2,1,0)3(16,14,3)1(17,16,2,1,0)3(18,*17,16,3,2,1,0)4(19,*18,*17,16,14,3,2,1,0)5(20,*19,*18,*17,16,14,3,2,1,0)5(21,17,2,1,0)3(22,*21,17,3,2,1,0)4(23,*22,*21,17,14,3,2,1,0)5(24,*23,*22,*21,17,16,14,3,2,1,0)6(25,*22,*21,17,14,3,2,1,0)5(26,14,3)1(27,26)1
|1,3,4,3,4,2,5,9,5,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12)1(14,3,2)1
|1,3,4,3,4,2,5,9,5,6,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3
|1,3,4,3,4,2,5,9,5,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,3,2)1
|1,3,4,3,4,2,5,9,5,7,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,13,2,1,0)3(15,3,2)1
|1,3,4,3,4,2,5,9,5,7,9,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,13,12)1
|1,3,4,3,4,2,5,9,5,7,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,3,2)1
|1,3,4,3,4,2,5,9,5,7,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,14,13,12)2
|1,3,4,3,4,2,5,9,5,7,10,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,16,15)1
|1,3,4,3,4,2,5,9,5,7,10,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3
|1,3,4,3,4,2,5,9,5,7,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14)1
|1,3,4,3,4,2,5,9,5,7,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14)1(17,16,14,13,12)3(18,*17,16,15,14,13,12)4(19,18,17,16)2(20,19,18)1
|1,3,4,3,4,2,5,9,5,7,12,16,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14)1(17,16,14,13,12)3(18,*17,16,15,14,13,12)4(19,*18,*17,16,15,14,13,12)4
|1,3,4,3,4,2,5,9,5,7,12,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14)1(17,16,14,13,12)3(18,*17,16,15,14,13,12)4(19,*18,*17,16,15,14,13,12)4(20,17,14,13,12)3(21,*20,17,15,14,13,12)4(22,*21,*20,17,16,15,14,13,12)5
|1,3,4,3,4,2,5,9,5,7,12,17,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14)1(17,16,14,13,12)3(18,*17,16,15,14,13,12)4(19,*18,*17,16,15,14,13,12)4(20,17,14,13,12)3(21,*20,17,15,14,13,12)4(22,*21,*20,17,16,15,14,13,12)5(23,20,17)1
|1,3,4,3,4,2,5,9,5,7,12,18
|-
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|1,3,4,3,4,2,5,9,5,7,12,18,5
|-
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|1,3,4,3,4,2,5,9,5,7,12,19
|-
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|1,3,4,3,4,2,5,9,5,7,12,21,12
|-
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|1,3,4,3,4,2,5,9,5,8
|-
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|1,3,4,3,4,2,5,9,5,8,11
|-
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|1,3,4,3,4,2,5,9,5,9
|-
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|1,3,4,3,4,2,5,9,5,9,4,9,18,9,16
|-
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|1,3,4,3,4,3
|-
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|1,3,4,4
|-
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|1,3,4,4,2,5,9,5
|-
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|1,3,4,4,2,5,9,6
|-
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|1,3,4,4,2,5,9,6,5
|-
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|1,3,4,4,2,5,9,7
|-
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|1,3,4,4,2,5,9,7,10,5
|-
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|1,3,4,4,2,5,9,7,11
|-
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|1,3,4,4,2,5,9,7,12
|-
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|1,3,4,4,2,5,9,8
|-
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|1,3,4,4,2,5,9,8,11
|-
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|1,3,4,4,2,5,9,8,12
|-
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|1,3,4,4,2,5,9,8,12,4,9
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,9
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,19
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,20
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,20,8,17
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,20,9
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,20,20
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,20,26
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,20,29
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,21
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,23
|-
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|1,3,4,4,2,5,9,8,12,5
|-
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|1,3,4,4,2,5,9,8,12,8
|-
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|1,3,4,4,2,5,9,8,12,8,12,5
|-
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|1,3,4,4,2,5,9,8,12,9
|-
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|1,3,4,4,2,5,9,8,12,10
|-
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|1,3,4,4,2,5,9,8,12,11
|-
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|1,3,4,4,2,5,9,8,12,11,15
|-
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|1,3,4,4,2,5,9,8,12,11,15,5
|-
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|1,3,4,4,2,5,9,8,12,11,15,12
|-
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|1,3,4,4,2,5,9,8,12,11,15,14,18
|-
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|1,3,4,4,2,5,9,9
|-
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|1,3,4,4,2,5,9,9,4,9,18,15
|-
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|1,3,4,4,2,5,9,9,4,9,18,15,9
|-
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|1,3,4,4,2,5,9,9,4,9,18,16
|-
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|1,3,4,4,2,5,9,9,4,9,18,18
|-
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|1,3,4,4,3
|-
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|1,3,4,4,3,4,4,3
|-
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|1,3,4,4,4
|-
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|1,3,4,4,4,2,5,9,9,6,5
|-
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|1,3,4,4,4,2,5,9,9,9
|-
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|1,3,4,4,4,2,5,9,9,9,4,9,18,18,16
|-
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|1,3,4,4,4,3
|-
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|1,3,4,5
|-
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|1,3,4,5,2,5,9,10
|-
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|1,3,4,5,2,5,9,10,5
|-
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|1,3,4,5,2,5,9,10,7
|-
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|1,3,4,5,2,5,9,10,8
|-
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|1,3,4,5,2,5,9,10,8,12,5
|-
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|-
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|1,3,4,5,2,5,9,10,8,12,13
|-
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|-
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|1,3,4,5,2,5,9,10,9
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|1,3,4,5,2,5,9,10,9,5
|-
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|1,3,4,5,2,5,9,10,10
|-
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|1,3,4,5,2,5,9,10,13
|-
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|1,3,4,5,2,5,9,11
|-
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|1,3,4,5,2,5,9,11,16
|-
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|1,3,4,5,2,5,9,11,16,22
|-
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|1,3,4,5,2,5,9,11,16,25,16
|-
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|1,3,4,5,2,5,9,11,16,25,27
|-
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|1,3,4,5,2,5,9,11,16,25,29
|-
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|1,3,4,5,2,5,9,12
|-
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|1,3,4,5,2,5,9,12,15
|-
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|1,3,4,5,2,5,9,12,16
|-
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|1,3,4,5,2,5,9,12,16,5
|-
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|1,3,4,5,2,5,9,12,16,16
|-
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|1,3,4,5,2,5,9,12,16,16,5
|-
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|1,3,4,5,2,5,9,12,16,19
|-
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|1,3,4,5,2,5,9,12,16,19,23,5
|-
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|1,3,4,5,2,5,9,13
|-
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|1,3,4,5,2,5,9,13,17
|-
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|1,3,4,5,2,5,9,14
|-
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|1,3,4,5,2,5,9,14,4,9,18,28
|-
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|1,3,4,5,2,5,9,14,4,9,18,28,9
|-
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|1,3,4,5,2,5,9,14,4,9,18,29
|-
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|1,3,4,5,3
|-
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|1,3,4,5,4
|-
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|1,3,4,5,4,2,5,9,14,6,5
|-
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|1,3,4,5,4,2,5,9,14,9
|-
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|1,3,4,5,4,2,5,9,14,9,4,9,18,32,16
|-
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|1,3,4,5,4,3
|-
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|1,3,4,5,4,5
|-
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|1,3,4,5,4,5,2,5,9,14,9,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,*8,5,3,2,1,0)4(16,15,8,5)2
|1,3,4,5,4,5,2,5,9,14,9,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,*8,5,3,2,1,0)4(16,15,8,5)2(17,16,15,8,5)3(18,17,16)1
|1,3,4,5,4,5,2,5,9,14,9,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,*8,5,3,2,1,0)4(16,15,8,5)2(17,16,15,8,5)3(18,*17,16,3,2,1,0)4
|1,3,4,5,4,5,2,5,9,14,9,14,4,9,18,32,18,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,*8,5,3,2,1,0)4(16,15,8,5)2(17,16,15,8,5)3(18,*17,16,3,2,1,0)4(19,3,2)1
|1,3,4,5,4,5,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,11)1
|1,3,4,5,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,11)1(16,3,2)1
|1,3,4,5,5,2,5,9,14,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,11,2,1,0)3
|1,3,4,5,5,2,5,9,14,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,11,8,5)2
|1,3,4,5,5,2,5,9,14,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,11,8,5)2(16,15,11,8,5)2(17,16,15)1
|1,3,4,5,5,2,5,9,14,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,3,2)1
|1,3,4,5,5,2,5,9,14,13,18,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,12,11,8,5)3
|1,3,4,5,5,2,5,9,14,13,18,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,3,2)1
|1,3,4,5,5,2,5,9,14,13,18,17,22,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,13,11,8,5)3(16,*15,13,3,2,1,0)4(17,3,2)1
|1,3,4,5,5,2,5,9,14,13,18,17,22,21,26,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,13,12)1
|1,3,4,5,5,2,5,9,14,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,*13,12,3,2,1,0)4(16,3,2)1
|1,3,4,5,5,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,14)1
|1,3,4,5,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,14)1(16,3,2)1
|1,3,4,5,6,2,5,9,14,15,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,14,2,1,0)3
|1,3,4,5,6,2,5,9,14,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,4,3,2,1,0)5
|1,3,4,5,6,2,5,9,14,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,14,11,8,5)3
|1,3,4,5,6,2,5,9,14,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,14,13,12)2
|1,3,4,5,6,2,5,9,14,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,16,15)1
|1,3,4,5,6,2,5,9,14,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,3,2,1,0)4(18,3,2)1
|1,3,4,5,6,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3
|1,3,4,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,3,2)1
|1,3,4,6,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,*8,5,3,2,1,0)4(16,3,2)1
|1,3,4,6,4,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,*8,5,3,2,1,0)4(16,15,8,5)2(17,16,15,8,5)3(18,*17,16,15,8,5)3
|1,3,4,6,4,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11)1
|1,3,4,6,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11)1(16,3,2)1
|1,3,4,6,5,2,5,9,15,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2
|1,3,4,6,5,2,5,9,15,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,16,15)1
|1,3,4,6,5,2,5,9,15,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,3,2)1
|1,3,4,6,5,2,5,9,15,13,18,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,*16,15,3,2,1,0)4(19,3,2)1
|1,3,4,6,5,2,5,9,15,13,18,18,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2
|1,3,4,6,5,2,5,9,15,13,18,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17,16,15)3(20,*19,18,17,16,15)3
|1,3,4,6,5,2,5,9,15,13,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17,16,15)3(20,*19,18,17,16,15)3(21,17,16,15)2
|1,3,4,6,5,2,5,9,15,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17,16,15)3(20,*19,18,17,16,15)3(21,17,16,15)2(22,21,17,16,15)3(23,*22,21,3,2,1,0)4(24,3,2)1
|1,3,4,6,5,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17,16,15)3(20,*19,18,17,16,15)3(21,17,16,15)2(22,21,17,16,15)3(23,*22,21,3,2,1,0)4(24,23,22,21)2(25,24,23,22,21)3(26,*25,24,23,22,21)3
|1,3,4,6,5,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,11,8,5)3
|1,3,4,6,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12)1
|1,3,4,6,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12)1(16,3,2)1
|1,3,4,6,7,2,5,9,15,16,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12,2,1,0)3
|1,3,4,6,7,2,5,9,15,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12,2,1,0)3(16,*15,12,3,2,1,0)4(17,*16,*15,12,4,3,2,1,0)5
|1,3,4,6,7,2,5,9,15,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12,11,8,5)3
|1,3,4,6,7,2,5,9,15,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3
|1,3,4,6,7,2,5,9,15,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3
|1,3,4,6,7,2,5,9,15,21,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,15,13)1
|1,3,4,6,7,2,5,9,15,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,*15,13,3,2,1,0)4(18,3,2)1
|1,3,4,6,7,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,*15,13,3,2,1,0)4(18,17,15,13)2(19,18,17,15,13)3(20,*19,18,3,2,1,0)4(21,3,2)1
|1,3,4,6,7,8,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,*15,13,3,2,1,0)4(18,17,15,13)2(19,18,17,15,13)3(20,*19,18,17,15,13)3
|1,3,4,6,7,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,*15,13,12,11,8,5)4
|1,3,4,6,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,16,15,13)2(18,17,16,15,13)3(19,*18,17,16,15,13)3
|1,3,4,6,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,*16,*15,13,12,11,8,5)4
|1,3,4,6,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1
|1,3,4,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,12,11)1
|1,3,4,7,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13)1
|1,3,4,7,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13)1(15,3,2,1,0)3(16,*15,3,2,1,0)3(17,15,3)1(18,17,2,1,0)3(19,*18,17,3,2,1,0)4(20,*19,*18,17,15,3,2,1,0)5(21,*20,*19,*18,17,15,3,2,1,0)5(22,18,2,1,0)3(23,*22,18,3,2,1,0)4(24,*23,*22,18,15,3,2,1,0)5(25,*24,*23,*22,18,17,15,3,2,1,0)6(26,*23,*22,18,15,3,2,1,0)5(27,26,23,22,18)3(28,*27,26,23,22,18)3(29,27,26)1(30,29)1
|1,3,4,7,8,2,5,9,16,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13)1(15,3,2)1
|1,3,4,7,8,2,5,9,16,17,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,2,1,0)3
|1,3,4,7,8,2,5,9,16,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,2,1,0)3(15,*14,13,3,2,1,0)4(16,*15,*14,13,4,3,2,1,0)5
|1,3,4,7,8,2,5,9,16,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3
|1,3,4,7,8,2,5,9,16,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,2,1,0)2(16,15,2)1
|1,3,4,7,8,2,5,9,16,20,4,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,2,1,0)2(16,15,2)1(17,16,2,1,0)3(18,*17,16,15,2,1,0)4(19,*18,*17,16,15,2,1,0)4(20,17,2,1,0)3(21,*20,17,15,2,1,0)4(22,*21,*20,17,16,15,2,1,0)5(23,*20,17,15,2,1,0)4(24,23,20,17)2(25,24,23)1
|1,3,4,7,8,2,5,9,16,20,4,9,18,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,2,1,0)2(16,15,2)1(17,16,2,1,0)3(18,*17,16,15,2,1,0)4(19,*18,*17,16,15,2,1,0)4(20,17,2,1,0)3(21,*20,17,15,2,1,0)4(22,*21,*20,17,16,15,2,1,0)5(23,*20,17,15,2,1,0)4(24,23,20,17)2(25,24,23)1(26,25,2,1,0)3(27,*26,25,15,2,1,0)4(28,*27,26,25,16,15,2,1,0)5
|1,3,4,7,8,2,5,9,16,20,4,9,18,34,39
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,40
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,40,8,17,35,69,79
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,40,9
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,41
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,42
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,42,54,73
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,43
|-
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|1,3,4,7,8,2,5,9,16,20,5
|-
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|1,3,4,7,8,2,5,9,16,20,9
|-
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|1,3,4,7,8,2,5,9,16,20,9,4,9,18,34,43,16
|-
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|1,3,4,7,8,2,5,9,16,20,9,5
|-
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|1,3,4,7,8,2,5,9,16,20,9,16,20
|-
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|1,3,4,7,8,2,5,9,16,20,12
|-
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|1,3,4,7,8,2,5,9,16,20,13
|-
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|1,3,4,7,8,2,5,9,16,20,13,18
|-
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|1,3,4,7,8,2,5,9,16,20,13,18,5
|-
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|1,3,4,7,8,2,5,9,16,20,13,20
|-
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|1,3,4,7,8,2,5,9,16,20,13,20,24
|-
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|1,3,4,7,8,2,5,9,16,20,13,20,24,17,24,28
|-
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|1,3,4,7,8,2,5,9,16,20,14
|-
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|1,3,4,7,8,2,5,9,16,20,15,26,30
|-
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|1,3,4,7,8,2,5,9,16,20,16
|-
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|1,3,4,7,8,2,5,9,16,20,25
|-
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|1,3,4,7,8,2,5,9,16,20,27
|-
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|1,3,4,7,8,2,5,9,16,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17)1(20,19,17,16,15)3(21,17,16,15)2(22,21,17,16,15)3(23,*22,21,3,2,1,0)4(24,23,22,21)2(25,24,23)1(26,25,23,22,21)3
|1,3,4,7,8,2,5,9,16,21,14,22,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,11,8,5)3
|1,3,4,7,8,2,5,9,16,21,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11)1
|1,3,4,7,8,2,5,9,16,21,15,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11)1(17,16,11,8,5)3
|1,3,4,7,8,2,5,9,16,21,15,26,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11)1(17,16,11,8,5)3(18,11,8,5)2(19,18,11)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,15,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3
|1,3,4,7,8,2,5,9,16,21,15,26,31,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,11,8,5)2(17,16,11)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,15,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,16,15,12)2(18,17,16)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,16,15,12)2(18,17,16)1(19,18,11,8,5)3(20,19,18)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,28,33,39
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,16,15,12)2(18,17,16)1(19,18,11,8,5)3(20,*19,18,3,2,1,0)4(21,20,19,18)2(22,21,20)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,28,33,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,16,15,12)2(18,17,16)1(19,18,16,15,12)3
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,28,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,16,15,12)2(18,17,16)1(19,18,16,15,12)3(20,16,15,12)2(21,20,16)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,28,34,27,39
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3
|1,3,4,7,8,2,5,9,16,21,15,26,31,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,12,11,8,5)3(18,*17,12,11,8,5)3
|1,3,4,7,8,2,5,9,16,21,15,26,31,21,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,*17,15,3,2,1,0)4(20,19,17,15)2(21,20,19)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,21,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,*17,15,3,2,1,0)4(20,19,17,15)2(21,20,19)1(22,21,11,8,5)3(23,11,8,5)2(24,23,11)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,21,32,37,15,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,*17,15,3,2,1,0)4(20,19,17,15)2(21,20,19)1(22,21,11,8,5)3(23,*22,21,12,11,8,5)4
|1,3,4,7,8,2,5,9,16,21,15,26,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,*17,15,3,2,1,0)4(20,19,17,15)2(21,20,19)1(22,21,19,17,15)3
|1,3,4,7,8,2,5,9,16,21,15,26,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,*17,15,12,11,8,5)4
|1,3,4,7,8,2,5,9,16,21,15,26,33,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,18,17,15)2(20,19,18)1
|1,3,4,7,8,2,5,9,16,21,15,26,33,23,36
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,*18,*17,15,12,11,8,5)4
|1,3,4,7,8,2,5,9,16,21,15,26,33,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,12)1
|1,3,4,7,8,2,5,9,16,21,15,26,33,25,44
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,12)1(18,17,11,8,5)3
|1,3,4,7,8,2,5,9,16,21,15,26,33,25,44
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,12)1(18,17,11,8,5)3(19,15,11,8,5)3(20,*19,15,12,11,8,5)4(21,*20,*19,15,12,11,8,5)4(22,19,15)1
|1,3,4,7,8,2,5,9,16,21,15,26,33,25,44,55,25,44
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,12)1(18,17,11,8,5)3(19,15,12)1
|1,3,4,7,8,2,5,9,16,21,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,12)1(18,17,11,8,5)3(19,*18,17,3,2,1,0)4(20,19,18,17)2(21,20,19)1
|1,3,4,7,8,2,5,9,16,21,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,12)1(18,17,11,8,5)3(19,*18,17,12,11,8,5)4
|1,3,4,7,8,2,5,9,16,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11)1
|1,3,4,7,8,2,5,9,16,22,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,14,13)1
|1,3,4,7,8,2,5,9,16,22,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,3,2,1,0)4(16,3,2)1
|1,3,4,7,8,2,5,9,16,22,29,5
|-
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|1,3,4,7,8,2,5,9,16,22,29,16
|-
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|1,3,4,7,8,2,5,9,16,22,29,39
|-
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|1,3,4,7,8,2,5,9,16,22,30
|-
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|1,3,4,7,8,2,5,9,16,22,31,16
|-
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|1,3,4,7,8,2,5,9,16,22,33
|-
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|1,3,4,7,8,2,5,9,16,22,33,39
|-
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|1,3,4,7,8,2,5,9,16,22,33,43,33
|-
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|1,3,4,7,8,2,5,9,16,23
|-
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|1,3,4,7,8,2,5,9,16,23,30
|-
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|1,3,4,7,8,2,5,9,16,24
|-
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|1,3,4,7,8,3
|-
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|1,3,4,7,8,4,3
|-
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|1,3,4,7,8,6,11
|-
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|1,3,4,7,8,6,11,12,3
|-
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|1,3,4,7,8,7
|-
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|1,3,4,7,8,7,8,3
|-
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|1,3,4,7,8,8,3
|-
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|1,3,4,7,8,9
|-
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|1,3,4,7,8,9,2,5,9,16,24,28
|-
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|1,3,4,7,8,9,2,5,9,16,24,31
|-
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|1,3,4,7,8,9,2,5,9,16,24,32
|-
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|1,3,4,7,8,9,2,5,9,16,24,33
|-
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|1,3,4,7,8,9,3
|-
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|1,3,4,7,8,10
|-
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|1,3,4,7,8,11
|-
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|1,3,4,7,8,11,12,2,5,9,16,24,35,43
|-
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|1,3,4,7,8,11,12,3
|-
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|1,3,4,7,9
|-
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|1,3,4,7,9,6,11,15
|-
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|1,3,4,7,9,7
|-
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|1,3,4,7,9,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,11,8,5)3(22,*21,20,12,11,8,5)4(23,*22,*21,20,13,12,11,8,5)5
|1,3,4,7,9,10,2,5,9,16,25,32
|-
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|1,3,4,7,9,10,2,5,9,16,25,32,40,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,11,8,5)3(22,*21,20,12,11,8,5)4(23,*22,*21,20,13,12,11,8,5)5(24,*21,20,12,11,8,5)4
|1,3,4,7,9,10,2,5,9,16,25,32,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2
|1,3,4,7,9,10,2,5,9,16,25,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,12,11)1
|1,3,4,7,9,10,2,5,9,16,25,34,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20,17,14)3(23,22,21)1
|1,3,4,7,9,10,2,5,9,16,25,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20,17,14)3(23,*22,21,3,2,1,0)4(24,3,2)1
|1,3,4,7,9,10,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20,17,14)3(23,*22,21,12,11,8,5)4
|1,3,4,7,9,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20,17,14)3(23,*22,21,20,17,14)3
|1,3,4,7,9,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1
|1,3,4,7,9,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,21,20)1
|1,3,4,7,9,14,18,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4
|1,3,4,7,9,14,18,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,24,23,22)2(26,25,24)1
|1,3,4,7,9,14,18,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4
|1,3,4,7,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4(26,23,20,17,14)3(27,*26,23,21,20,17,14)4(28,*27,*26,23,22,21,20,17,14)5
|1,3,4,7,10,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4(26,23,20,17,14)3(27,*26,23,21,20,17,14)4(28,*27,*26,23,22,21,20,17,14)5(29,26,23)1
|1,3,4,7,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4(26,23,20,17,14)3(27,*26,23,21,20,17,14)4(28,*27,*26,23,22,21,20,17,14)5(29,*26,23,3,2,1,0)4(30,3,2)1
|1,3,4,7,11,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4(26,23,20,17,14)3(27,*26,23,21,20,17,14)4(28,*27,*26,23,22,21,20,17,14)5(29,*26,23,12,11,8,5)4(30,12,11)1
|1,3,4,7,11,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4(26,23,20,17,14)3(27,*26,23,21,20,17,14)4(28,*27,*26,23,22,21,20,17,14)5(29,*26,23,12,11,8,5)4(30,29,26,23)2(31,30,29)1
|1,3,4,7,11,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,*11,*8,5,4,3,2,1,0)5
|1,3,5
|}
[[分类:分析]]

IBLP分析Part2

2026-04-30T16:30:30Z

Baixie01000a7：

{| class="wikitable"
|Infinite Basic Laver Pattern
|ω-Y Sequence
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3
|1,2,4,8,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2
|1,2,4,8,10,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1
|1,2,4,8,10,6,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3
|1,2,4,8,10,6,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,9,8,7)2(14,13,9,8,7)3(15,*14,13,9,8,7)3
|1,2,4,8,10,6,10,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3
|1,2,4,8,10,6,10,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,8,7)1
|1,2,4,8,10,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,8,7)1(15,14,8,7)2(16,15,14,8,7)3(17,*16,15,14,8,7)3
|1,2,4,8,10,7,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,8,7)1(15,14,8,7)2(16,15,14,8,7)3(17,*16,15,14,8,7)3(18,15,2,1,0)3
|1,2,4,8,10,7,12,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,9,2,1,0)3
|1,2,4,8,10,7,12,14,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,9,2,1,0)3(15,14,9)1(16,15,14,9)2(17,16,15,14,9)3(18,*17,16,15,14,9)3(19,16,2,1,0)3
|1,2,4,8,10,7,12,14,9,14,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,9,8,7)2
|1,2,4,8,10,7,12,14,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,9,8,7)2(15,14,9,8,7)3(16,15,14)1(17,16,15,14)2(18,17,16,15,14)3(19,*18,17,16,15,14)3(20,17,2,1,0)3
|1,2,4,8,10,7,12,14,10,15,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,9,8,7)2(15,14,9,8,7)3(16,15,14)1(17,16,15,14)2(18,17,16,15,14)3(19,*18,17,16,15,14)3(20,17,2,1,0)3(21,15,14)1
|1,2,4,8,10,7,12,14,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,9,8,7)2(15,14,9,8,7)3(16,*15,14,9,8,7)3
|1,2,4,8,10,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,9,8,7)2(15,14,9,8,7)3(16,*15,14,9,8,7)3(17,9,8,7)2(18,17,9,8,7)3(19,*18,17,9,8,7)3
|1,2,4,8,10,8,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,9,8,7)2(15,14,9,8,7)3(16,*15,14,9,8,7)3(17,14,2,1,0)3
|1,2,4,8,10,8,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,10)1
|1,2,4,8,10,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,10,2,1,0)3
|1,2,4,8,10,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,13,2,1,0)3
|1,2,4,8,10,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,13,10)1
|1,2,4,8,10,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,2,1,0)3(14,13,10)1(15,14,13,10)2(16,15,14,13,10)3(17,*16,15,14,13,10)3
|1,2,4,8,10,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,9,8,7)3
|1,2,4,8,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,9,8,7)3(14,8,7)1
|1,2,4,8,11,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,9,8,7)3(14,8,7)1(15,14,8,7)2(16,15,14,8,7)3(17,*16,15,14,8,7)3(18,15,14,8,7)3
|1,2,4,8,11,7,12,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,9,8,7)3(14,9,8,7)2
|1,2,4,8,11,7,12,15,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,9,8,7)3(14,9,8,7)2(15,14,9,8,7)3(16,15,14)1
|1,2,4,8,11,7,12,15,10,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,9,8,7)3(14,9,8,7)2(15,14,9,8,7)3(16,15,14)1(17,16,15,14)2(18,17,16,15,14)3(19,*18,17,16,15,14)3
|1,2,4,8,11,7,12,15,10,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,9,8,7)3(14,9,8,7)2(15,14,9,8,7)3(16,15,14)1(17,16,15,14)2(18,17,16,15,14)3(19,*18,17,16,15,14)3(20,17,9,8,7)3
|1,2,4,8,11,7,12,15,10,15,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,9,8,7)3(14,9,8,7)2(15,14,9,8,7)3(16,15,14)1(17,16,15,14)2(18,17,16,15,14)3(19,*18,17,16,15,14)3(20,17,9,8,7)3(21,15,14)1
|1,2,4,8,11,7,12,15,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,9,8,7)3(13,10,9,8,7)3(14,9,8,7)2(15,14,9,8,7)3(16,15,14)1(17,16,15,14)2(18,17,16,15,14)3(19,*18,17,16,15,14)3(20,17,16,15,14)3
|1,2,4,8,11,7,12,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,*8,7,2,1,0)3
|1,2,4,8,11,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,*8,7,2,1,0)3(10,2,1,0)2(11,10,2,1,0)3(12,*11,10,2,1,0)3
|1,2,4,8,11,8,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,*8,7,2,1,0)3(10,7,2,1,0)3
|1,2,4,8,11,8,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,2,1,0)2(8,7,2,1,0)3(9,*8,7,2,1,0)3(10,7,2,1,0)3(11,2,1,0)2(12,11,2,1,0)3(13,*12,11,2,1,0)3
|1,2,4,8,11,8,11,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,3,2,1,0)3
|1,2,4,8,11,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,3,2,1,0)3(8,2,1,0)2(9,8,2,1,0)3(10,*9,8,2,1,0)3
|1,2,4,8,11,11,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,6)1
|1,2,4,8,11,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,6,2,1,0)3
|1,2,4,8,11,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,3,2,1,0)3(7,6,2,1,0)3(8,2,1,0)2(9,8,2,1,0)3(10,*9,8,2,1,0)3
|1,2,4,8,11,14,8
|-
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|1,2,4,8,13,20,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,6,4)2(10,9,8,6,4)3(11,*10,9,8,6,4)3(12,10,8,6,4)3(13,*12,10,9,8,6,4)4
|1,2,4,8,13,20,27,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,6,4)1(9,8,6,4)2(10,9,8,6,4)3(11,*10,9,8,6,4)3(12,10,8,6,4)3(13,*12,10,9,8,6,4)4(14,12,10)1
|1,2,4,8,13,20,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*6,4,3,2,1,0)4
|1,2,4,8,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*6,4,3,2,1,0)4(9,6,4)1
|1,2,4,8,14,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*6,4,3,2,1,0)4(9,6,4)1(10,9,6,4)2(11,10,9,6,4)3(12,*11,10,9,6,4)3(13,11,9,6,4)3(14,*13,11,10,9,6,4)4(15,*13,11,10,9,6,4)4
|1,2,4,8,14,13,20,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*6,4,3,2,1,0)4(9,*6,4,3,2,1,0)4
|1,2,4,8,14,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7)1
|1,2,4,8,14,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,2,1,0)3(9,*8,7,3,2,1,0)4
|1,2,4,8,14,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,2,1,0)3(9,*8,7,3,2,1,0)4(10,*8,7,3,2,1,0)4
|1,2,4,8,14,18,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,2,1,0)3(9,*8,7,3,2,1,0)4(10,9)1
|1,2,4,8,14,18,24,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,2,1,0)3(9,*8,7,3,2,1,0)4(10,9,2,1,0)3(11,*10,9,3,2,1,0)4
|1,2,4,8,14,18,24,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2
|1,2,4,8,14,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,*6,4,3,2,1,0)4
|1,2,4,8,14,19,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,7,2,1,0)3(10,*9,7,3,2,1,0)4
|1,2,4,8,14,19,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,7,6,4)2
|1,2,4,8,14,19,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,2,1,0)3
|1,2,4,8,14,19,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,2,1,0)3(10,*9,8,3,2,1,0)4
|1,2,4,8,14,19,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,*9,8,3,2,1,0)4
|1,2,4,8,14,19,23,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,10)1
|1,2,4,8,14,19,23,29,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,10,9,8)2
|1,2,4,8,14,19,23,29,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3
|1,2,4,8,14,19,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,9,7,6,4)3
|1,2,4,8,14,19,24,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,9,8)1
|1,2,4,8,14,19,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,9,8)1(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,10,9,8)3
|1,2,4,8,14,19,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,9,8)1(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,10,9,8)3(14,12,10,9,8)3(15,*14,12,11,10,9,8)4(16,*14,12,11,10,9,8)4
|1,2,4,8,14,19,26,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4
|1,2,4,8,14,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,*6,4,3,2,1,0)4
|1,2,4,8,14,20,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,7,6,4)2
|1,2,4,8,14,20,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4
|1,2,4,8,14,20,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,8,2,1,0)3(12,*11,8,3,2,1,0)4
|1,2,4,8,14,20,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,8,7,6,4)3
|1,2,4,8,14,20,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,8,7,6,4)3(12,*11,8,3,2,1,0)4
|1,2,4,8,14,20,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,8,7,6,4)3(12,*11,8,3,2,1,0)4(13,8,7,6,4)(14,*13,8,3,2,1,0)4
|1,2,4,8,14,20,26,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,9,2,1,0)3(12,*11,9,3,2,1,0)4
|1,2,4,8,14,20,26,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,9,7,6,4)3(12,*11,9,3,2,1,0)4
|1,2,4,8,14,20,26,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,9,8)1
|1,2,4,8,14,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,*9,8,3,2,1,0)4
|1,2,4,8,14,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,*9,8,3,2,1,0)4(12,*9,8,3,2,1,0)4
|1,2,4,8,14,22,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,2,1,0)3(12,*11,10,3,2,1,0)4
|1,2,4,8,14,22,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,7,6,4)3(12,*11,10,3,2,1,0)4
|1,2,4,8,14,22,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,9,8)2
|1,2,4,8,14,22,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,9,8)2(12,11,10,9,8)3(13,12,11)1
|1,2,4,8,14,22,29,37
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,3,2,1,0)4
|1,2,4,8,14,22,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,3,2,1,0)4(14,10,9,8)2(15,14,10,9,8)3(16,*15,14,3,2,1,0)4
|1,2,4,8,14,22,30,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,3,2,1,0)4(14,13,10,9,8)3(15,*14,13,3,2,1,0)4
|1,2,4,8,14,22,30,38
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,3,2,1,0)4(14,13,12,11)2
|1,2,4,8,14,22,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,3,2,1,0)4(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,3,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,3,2,1,0)4
|1,2,4,8,14,22,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3
|1,2,4,8,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,2,1,0)2(12,11,2,1,0)3(13,*12,11,2,1,0)3(14,12,2,1,0)3(15,*14,12,11,2,1,0)4(16,15,14,12)2(17,16,15,14,12)3(18,*17,16,15,14,12)3
|1,2,4,8,15,8,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,3,2,1,0)3(12,*11,3,2,1,0)3(14,*13,11,3,2,1,0)4(15,14,13,11)2(16,15,14,13,11)3(17,*16,15,14,13,11)3
|1,2,4,8,15,12,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,6,4)1
|1,2,4,8,15,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,*6,4,3,2,1,0)4
|1,2,4,8,15,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,*6,4,3,2,1,0)4(12,11,6,4)2(13,12,11,6,4)3(14,*13,12,11,6,4)3
|1,2,4,8,15,14,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,2,1,0)3(12,*11,7,3,2,1,0)4
|1,2,4,8,15,14,23,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,2,1,0)3(12,*11,7,3,2,1,0)4(13,12,11,7)2(14,13,12,11,7)3(15,*14,13,12,11,7)3
|1,2,4,8,15,14,23,18,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2
|1,2,4,8,15,14,23,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4
|1,2,4,8,15,14,23,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,12,7,6,4)3(15,*14,12,3,2,1,0)4
|1,2,4,8,15,14,23,20,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,12,11)1
|1,2,4,8,15,14,23,20,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,*12,11,3,2,1,0)4
|1,2,4,8,15,14,23,20,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,13,7,6,4)3(15,*14,13,3,2,1,0)4
|1,2,4,8,15,14,23,20,28,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,13,12,11)2
|1,2,4,8,15,14,23,20,28,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,13,12,11)3
|1,2,4,8,15,14,23,20,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,13,12,11)3(17,12,11)1
|1,2,4,8,15,14,23,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,13,12,11)3(17,*12,11,3,2,1,0)4
|1,2,4,8,15,14,23,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,13,12,11)3(17,*12,11,3,2,1,0)4(18,17,12,11)2(19,18,17,12,11)3(20,*19,18,17,12,11)3
|1,2,4,8,15,14,23,22,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,3,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,13,12,11)3(17,13,12,11)2
|1,2,4,8,15,14,23,22,33,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,7,6,4)2(12,11,7,6,4)3(13,*12,11,7,6,4)3
|1,2,4,8,15,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,2,1,0)3
|1,2,4,8,15,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,2,1,0)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,7,6,4)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3
|1,2,4,8,15,17,14,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,2,1,0)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,7,6,4)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,15,2,1,0)3
|1,2,4,8,15,17,14,23,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,2,1,0)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,7,6,4)3(14,*13,12,7,6,4)3
|1,2,4,8,15,17,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,2,1,0)3(12,*11,8,3,2,1,0)4
|1,2,4,8,15,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,2,1,0)3(12,*11,8,3,2,1,0)4(13,12,11,8)2(14,13,12,11,8)3(15,*14,13,12,11,8)3
|1,2,4,8,15,19,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3
|1,2,4,8,15,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3
|1,2,4,8,15,20,14,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,15,7,6,4)3
|1,2,4,8,15,20,14,23,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,15,7,6,4)3(19,14,13,12)2(20,19,14,13,12)3(21,*20,19,14,13,12)3
|1,2,4,8,15,20,14,23,28,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,15,14,13,12)3
|1,2,4,8,15,20,14,23,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,7,6,4)2(13,12,7,6,4)3(14,*13,12,7,6,4)3
|1,2,4,8,15,20,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,8,7,6,4)3
|1,2,4,8,15,20,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,11,7,6,4)3
|1,2,4,8,15,20,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,11,8)1
|1,2,4,8,15,20,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,*11,8,3,2,1,0)4
|1,2,4,8,15,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,*11,8,7,6,4)3
|1,2,4,8,15,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,8,7,6,4)3(12,*11,8,7,6,4)3(13,8,7,6,4)3(14,*13,8,7,6,4)3
|1,2,4,8,15,22,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,9,7,6,4)3
|1,2,4,8,15,22,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,9,7,6,4)3(12,*11,9,3,2,1,0)4
|1,2,4,8,15,22,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,9,7,6,4)3(12,*11,9,8,7,6,4)4
|1,2,4,8,15,22,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,9,7,6,4)3(12,*11,9,8,7,6,4)4(13,9,7,6,4)3(14,*13,9,8,7,6,4)4
|1,2,4,8,15,22,29,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,9,7,6,4)3(12,*11,9,8,7,6,4)4(13,11,7,6,4)3(14,*13,11,8,7,6,4)4
|1,2,4,8,15,22,29,36
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,9,7,6,4)3(12,*11,9,8,7,6,4)4(13,11,9)1
|1,2,4,8,15,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,7,6,4)2(9,8,7,6,4)3(10,*9,8,7,6,4)3(11,9,7,6,4)3(12,*11,9,8,7,6,4)4(13,*11,9,3,2,1,0)4
|1,2,4,8,15,24
|-
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|1,2,4,8,15,25
|-
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|1,2,4,8,15,25,25
|-
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|1,2,4,8,15,25,27
|-
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|1,2,4,8,15,25,30
|-
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|1,2,4,8,15,25,32
|-
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|1,2,4,8,15,25,32,39
|-
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|1,2,4,8,15,25,33
|-
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|1,2,4,8,15,25,35
|-
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|1,2,4,8,15,25,36
|-
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|1,2,4,8,15,25,39
|-
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|1,2,4,8,15,25,39,50
|-
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|1,2,4,8,15,26
|-
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|1,2,4,8,15,26,26
|-
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|1,2,4,8,15,26,28
|-
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|1,2,4,8,15,26,30
|-
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|1,2,4,8,15,26,31
|-
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|1,2,4,8,15,26,33
|-
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|1,2,4,8,15,26,34
|-
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|1,2,4,8,15,26,37
|-
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|1,2,4,8,15,26,40
|-
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|1,2,4,8,15,26,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4
|1,2,4,8,16
|}
{| class="wikitable"
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|1,2,4,8,16,8,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3
|1,2,4,8,16,10
|-
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|1,2,4,8,16,11,8
|-
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|1,2,4,8,16,11,8,16
|-
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|1,2,4,8,16,11,13
|-
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|1,2,4,8,16,12
|-
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|1,2,4,8,16,12,16
|-
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|1,2,4,8,16,12,17
|-
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|1,2,4,8,16,12,18
|-
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|1,2,4,8,16,12,19
|-
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|1,2,4,8,16,12,20
|-
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|1,2,4,8,16,12,20,16
|-
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|1,2,4,8,16,12,20,16,24,20
|-
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|1,2,4,8,16,13
|-
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|1,2,4,8,16,14
|-
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|1,2,4,8,16,14,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,*11,9,3,2,1,0)4(20,19,11,9)2(21,20,19,11,9)3(22,*21,20,3,2,1,0)4
|1,2,4,8,16,14,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,*11,9,3,2,1,0)4(20,19,11,9)2(21,20,19,11,9)3(22,*21,20,19,11,9)3
|1,2,4,8,16,14,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,*11,9,3,2,1,0)4(20,19,11,9)2(21,20,19,11,9)3(22,*21,20,19,11,9)3(23,21,19,11,9)3(24,*23,21,20,19,11,9)4(25,*24,*23,21,20,19,11,9)4
|1,2,4,8,16,14,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,12,11,9)2
|1,2,4,8,16,14,22,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,12,11,9)2(20,19,12,11,9)3(21,*20,19,3,2,1,0)4
|1,2,4,8,16,14,22,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,12,11,9)2(20,19,12,11,9)3(21,*20,19,12,11,9)3
|1,2,4,8,16,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,12,11,9)2(20,19,12,11,9)3(21,*20,19,12,11,9)3(22,20,12,11,9)3(23,*22,20,19,12,11,9)4(,24,*23,*22,20,19,12,11,9)4
|1,2,4,8,16,15,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,13,12,11,9)3
|1,2,4,8,16,15,27,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,13,12,11,9)3(20,*19,13,12,11,9)3
|1,2,4,8,16,15,27,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,12,11,9)2(14,13,12,11,9)3(15,*14,13,12,11,9)3(16,14,12,11,9)3(17,*16,14,13,12,11,9)4(18,*17,*16,14,13,12,11,9)4(19,13,12,11,9)3(20,*19,13,12,11,9)3(21,19,12,11,9)3(22,*21,19,13,12,11,9)
4(23,22,21,19)2(24,23,22,21,19)3(25,*24,23,22,21,19)3(26,24,22,21,19)3(27,*26,24,23,22,21,19)4(28,*27,*26,24,23,22,21,19)4
|1,2,4,8,16,15,27,22,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,3,2,1,0)3(10,*9,3,2,1,0)3(11,9,2,1,0)3(12,*11,9,3,2,1,0)4(13,*12,*11,9,3,2,1,0)4
|1,2,4,8,16,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3
|1,2,4,8,16,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,2,1,0)2(11,10,2,1,0)3(12,*11,10,2,1,0)3
|1,2,4,8,16,19,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,2,1,0)2(11,10,2,1,0)3(12,*11,10,2,1,0)3(13,11,2,1,0)3(14,*13,11,10,2,1,0)4(15,*14,*13,11,10,2,1,0)4
|1,2,4,8,16,19,8,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3
|1,2,4,8,16,19,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4
|1,2,4,8,16,19,12,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,12,10)1
|1,2,4,8,16,19,12,20,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,*12,10,3,2,1,0)4
|1,2,4,8,16,19,12,20,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,13,12,10)2(21,20,13,12,10)3(22,*21,20,13,12,10)3
|1,2,4,8,16,19,12,20,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,13,12,10)2(21,20,13,12,10)3(22,*21,20,13,12,10)3(23,21,13,12,10)3(24,*23,21,20,13,12,10)4(25,*24,*23,21,20,13,12,10)4
|1,2,4,8,16,19,12,20,19,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,14,13,12,10)3(21,*20,14,13,12,10)3(22,20,13,12,10)3(23,*22,20,14,13,12,10)4(24,*23,*22,20,14,13,12,10)4
|1,2,4,8,16,19,12,20,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,15,2,1,0)3
|1,2,4,8,16,19,12,20,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,15,2,1,0)3(21,2,1,0)2(22,21,2,1,0)3(23,*22,21,2,1,0)3
|1,2,4,8,16,19,12,20,23,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,15,2,1,0)3(21,14,13,12,10)3(22,*21,14,13,12,11,10)3(23,21,13,12,10)3(24,*23,21,14,13,12,10)4(25,*24,*23,21,14,13,12,10)4
|1,2,4,8,16,19,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,15,2,1,0)3(21,*20,15,3,2,1,0)4
|1,2,4,8,16,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,15,2,1,0)3(21,*20,15,3,2,1,0)4(22,20,15)1
|1,2,4,8,16,20,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,15,2,1,0)3(21,*20,15,3,2,1,0)4(22,21,20,15)
2(23,22,21,20,15)3(24,*23,22,21,20,15)3(25,23,21,20,15)3(26,*25,23,22,21,20,15)4(27,*26,*25,23,22,21,20,15)4
|1,2,4,8,16,20,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,13,12,10)2(15,14,13,12,10)3(16,*15,14,13,12,10)3(17,15,13,12,10)3(18,*17,15,14,13,12,10)4(19,*18,*17,15,14,13,12,10)4(20,15,13,12,10)3
|1,2,4,8,16,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,*13,*12,10,3,2,1,0)4
|1,2,4,8,16,21,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,4,2,1,0)4
|1,2,4,8,16,21,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,9,2,1,0)4
|1,2,4,8,16,21,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,9,4)1
|1,2,4,8,16,21,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4
|1,2,4,8,16,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,3,2,1,0)3(12,*11,3,2,1,0)3(13,11,2,1,0)3(14,*13,11,3,2,1,0)4(15,14,13,11)2(16,15,14,13,11)3(17,*16,15,14,13,11)3(18,16,14,13,11)3(19,*18,16,15,14,13,11)4(20,*19,*18,16,15,14,13,11)4
|1,2,4,8,16,22,12,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,3,2,1,0)3(12,*11,3,2,1,0)3(13,11,2,1,0)3(14,*13,11,3,2,1,0)4(15,14,13,11)2(16,15,14,13,11)3(17,*16,15,14,13,11)3(18,16,14,13,11)3(19,*18,16,15,14,13,11)4(20,*19,*18,16,15,14,13,11)4(21,16,2,1,0)3(22,*21,16,3,2,1,0)
4(23,22,21,16)2(24,23,22,21,16)3(25,*24,23,22,21,16)3(26,24,22,21,16)3(27,*26,24,23,22,21,16)4(28,*27,*26,24,23,22,21,16)4
|1,2,4,8,16,22,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,3,2,1,0)3(12,*11,3,2,1,0)3(13,11,2,1,0)3(14,*13,11,3,2,1,0)4(15,14,13,11)2(16,15,14,13,11)3(17,*16,15,14,13,11)3(18,16,14,13,11)3(19,*18,16,15,14,13,11)4(20,*19,*18,16,15,14,13,11)4(21,16,14,13,11)3(22,*21,16,15,14,13,11)4(23,15,14,13,11)3(24,*23,15,14,13,11)3(25,23,14,13,11)3(26,*25,23,15,14,13,11)4
|1,2,4,8,16,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,3,2,1,0)3(12,*11,3,2,1,0)3(13,11,2,1,0)3(14,*13,11,3,2,1,0)4(15,*14,*13,11,3,2,1,0)4
|1,2,4,8,16,23,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,4,2,1,0)3
|1,2,4,8,16,23,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,9,2,1,0)3
|1,2,4,8,16,23,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,9,2,1,0)3(12,*11,9,3,2,1,0)4
|1,2,4,8,16,23,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,9,4)1
|1,2,4,8,16,23,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,*9,4,3,2,1,0)4
|1,2,4,8,16,23,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,10,9,4)2
|1,2,4,8,16,23,32,40
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,10,9,4)2(12,11,10,9,4)3(13,*12,11,10,9,4)3
|1,2,4,8,16,23,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,10,9,4)2(12,11,10,9,4)3(13,*12,11,10,9,4)3(14,12,10,9,4)3(15,*14,12,11,10,9,4)4(16,*15,*14,12,11,10,9,4)4
|1,2,4,8,16,23,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,4,2,1,0)3(10,*9,4,3,2,1,0)4(11,*10,*9,4,3,2,1,0)4
|1,2,4,8,16,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5
|1,2,4,8,16,24,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,9,2,1,0)3(13,*12,9,3,2,1,0)4(14,*13,*12,9,4,3,2,1,0)5
|1,2,4,8,16,24,32,40
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,9,6)1
|1,2,4,8,16,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,*9,6,3,2,1,0)4
|1,2,4,8,16,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,*9,6,3,2,1,0)4(13,3,2,1,0)3(14,*13,3,2,1,0)3(15,13,2,1,0)3(16,*15,13,3,2,1,0)4(17,*16,*15,13,3,2,1,0)4
|1,2,4,8,16,27,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,*9,6,3,2,1,0)4(13,*12,*9,6,4,3,2,1,0)5
|1,2,4,8,16,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,*9,6,3,2,1,0)4(13,*12,*9,6,4,3,2,1,0)5(14,*9,6,3,2,1,0)4(15,*14,*9,6,4,3,2,1,0)5
|1,2,4,8,16,28,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,10,9,6)2
|1,2,4,8,16,28,37
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,10,9,6)2(13,12,10,9,6)3(14,*13,12,3,2,1,0)4
|1,2,4,8,16,28,38
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,10,9,6)2(13,12,10,9,6)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,4,3,2,1,0)5
|1,2,4,8,16,28,40
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,10,9,6)2(13,12,10,9,6)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,4,3,2,1,0)5(16,13,12)1
|1,2,4,8,16,28,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,10,9,6)2(13,12,10,9,6)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,4,3,2,1,0)5(16,*13,12,3,2,1,0)4(17,*16,*13,12,4,3,2,1,0)5
|1,2,4,8,16,28,44
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,10,9,6)2(13,12,10,9,6)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,4,3,2,1,0)5(16,14,13,12)2
|1,2,4,8,16,28,44,57
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,10,9,6)2(13,12,10,9,6)3(14,*13,12,10,9,6)3
|1,2,4,8,16,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,*10,*0,6,4,3,2,1,0)5
|1,2,4,8,16,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,11,2,1,0)3(13,*12,11,3,2,1,0)4(14,*13,*12,11,4,3,2,1,0)5
|1,2,4,8,16,30,38
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,11,10,9,6)3
|1,2,4,8,16,30,39
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,11,10,9,6)3(13,*12,11,10,9,6)3(14,12,10,9,6)3(15,*14,12,11,10,9,6)4(16,*15,*14,12,4,3,2,1,0)5
|1,2,4,8,16,30,44
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,11,10,9,6)3(13,*12,11,10,9,6)3(14,12,10,9,6)3(15,*14,12,11,10,9,6)4(16,*15,*14,12,4,3,2,1,0)5(17,14,12)1
|1,2,4,8,16,30,45
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,11,10,9,6)3(13,*12,11,10,9,6)3(14,12,10,9,6)3(15,*14,12,11,10,9,6)4(16,*15,*14,12,4,3,2,1,0)5(17,16,15,14,12)3
|1,2,4,8,16,30,52,67
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,11,10,9,6)3(13,*12,11,10,9,6)3(14,12,10,9,6)3(15,*14,12,11,10,9,6)4(16,*15,*14,12,11,10,9,6)4
|1,2,4,8,16,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,11,10,9,6)3(13,*12,11,10,9,6)3(14,12,10,9,6)3(15,*14,12,11,10,9,6)4(16,*15,*14,12,11,10,9,6)4
(17,14,10,9,6)3(18,*17,14,11,10,9,6)4(19,*18,*17,14,12,11,10,9,6)5(20,19,18,17,14)3(21,*20,19,18,17,14)3(22,20,18,17,16)3(23,*22,20,19,18,17,14)4(24,*23,*22,20,19,18,17,14)4
|1,2,4,8,16,31,57
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,*11,*10,*9,6,4,3,2,1,0)5
|1,2,4,8,16,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4(9,6,2,1,0)(10,*9,6,3,2,1,0)4(11,*10,*9,6,4,3,2,1,0)5(12,*11,*10,*9,6,4,3,2,1,0)5(13,9,2,1,0)3(14,*13,9,3,2,1,0)4(15,*14,*13,9,4,3,2,1,0)5(16,*15,*14,*13,9,6,4,3,2,1,0)6(17,*16,*15,*14,*13,9,6,4,3,2,1,0)6
|1,2,4,8,16,32,64
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1
|1,3
|}
[[分类:分析]]

IBLP分析Part3

2026-04-30T16:28:58Z

Baixie01000a7：

{| class="wikitable"
|Infinite Basic Laver Pattern
|ω-Y Sequence
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1
|1,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,1)1(6,5,1)1(7,6,5,1)2(8,7,6)1
|1,3,2,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,1,0)1
|1,3,2,5,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,1,0)1(6,5,1,0)2(7,6,5)1
|1,3,2,5,4,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2
|1,3,2,5,4,9,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1
|1,3,2,5,4,9,6,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7,6,5)3(10,9,8)1
|1,3,2,5,4,9,6,9,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7,6,5)3(10,*9,8,7,6,5)3
|1,3,2,5,4,9,6,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1
|1,3,2,5,4,9,6,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,2,1,0)3(11,10,6)1(12,11,10,6)2(13,12,11)1
|1,3,2,5,4,9,6,11,8,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,5)1
|1,3,2,5,4,9,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,5)1(11,10,6,5)2(12,11,10)1
|1,3,2,5,4,9,7,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,5)1(11,10,6,5)2(12,11,10)1(10,7,6,5)2
|1,3,2,5,4,9,7,13,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,5)1(11,10,6,5)2(12,11,10)1(10,7,6,5)2(11,10,7,6,5)2(12,11,10)1(13,12,11,10)2(14,13,12)1
|1,3,2,5,4,9,7,13,10,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,5)1(11,10,6,5)2(12,11,10)1(10,7,6,5)2(11,10,7,6,5)2(12,11,10)1(13,12,11,10)2(14,13,12)1(15,11,10)1
|1,3,2,5,4,9,7,13,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,*6,5,2,1,0)3
|1,3,2,5,4,9,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,*6,5,2,1,0)3(8,6,2,1,0)3(9,*8,6,5,2,1,0)3(10,*9,*8,6,5,2,1,0)4
|1,3,2,5,4,9,8,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2)1
|1,3,2,5,4,9,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3
|1,3,2,5,4,9,8,17,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,2,1,0)2(7,6,2)1
|1,3,2,5,4,9,8,17,11,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,2,1,0)3
|1,3,2,5,4,9,8,17,11,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1
|1,3,2,5,4,9,8,17,11,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6,5,3)3(9,*8,7,6,5,3)3
|1,3,2,5,4,9,8,17,11,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1
|1,3,2,5,4,9,8,17,11,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,5,3)1
|1,3,2,5,4,9,8,17,11,17,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,5,3)1(10,9,5,3)2(11,10,9)1
|1,3,2,5,4,9,8,17,11,17,15,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,6,5,3)2
|1,3,2,5,4,9,8,17,11,17,15,22,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,6,5,3)2(10,9,6,5,3)3(11,10,9)1
|1,3,2,5,4,9,8,17,11,17,15,22,19,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,6,5,3)2(10,9,6,5,3)3(11,*10,9,6,5,3)3
|1,3,2,5,4,9,8,17,11,17,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,6,5,3)2(10,9,6,)1
|1,3,2,5,4,9,8,17,11,17,16,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3
|1,3,2,5,4,9,8,17,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4
|1,3,2,5,4,9,8,17,12,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1
|1,3,2,5,4,9,8,17,12,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1
|1,3,2,5,4,9,8,17,12,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,9,8)1
|1,3,2,5,4,9,8,17,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,9,8)1(15,14,9,8)2(16,15,14)1
|1,3,2,5,4,9,8,17,13,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,2,1,0)3
|1,3,2,5,4,9,8,17,13,21,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,2,1,0)3(15,*14,11,3,2,1,0)4
|1,3,2,5,4,9,8,17,13,21,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,2,1,0)3(15,*14,11,3,2,1,0)4(16,14,11)1
|1,3,2,5,4,9,8,17,13,21,17,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,2,1,0)3(15,*14,11,3,2,1,0)4(16,14,11)1(17,16,14,11)2(18,17,16)1
|1,3,2,5,4,9,8,17,13,21,17,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,9,8)2
|1,3,2,5,4,9,8,17,13,21,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,9,8)2(15,14,11)1
|1,3,2,5,4,9,8,17,13,21,18,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,12,11,9,8)3
|1,3,2,5,4,9,8,17,13,21,18,26,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,12,11,9,8)3(15,14,12)1(16,15,14,12)2(17,16,15)1
|1,3,2,5,4,9,8,17,13,21,18,26,23,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,12,11,9,8)3(15,14,12)1(16,15,14,12)2(17,16,15)1(18,14,12)1
|1,3,2,5,4,9,8,17,13,21,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,12,11,9,8)3(15,*14,12,11,9,8)3
|1,3,2,5,4,9,8,17,13,21,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,*9,8,3,2,1,0)4
|1,3,2,5,4,9,8,17,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,7,5)2
|1,3,2,5,4,9,8,17,14,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,7,5)2(10,9,8)1
|1,3,2,5,4,9,8,17,14,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,7,5)2(10,9,8)1(11,9,8,7,5)2(12,*11,9,8,7,5)3
|1,3,2,5,4,9,8,17,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,7,5)2(10,9,8)1(11,9,8,7,5)2(12,*11,9,8,7,5)3(13,11,8,7,5)3(14,*13,11,9,8,7,5)4(15,14,13,11,)2(16,15,14)1
|1,3,2,5,4,9,8,17,15,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4
|1,3,2,5,4,9,8,17,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,*13,*12,10,3,2,1,0)4
|1,3,2,5,4,9,8,17,16,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,5,2,1,0)3
|1,3,2,5,4,9,8,17,16,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,5,2,1,0)3(11,*10,5,3,2,1,0)4
|1,3,2,5,4,9,8,17,16,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,5,2,1,0)3(11,*10,5,3,2,1,0)4(12,*11,*10,5,3,2,1,0)4
|1,3,2,5,4,9,8,17,16,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,7,2,1,0)3(11,*10,7,3,2,1,0)4(12,*11,*10,7,5,3,2,1,0)5
|1,3,2,5,4,9,8,17,16,24,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,7,2,1,0)3(11,*10,7,3,2,1,0)4(12,*11,*10,7,5,3,2,1,0)5(13,10,7)1
|1,3,2,5,4,9,8,17,16,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,7,2,1,0)3(11,*10,7,3,2,1,0)4(12,*11,*10,7,5,3,2,1,0)5(13,*10,7,3,2,1,0)4(14,*13,*10,7,5,3,2,1,0)5
|1,3,2,5,4,9,8,17,16,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,7,2,1,0)3(11,*10,7,3,2,1,0)4(12,*11,*10,7,5,3,2,1,0)5(13,*12,*11,*10,7,5,3,2,1,0)5
|1,3,2,5,4,9,8,17,16,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,3)1
|1,3,2,5,4,9,8,17,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,3)1(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,3,2,1,0)4(11,8,2,1,0)3(12,*11,8,3,2,1,0)4(13,*12,*11,8,5,3,2,1,0)5(14,*13,*12,*11,8,5,3,2,1,0)5
|1,3,2,5,4,9,8,17,16,33,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,3)1(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,3,2,1,0)4(11,8,5)1
|1,3,2,5,4,9,8,17,16,33,32,65
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2)1
|1,3,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2)1(6,3,2)1
|1,3,3,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1
|1,3,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,1)1(7,6,1)1(8,7,6,1)2(9,8,7)1(10,9)1
|1,3,4,2,5,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,1,0)1
|1,3,4,2,5,6,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,1,0)1(7,6,1,0)2(8,7,6)1(9,8)1
|1,3,4,2,5,6,4,9,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,2,1,0)2(7,6,2,1,0)3(8,*7,6,2,1,0)3
|1,3,4,2,5,6,4,9,10,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,2,1,0)2(7,6,2)1(8,7)1
|1,3,4,2,5,6,4,9,10,8,17,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,3,2,1,0)2(7,*6,3,2,1,0)3(8,6,3)1(9,8)1
|1,3,4,2,5,6,4,9,10,8,17,18,16,33,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,3,2)1
|1,3,4,2,5,6,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,5,4)1
|1,3,4,2,5,6,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,5,4)1(7,6,5,4)2(8,7,6)1
|1,3,4,2,5,6,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3
|1,3,4,2,5,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,1)1(7,6,1,)2(8,7,6,1)2(9,8,7)1(10,9,8,6,1)3
|1,3,4,2,5,7,2,5,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,1,0)1
|1,3,4,2,5,7,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,1,0)1(7,6,1,0)2(8,7,6)1(9,8,6,1,0)3
|1,3,4,2,5,7,4,9,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2
|1,3,4,2,5,7,4,9,11,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1
|1,3,4,2,5,7,4,9,11,6,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,2,1,0)3
|1,3,4,2,5,7,4,9,11,6,11,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,2,1,0)3(12,7,6)1
|1,3,4,2,5,7,4,9,11,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,2,1,0)3(12,7,6)1(13,12,7,6)2(14,13,12)1(15,14,2,1,0)3
|1,3,4,2,5,7,4,9,11,7,13,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,2,1,0)3(12,9,8,7,6)3(13,*12,9,8,7,6)3
|1,3,4,2,5,7,4,9,11,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,2,1,0)3(12,9,8)1
|1,3,4,2,5,7,4,9,11,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,8,7,6)3
|1,3,4,2,5,7,4,9,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,8,7,6)3(12,8,7,6)2(13,12,8,7,6)3(14,13,12)1(15,14,13,12)2(16,15,14)1(17,16,14,13,12)3
|1,3,4,2,5,7,4,9,12,7,13,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,*7,6,2,1,0)3
|1,3,4,2,5,7,4,9,12,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,*7,6,2,1,0)3(9,7,2,1,0)3(10,*9,7,6,2,1,0)4(11,*10,*9,7,6,2,1,0)4
|1,3,4,2,5,7,4,9,12,8,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2)1
|1,3,4,2,5,7,4,9,12,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2)1(8,7,2,1,0)3
|1,3,4,2,5,7,4,9,12,8,17,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3
|1,3,4,2,5,7,4,9,12,8,17,20,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,2,1,0)3(9,*8,6,3,2,1,0)4(10,*9,*8,6,3,2,1,0)4
|1,3,4,2,5,7,4,9,12,8,17,22,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1
|1,3,4,2,5,7,4,9,12,8,17,22,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3
|1,3,4,2,5,7,4,9,12,8,17,22,16,33,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,6,2,1,0)3(11,*10,6,3,2,1,0)4(12,*11,*10,6,3,2,1,0)4(13,10,2,1,0)3(14,*13,10,3,2,1,0)4(15,*14,*13,10,6,3,2,1,0)5(16,*15,*14,*13,10,6,3,2,1,0)5
|1,3,4,2,5,7,4,9,12,8,17,22,16,33,42,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,6,3)
|1,3,4,2,5,7,4,9,12,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,9,2,1,0)3
|1,3,4,2,5,7,4,9,12,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,9,8)1
|1,3,4,2,5,7,4,9,12,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,10,9,8)3
|1,3,4,2,5,7,4,9,12,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1
|1,3,4,2,5,7,4,9,12,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,*9,8,3,2,1,0)4
|1,3,4,2,5,7,4,9,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,2,1,0)2(12,11,2)1(13,12,2,1,0)3(14,11,2,1,0)3(15,*14,11,2,1,0)3(16,14,11)1(17,16,2,1,0)3(18,*17,16,11,2,1,0)4
|1,3,4,2,5,7,4,9,13,8,17,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,6,2,1,0)3(12,*11,6,3,2,1,0)4(13,*12,*11,6,3,2,1,0)4(14,11,6)1
|1,3,4,2,5,7,4,9,13,8,17,21,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,6,2,1,0)3(12,*11,6,3,2,1,0)4(13,*12,*11,6,3,2,1,0)4(14,11,6)1(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,6,3,2,1,0)5
|1,3,4,2,5,7,4,9,13,8,17,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2)1
|1,3,4,2,5,7,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2)1(7,3,2)1
|1,3,4,2,5,7,5,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2)1(7,6,2,1,0)3
|1,3,4,2,5,7,5,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2)1(7,6,2,1,0)3(8,3,2)1
|1,3,4,2,5,7,5,7,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,4,2,1,0)3
|1,3,4,2,5,7,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,2,1,0)3
|1,3,4,2,5,7,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1
|1,3,4,2,5,7,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,1,0)1
|1,3,4,2,5,7,10,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,1,0)1(8,7,1,0)2(9,8,7)1(10,9,7,1,0)3(11,8,7)1
|1,3,4,2,5,7,10,4,9,13,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,1,0)1(8,7,1,0)2(9,8,7)1(10,9,7,1,0)3(11,10,9)1
|1,3,4,2,5,7,10,4,9,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2
|1,3,4,2,5,7,10,4,9,13,18,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,12,11)1
|1,3,4,2,5,7,10,4,9,13,18,6,11,15,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,12,11)1(14,8,7)1
|1,3,4,2,5,7,10,4,9,13,18,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2,1,0)3(9,*8,7,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,18,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2,1,0)3(9,*8,7,2,1,0)3(10,8,2,1,0)3(11,*10,8,7,2,1,0)4(12,*11,*10,8,7,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,18,8,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2)1
|1,3,4,2,5,7,10,4,9,13,18,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2)1(9,8,2,1,0)3(10,9,8)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,12,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,12,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,2,1,0)3(15,*14,13,3,2,1,0)4(16,14,13)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,12,21,29,37
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*9,7,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*10,*9,7,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,10,9)1(13,7,2,1,0)3(14,*13,7,3,2,1,0)4(15,*14,*13,7,3,2,1,0)4(16,13,2,1,0)3(17,*16,13,3,2,1,0)4(18,*17,*16,13,7,3,2,1,0)5(19,16,13)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,16,33,49,66
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2)1(8,7,2,1,0)3(9,8,7)1
|1,3,4,2,5,7,10,4,9,13,18,9,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,4,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,18,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,4,2,1,0)3(8,2,1,0)2(9,8,2)1
|1,3,4,2,5,7,10,4,9,13,18,12,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,4,2,1,0)3(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,18,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,4,2,1,0)3(8,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,13,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,4,2,1,0)3(8,7,4)1
|1,3,4,2,5,7,10,4,9,13,18,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,5,4)1
|1,3,4,2,5,7,10,4,9,13,18,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2
|1,3,4,2,5,7,10,4,9,13,18,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1
|1,3,4,2,5,7,10,4,9,13,18,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,18,26,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,5,4)1(11,10,5,4)2(12,11,10)1(13,12,2,1,0)3(14,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,18,26,30,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,6,5,4)2(11,10,6)1(12,11,2,1,0)3(13,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,23,31,35,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6,5,4)3(11,10,7)1(12,11,10,7)2(13,12,11)1(14,13,2,1,0)3(15,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,23,31,35,28,36,40,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6,5,4)3(11,10,7)1(12,11,10,7)2(13,12,11)1(14,13,2,1,0)3(15,10,7)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6,5,4)3(11,*10,7,6,5,4)3
|1,3,4,2,5,7,10,4,9,13,18,26,30,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,9,8)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,35,43
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,2,1,0)3(14,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,35,43,47,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3
|1,3,4,2,5,7,10,4,9,13,18,26,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3
|1,3,4,2,5,7,10,4,9,13,18,26,31,23,31,36,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3(11,10,7)1(12,11,10,7)2(13,12,11)1(14,13,6,5,4)3
|1,3,4,2,5,7,10,4,9,13,18,26,31,23,31,36,28,36,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3(11,10,7)1(12,11,10,7)2(13,12,11)1(14,13,11,10,7)3
|1,3,4,2,5,7,10,4,9,13,18,26,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3(11,*10,7,6,5,4)3
|1,3,4,2,5,7,10,4,9,13,18,26,32,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3(11,*10,7,6,5,4)3(12,10,7)1(13,12,6,5,4)3(14,*13,12,7,6,5,4)4
|1,3,4,2,5,7,10,4,9,13,18,26,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6)1
|1,3,4,2,5,7,10,4,9,13,18,26,33,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6)1(10,9,8)1
|1,3,4,2,5,7,10,4,9,13,18,26,33,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6)1(10,9,8)1(11,10,9,8)2(12,11,10)1
|1,3,4,2,5,7,10,4,9,13,18,26,33,41,52
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,1,0)1(8,7,1,0)2(9,8,7)1(10,9,7,1,0)3(11,*10,9,8,7,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,4,9,13,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2
|1,3,4,2,5,7,10,4,9,13,19,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1
|1,3,4,2,5,7,10,4,9,13,19,6,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3
|1,3,4,2,5,7,10,4,9,13,19,6,11,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,10,9)1
|1,3,4,2,5,7,10,4,9,13,19,6,11,15,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,*12,11,10,9,8,7)4
|1,3,4,2,5,7,10,4,9,13,19,6,11,15,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,*12,11,10,9,8,7)4(14,7,2,1,0)3(15,14,7)1(16,15,14,7)2(17,16,15)1(18,17,15,14,7)3(19,*18,17,16,15,14,7)4
|1,3,4,2,5,7,10,4,9,13,19,6,11,15,21,8,13,17,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,*12,11,10,9,8,7)4(14,8,7)1
|1,3,4,2,5,7,10,4,9,13,19,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,*12,11,10,9,8,7)4(14,8,7)1(15,14,8,7)2(16,15,14)1(17,16,14,8,7)3(18,*17,16,15,14,8,7)4
|1,3,4,2,5,7,10,4,9,13,19,7,13,18,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,*8,7,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2)1
|1,3,4,2,5,7,10,4,9,13,19,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2)1(9,8,2,1,0)3(10,7,2)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2)1(9,8,2,1,0)3(10,9,8)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2)1(9,8,2,1,0)3(10,*9,8,7,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,2,1,0)3(15,12,11)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,23,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,12,11)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,29,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,14,13)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,29,38
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,29,39
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,9,2,1,0)3(17,*16,9,3,2,1,0)4(18,16,9)1(19,18,16,9)2(20,19,18)1(21,20,18,16,9)3(22,*21,20,19,18,16,9)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,29,39,16,25,33,43
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,9,7)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,9,7)1(17,16,9,7)2(18,17,16)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,9,7)1(17,16,9,7)2(18,17,16)1(19,18,16,9,7)3(20,*19,18,17,16,9,7)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,11,2,1,0)3(17,*16,11,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,37,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,11,9,7)2(17,16,11)1(18,17,11,9,7)3(19,*18,17,16,11,9,7)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,18,26,33,42
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,18,26,33,42,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3(17,16,12)1(18,17,16,12)2(19,18,17)1(20,19,17,16,12)3(21,*20,19,18,17,16,12)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,18,26,33,42,23,31,38,47
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3(17,16,12)1(18,17,16,12)2(19,18,17)1(20,19,17,16,12)3(21,*20,19,18,17,16,12)4(22,16,12)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3(17,*16,12,11,9,7)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3(17,*16,12,11,9,7)3(18,16,11,9,7)3(19,18,16)1(20,19,18,16)2(21,20,19)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,20,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3(17,*16,12,11,9,7)3(18,16,11,9,7)3(19,18,16)1(20,19,18,16)2(21,20,19)1(22,21,19,18,16)3(23,*22,21,20,19,18,16)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,20,32,43,56
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*9,7,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*9,7,3,2,1,0)4(12,9,7)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*9,7,3,2,1,0)4(12,*9,7,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25,35,47
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,10,9,7)2
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25,35,47,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25,35,47,19,27,34,43
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,3,2,1,0)4(20,15,11)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25,35,47,19,27,34,43,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,3,2,1,0)4(20,*18,17,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25,35,47,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,11,10,9,7)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,11,10,9,7)4(20,18,17)1(21,20,18,17)2(22,21,20)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,15,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,11,10,9,7)4(20,18,17)1(21,20,18,17)2(22,21,20)1(23,22,20,18,17)3(24,*23,22,21,20,18,17)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,15,28,40,54
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,11,10,9,7)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,11,10,9,7)4(15,11,10,9,7)3(16,*15,11,10,9,7)3(17,15,10,9,7)3(18,*17,15,11,10,9,7)4(19,18,17,15)2(20,19,18)1(21,20,18,17,15)3(22,*21,20,19,18,17,15)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,15,28,40,56
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*10,*9,7,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,2,1,0)2(12,11,2,1,0)3(13,*12,11,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,36,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,3,2,1,0)2(12,*11,3,2,1,0)3(13,11,2,1,0)3(14,*13,11,3,2,1,0)4(15,*14,*13,11,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,38,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,3,2,1,0)2(12,*11,3,2,1,0)3(13,11,3)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,38,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,7,2,1,0)2(12,*11,7,3,2,1,0)3(13,*12,*11,7,3,2,1,0)4(14,11,7)1(15,14,2,1,0)3(16,11,2,1,0)3(17,*16,11,3,2,1,0)4(18,*17,*16,11,7,3,2,1,0)5(19,*18,*17,*16,11,7,3,2,1,0)5
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,42,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,7,3)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,42,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,42,53
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,7,3)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,49,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,9,2,1,0)3(13,*12,9,3,2,1,0)4(14,7,3)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,49,49,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,10,9)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,49,66
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,*10,9,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,49,67
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,*10,9,3,2,1,0)4(13,7,2,1,0)3(14,*13,7,3,2,1,0)4(15,*14,*13,7,3,2,1,0)4(16,13,7)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,49,67,24,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,*10,9,3,2,1,0)4(13,7,2,1,0)3(14,*13,7,3,2,1,0)4(15,*14,*13,7,3,2,1,0)4(16,13,7)1(17,16,2,1,0)3(18,*17,16,3,2,1,0)4(19,*18,*17,16,7,3,2,1,0)5(20,*17,16,3,2,1,0)4(21,*20,*17,16,7,3,2,1,0)5
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,37
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,*10,9,3,2,1,0)4(13,7,3)1
|1,3,4,2,5,7,10,4,9,13,19,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,11,10,9)2(13,12,11)1(14,13,11,10,9)3(15,*14,13,12,11,10,9)4(16,12,11,10,9)3(17,*16,12,11,10,9)3(18,16,12)1(19,18,11,10,9)3(20,*19,18,12,11,10,9)4
|1,3,4,2,5,7,10,4,9,13,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,*11,*10,9,7,3,2,1,0)5
|1,3,4,2,5,7,10,4,9,13,20,8,17,25,39
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2)1
|1,3,4,2,5,7,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2)1(8,7,2,1,0)3(9,8,7)1
|1,3,4,2,5,7,10,5,7,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2)1(8,7,2,1,0)3(9,*8,7,3,2,1,0)4
|1,3,4,2,5,7,10,5,7,10,4,9,13,20,9,13,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2)1(8,7,2,1,0)3(9,*8,7,3,2,1,0)4(10,3,2)1
|1,3,4,2,5,7,10,5,7,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,4,2,1,0)3(8,3,2)1
|1,3,4,2,5,7,10,7,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,4,2,1,0)3(8,*7,4,3,2,1,0)4(9,3,2)1
|1,3,4,2,5,7,10,7,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,5,4)1
|1,3,4,2,5,7,10,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*5,4,3,2,1,0)4(8,3,2)1
|1,3,4,2,5,7,10,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,2,1,0)3(8,7,6)1
|1,3,4,2,5,7,10,12,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,2,1,0)3(8,*7,6,3,2,1,0)4(9,3,2)1
|1,3,4,2,5,7,10,12,15,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2
|1,3,4,2,5,7,10,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,11,10)1
|1,3,4,2,5,7,10,13,4,9,13,20,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,14,10,9,8)3(16,11,10)1
|1,3,4,2,5,7,10,13,4,9,13,20,24,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,14,13,12)2
|1,3,4,2,5,7,10,13,4,9,13,20,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,2,1,0)2(9,8,2,1,0)3(10,*9,8,2,1,0)3
|1,3,4,2,5,7,10,13,4,9,13,20,25,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,2,1,0)2(9,8,2)1
|1,3,4,2,5,7,10,13,4,9,13,20,25,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3
|1,3,4,2,5,7,10,13,4,9,13,20,25,8,17,25,40,49,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1
|1,3,4,2,5,7,10,13,4,9,13,20,25,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,8,3)1
|1,3,4,2,5,7,10,13,4,9,13,20,25,9,13,20,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,10,2,1,0)3(14,*13,10,3,2,1,0)4(15,8,3)1
|1,3,4,2,5,7,10,13,4,9,13,20,25,9,13,20,24,31,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,11,10)1
|1,3,4,2,5,7,10,13,4,9,13,20,25,9,13,20,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,*11,10,3,2,1,0)4
|1,3,4,2,5,7,10,13,4,9,13,20,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,12,11,10)2
|1,3,4,2,5,7,10,13,4,9,13,20,26,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,12,11,10)2(14,13,12)1(15,14,12,11,10)3(16,*15,14,13,12,11,10)4
|1,3,4,2,5,7,10,13,4,9,13,20,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,*12,*11,10,8,3,2,1,0)5
|1,3,4,2,5,7,10,13,4,9,13,20,27,8,17,25,40,52
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2)1
|1,3,4,2,5,7,10,13,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,4,2,1,0)3
|1,3,4,2,5,7,10,13,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,5,4)1
|1,3,4,2,5,7,10,13,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,*5,4,3,2,1,0)4(9,3,2)1
|1,3,4,2,5,7,10,13,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,6,5,4)2
|1,3,4,2,5,7,10,13,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3
|1,3,4,2,5,7,10,13,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,2,1,0)2(10,9,2)1(11,10,2,1,0)3(12,*11,10,9,2,1,0)4(13,12,11,10)2(14,13,12,11,10)3
|1,3,4,2,5,7,10,13,16,4,9,13,20,27,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,3,2)1
|1,3,4,2,5,7,10,13,16,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,8,7)1
|1,3,4,2,5,7,10,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,8,7)1(10,2,1,0)2(11,10,2)1(12,11,2,1,0)3(13,*12,11,10,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,15,14)1
|1,3,4,2,5,7,10,14,4,9,13,20,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,8,7)1(10,3,2)1
|1,3,4,2,5,7,10,14,4,9,13,20,28,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4
|1,3,4,2,5,7,10,14,4,9,13,20,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,1,0)1(11,10,1,0)2(12,11,10)1
|1,3,4,2,5,7,10,14,4,9,13,20,29,4,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,1,0)1(11,10,1,0)2(12,11,10)1(13,12,10,1,0)3(14,*13,12,11,10,1,0)4(15,11,10)1
|1,3,4,2,5,7,10,14,4,9,13,20,29,4,9,13,20,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,1,0)1(11,10,1,0)2(12,11,10)1(13,12,10,1,0)3(14,*13,12,11,10,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,16,15)1
|1,3,4,2,5,7,10,14,4,9,13,20,29,4,9,13,20,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,1,0)1(11,10,1,0)2(12,11,10)1(13,12,10,1,0)3(14,*13,12,11,10,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,11,10,1,0)4
|1,3,4,2,5,7,10,14,4,9,13,20,29,4,9,13,20,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,2,1,0)2
|1,3,4,2,5,7,10,14,4,9,13,20,29,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,2,1,0)2(11,10,2)1
|1,3,4,2,5,7,10,14,4,9,13,20,29,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,2,1,0)2(11,10,2)1(12,11,2,1,0)3(13,*12,11,10,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,10,2,1,0)4
|1,3,4,2,5,7,10,14,4,9,13,20,29,8,17,25,40,57
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,3,2,1,0)3(11,*10,3,2,1,0)3
|1,3,4,2,5,7,10,14,4,9,13,20,29,8,17,25,40,58,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,3)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,10,3,2,1,0)5(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,16,14,13,12)3(19,*18,16,15,14,13,12)4(20,*18,16,15,14,13,12)4(21,10,3)1
|1,3,4,2,5,7,10,14,4,9,13,20,29,8,17,25,40,58,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,3)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,10,3,2,1,0)5(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,16,14,13,12)3(19,*18,16,15,14,13,12)4(20,19,18,16)2(21,20,19)1(22,21,19,18,16)3(23,*22,21,20,19,18,16)4(24,23,22,21)2(25,24,23,22,21)3(26,*25,24,20,19,18,16)4(27,20,19,18,16)3(28,*27,20,19,18,16)3(29,27,20)1(30,29,19,18,16)3(31,*30,29,20,19,18,16)4(32,*31,*30,29,27,20,19,18,16)5(33,32,31,30,29)3(34,*33,32,31,30,29)3(35,33,31,30,29)3(36,*35,33,32,31,30,29)4
|1,3,4,2,5,7,10,14,4,9,13,20,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,3)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,10,3,2,1,0)5(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,16,14,13,12)3(19,*18,16,15,14,13,12)4(20,*19,*18,16,10,3,2,1,0)5
|1,3,4,2,5,7,10,14,4,9,13,20,31,8,17,25,40,64
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,3,2)1
|1,3,4,2,5,7,10,14,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,*8,7,3,2,1,0)4(11,3,2)1
|1,3,4,2,5,7,10,14,14,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,2,1,0)4(11,3,2)1
|1,3,4,2,5,7,10,14,16,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,6,5,4)4(11,3,2)1
|1,3,4,2,5,7,10,14,17,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,6,5,4)4(11,*10,9,3,2,1,0)4(12,3,2)1
|1,3,4,2,5,7,10,14,17,21,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,8,7)2
|1,3,4,2,5,7,10,14,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,8,7)2(11,3,2)1
|1,3,4,2,5,7,10,14,18,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,8,7)2(11,10,9,8,7)3
|1,3,4,2,5,7,10,14,18,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,8,7)2(11,10,9,8,7)3(12,11,10)1
|1,3,4,2,5,7,10,14,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,3,2,1,0)4(13,3,2)1
|1,3,4,2,5,7,10,14,19,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3
|1,3,4,2,5,7,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,1,0)1(11,10,1,0)2(12,11,10)1
|1,3,4,2,5,7,11,4,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,1,0)1(11,10,1,0)2(12,11,10)1(13,12,10,1,0)3(14,*13,12,11,10,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3
|1,3,4,2,5,7,11,4,9,13,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,2,1,0)2(11,10,2)1
|1,3,4,2,5,7,11,4,9,13,21,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,2,1,0)2(11,10,2)1(12,11,2,1,0)3(13,*12,11,10,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,13,12,11)3
|1,3,4,2,5,7,11,4,9,13,21,8,17,25,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,3)1
|1,3,4,2,5,7,11,4,9,13,21,8,17,25,41,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,3,2)1
|1,3,4,2,5,7,11,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,3,2)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,12,11,10)2(14,13,12,11,10)3(15,*14,13,12,11,10)3
|1,3,4,2,5,7,11,5,7,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,4,2,1,0)3(11,*10,4,3,2,1,0)4(12,11,10,4)2(13,12,11,10,4)3(14,*13,12,11,10,4)3
|1,3,4,2,5,7,11,7,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,5,2,1,0)3(11,*10,5,3,2,1,0)4(12,11,10,5)2(13,12,11,10,5)3(14,*13,12,11,10,5)3
|1,3,4,2,5,7,11,9,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,5,4)1
|1,3,4,2,5,7,11,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,*5,4,3,2,1,0)4(11,3,2)1
|1,3,4,2,5,7,11,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,*5,4,3,2,1,0)4(11,10,5,4)2(12,11,10,5,4)3(13,*12,11,10,5,4)3
|1,3,4,2,5,7,11,10,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,6,5,4)2
|1,3,4,2,5,7,11,10,15,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,6,5,4)2(11,10,6,5,4)3(12,*11,10,3,2,1,0)4(13,12,11,10)2(14,13,12,11,10)3(15,*14,13,12,11,10)3
|1,3,4,2,5,7,11,10,15,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,6,5,4)2(11,10,6,5,4)3(12,*11,10,3,2,1,0)4(13,12,11,10)2(14,13,12,11,10)3(15,*14,13,12,11,10)3(16,12,11,10)2
|1,3,4,2,5,7,11,10,15,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,6,5,4)2(11,10,6,5,4)3(12,*11,10,6,5,4)3
|1,3,4,2,5,7,11,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,7,2,1,0)3
|1,3,4,2,5,7,11,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,7,2,1,0)3(11,*10,7,3,2,1,0)4(12,11,10,7)2(13,12,11,10,7)3(14,*13,12,11,10,7)3
|1,3,4,2,5,7,11,13,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,7,6,5,4)3
|1,3,4,2,5,7,11,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,7,6,5,4)3(11,*10,7,6,5,4)3
|1,3,4,2,5,7,11,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3
|1,3,4,2,5,7,11,15,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3(12,10,8)1
|1,3,4,2,5,7,11,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3(12,*10,8,3,2,1,0)4(13,3,2)1
|1,3,4,2,5,7,11,16,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3(12,*10,8,7,6,5,4)4
|1,3,4,2,5,7,11,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3(12,11,10,8)2(13,12,11,10,8)3(14,*13,12,11,10,8)3(15,13,11,10,8)3(16,*15,13,12,11,10,8)4
|1,3,4,2,5,7,11,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3(12,*11,*10,8,7,6,5,4)4
|1,3,4,2,5,7,11,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1
|1,3,4,2,5,7,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,7,6)1
|1,3,4,2,5,7,12,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3
|1,3,4,2,5,7,12,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,3,2)1
|1,3,4,2,5,7,12,14,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6,5,4)3(11,*10,7,6,5,4)3(12,10,7)1(13,12,2,1,0)3
|1,3,4,2,5,7,12,14,11,20,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6)1
|1,3,4,2,5,7,12,14,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3
|1,3,4,2,5,7,12,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3(11,*10,7,6,5,4)3(12,10,7)1(13,12,6,5,4)3(14,*13,12,7,6,5,4)4
|1,3,4,2,5,7,12,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6)1
|1,3,4,2,5,7,12,16,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,9,8)1
|1,3,4,2,5,7,12,16,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,3,2,1,0)4(11,3,2)1
|1,3,4,2,5,7,12,16,21,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4
|1,3,4,2,5,7,12,16,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,10,9,8)3
|1,3,4,2,5,7,12,16,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,10,9,8)3(14,12,10,9,8)3(15,*14,12,11,10,9,8)4(16,*15,*14,12,11,10,9,8)4
|1,3,4,2,5,7,12,16,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4(11,10,9,8)2(12,11,10)1
|1,3,4,2,5,7,12,16,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,11,10)1
|1,3,4,2,5,7,12,16,25,33,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14)1
|1,3,4,2,5,7,12,16,25,33,50
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4
|1,3,4,2,5,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,1,0)1(9,8,1,0)2(10,9,8)1(11,10,8,1,0)3(12,*11,10,9,8,1,0)4(13,*12,*11,10,9,8,1,0)4
|1,3,4,2,5,8,4,9,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1
|1,3,4,2,5,8,4,9,14,6,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,*14,*13,12,11,10,9,8)4
|1,3,4,2,5,8,4,9,14,6,11,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,*14,*13,12,11,10,9,8)4(16,9,8)1
|1,3,4,2,5,8,4,9,14,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,*14,*13,12,11,10,9,8)4(16,9,8)1(17,16,9,8)2(18,17,16)1(1918,16,9,8)3(20,*19,18,17,16,9,8)4(21,*20,*19,*18,17,16,9,8)4
|1,3,4,2,5,8,4,9,14,7,13,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2,1,0)3(10,*9,8,2,1,0)3
|1,3,4,2,5,8,4,9,14,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2)1
|1,3,4,2,5,8,4,9,14,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2)1(10,9,2,1,0)3(11,*10,9,8,2,1,0)3(12,*11,*10,9,8,2,1,0)4
|1,3,4,2,5,8,4,9,14,8,17,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1
|1,3,4,2,5,8,4,9,14,8,17,26,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,8,3)1
|1,3,4,2,5,8,4,9,14,8,17,26,16,33,49,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,12,11,10)2(14,13,12)1
|1,3,4,2,5,8,4,9,14,8,17,26,16,33,49,72
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,*12,*11,10,8,3,2,1,0)5
|1,3,4,2,5,8,4,9,14,8,17,26,16,33,50
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,3,2)1
|1,3,4,2,5,8,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,3,2)1(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,*10,*9,8,3,2,1,0)4
|1,3,4,2,5,8,5,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3
|1,3,4,2,5,8,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,3,2)1
|1,3,4,2,5,8,7,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,3,2)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,11,10,9)2(13,12,11)1
|1,3,4,2,5,8,7,5,7,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,3,2)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,11,10,9)2(13,12,11)1(14,13,11,10,9)3(15,*14,13,12,11,10,9)4(16,*15,*14,13,12,11,10,9)4
|1,3,4,2,5,8,7,5,7,12,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,3,2)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,11,10,9)2(13,12,11)1(14,13,11,10,9)3(15,*14,13,12,11,10,9)4(16,*15,*14,13,12,11,10,9)4(17,13,11,10,9)3(18,12,11)1
|1,3,4,2,5,8,7,5,7,12,17,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,3,2)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,*11,*10,9,3,2,1,0)4
|1,3,4,2,5,8,7,5,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,8,4)1
|1,3,4,2,5,8,7,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,*8,4,3,2,1,0)4(10,3,2)1
|1,3,4,2,5,8,7,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,*8,4,3,2,1,0)4(10,9,8,4)2(11,10,9,8,4)3(12,*11,10,9,8,4)3
|1,3,4,2,5,8,7,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,*8,4,3,2,1,0)4(10,9,8,4)2(11,10,9)1
|1,3,4,2,5,8,7,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,*8,4,3,2,1,0)4(10,9,8,4)2(11,10,9)1(12,11,9,8,4)3(13,*12,11,10,9,8,4)4(14,*13,*12,11,10,9,8,4)4
|1,3,4,2,5,8,7,12,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,*8,4,3,2,1,0)4(10,9,8,4)2(11,10,9)1(12,11,9,8,4)3(13,*12,11,10,9,8,4)4(14,*13,*12,11,10,9,8,4)4(15,11,9,8,4)3(16,*15,11,10,9,8,4)4
|1,3,4,2,5,8,7,12,17,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,*8,4,3,2,1,0)4(10,*9,*8,4,3,2,1,0)4
|1,3,4,2,5,8,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3
|1,3,4,2,5,8,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(6,3,2)1
|1,3,4,2,5,8,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5
|1,3,4,2,5,8,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,8,2,1,0)3(12,*11,8,3,2,1,0)4(13,*12,*11,8,4,3,2,1,0)5
|1,3,4,2,5,8,11,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,8,5)1
|1,3,4,2,5,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,8,5)1(12,1,0)1(13,12,1,0)2(14,13,12)1(15,14,12,1,0)3(16,*15,14,13,12,1,0)4(17,*16,*15,14,13,12,1,0)4
|1,3,4,2,5,9,4,9,14
|-
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|1,3,4,2,5,9,4,9,14,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,8,5)1(12,1,0)1(13,12,1,0)2(14,13,12)1(15,14,12,1,0)3(16,*15,14,13,12,1,0)4(17,*16,*15,14,13,12,1,0)4(18,15,12,1,0)3(19,*18,15,13,12,1,0)4(20,*19,*18,15,14,13,12,1,0)5(21,18,15)1
|1,3,4,2,5,9,4,9,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,8,5)1(12,2,1,0)2(13,12,2)1
|1,3,4,2,5,9,4,9,15,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,8,5)1(12,3,2)1
|1,3,4,2,5,9,4,9,15,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4
|1,3,4,2,5,9,4,9,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,2,1,0)2(13,12,2)1
|1,3,4,2,5,9,4,9,16,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,2,1,0)2(13,12,2)1(14,13,2,1,0)3(15,*14,13,12,2,1,0)4(16,*15,*14,13,12,2,1,0)4(17,14,2,1,0)3(18,*17,14,12,2,1,0)4(19,*18,*17,14,13,12,2,1,0)5
|1,3,4,2,5,9,4,9,16,8,17,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,2,1,0)2(13,12,2)1(14,13,2,1,0)3(15,*14,13,12,2,1,0)4(16,*15,*14,13,12,2,1,0)4(17,14,2,1,0)3(18,*17,14,12,2,1,0)4(19,*18,*17,14,13,12,2,1,0)5(20,17,14)1
|1,3,4,2,5,9,4,9,16,8,17,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,2,1,0)2(13,12,2)1(14,13,2,1,0)3(15,*14,13,12,2,1,0)4(16,*15,*14,13,12,2,1,0)4(17,14,2,1,0)3(18,*17,14,12,2,1,0)4(19,*18,*17,14,13,12,2,1,0)5(20,*17,14,12,2,1,0)4
|1,3,4,2,5,9,4,9,16,8,17,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2,1,0)3(13,*12,3,2,1,0)3
|1,3,4,2,5,9,4,9,16,8,17,28,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2,1,0)3(13,*12,3,2,1,0)3(14,12,3)1
|1,3,4,2,5,9,4,9,16,8,17,29,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2,1,0)3(13,*12,3,2,1,0)3(14,12,3)1(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,12,3,2,1,0)5(18,*17,*16,*15,14,12,3,2,1,0)5
|1,3,4,2,5,9,4,9,16,8,17,29,16,33,50
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2,1,0)3(13,*12,3,2,1,0)3(14,12,3)1(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,12,3,2,1,0)5(18,*17,*16,*15,14,12,3,2,1,0)5(19,15,2,1,0)3(20,*19,15,3,2,1,0)4(21,*20,*19,15,12,3,2,1,0)5(22,*21,*20,*19,15,14,12,3,2,1,0)6
|1,3,4,2,5,9,4,9,16,8,17,29,16,33,50,67
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2,1,0)3(13,*12,3,2,1,0)3(14,12,3)1(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,12,3,2,1,0)5(18,*17,*16,*15,14,12,3,2,1,0)5(19,15,2,1,0)3(20,*19,15,3,2,1,0)4(21,*20,*19,15,12,3,2,1,0)5(22,*21,*20,*19,15,14,12,3,2,1,0)6(23,19,15)1
|1,3,4,2,5,9,4,9,16,8,17,29,16,33,51
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2,1,0)3(13,*12,3,2,1,0)3(14,12,3)1(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,12,3,2,1,0)5(18,*17,*16,*15,14,12,3,2,1,0)5(19,15,2,1,0)3(20,*19,15,3,2,1,0)4(21,*20,*19,15,12,3,2,1,0)5(22,*21,*20,*19,15,14,12,3,2,1,0)6(23,*19,15,3,2,1,0)4
|1,3,4,2,5,9,4,9,16,8,17,29,16,33,52
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2,1,0)3(13,*12,3,2,1,0)3(14,12,3)1(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,12,3,2,1,0)5(18,*17,*16,*15,14,12,3,2,1,0)5(19,15,2,1,0)3(20,*19,15,3,2,1,0)4(21,*20,*19,15,12,3,2,1,0)5(22,*21,*20,*19,15,14,12,3,2,1,0)6(23,*19,15,3,2,1,0)4(24,12,3)1
|1,3,4,2,5,9,4,9,16,8,17,29,16,33,55,33
|-
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|1,3,4,2,5,9,4,9,16,8,17,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2,1,0)3(13,*12,3,2,1,0)3(14,12,3)1(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,12,3,2,1,0)5(18,*17,*16,*15,14,12,3,2,1,0)5(19,15,2,1,0)3(20,*19,15,3,2,1,0)4(21,*20,*19,15,12,3,2,1,0)5(22,*21,*20,*19,15,14,12,3,2,1,0)6(23,*19,15,3,2,1,0)4(24,*10,15,3,2,1,0)4(25,12,3)1
|1,3,4,2,5,9,4,9,16,9
|-
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|1,3,4,2,5,9,4,9,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1
|1,3,4,3
|}
[[分类:分析]]

iBLP

2026-04-29T14:49:51Z

Baixie01000a7：/* 分析 */

== 记号简介 ==
无限基本Laver图案(Infinite Basic Laver Pattern)是由test_alpha0的记号Basic Laver Pattern改造而来。IBLP目前尚不理想，还存在许多的坏图案。test_alpha0规定其极限表达式为(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,3,2)2(6,5,4)1，因为现在认为在该图案下方不存在坏图案，而其上方不远处就出现了很多坏图案。尽管如此，IBLP仍然被认为是目前最强的记号。本页面介绍的规则对应[https://hypcos.github.io/notation-explorer/ NE]上的DEN2。

== 定义 ==

=== 定义1 （IBLP） ===
一个IBLP是一个四元组<math>A=(n,(A_1,\dots,A_n),(l_1,\dots,l_n),(M_1,\dots,M_n))</math>，

其中：

<math>(1)n\in\N</math>。

<math>(2)</math>对每个<math>i\in\{1,\dots,n\}</math>，<math>A_i</math>是严格递增的非负整数序列，满足<math>\mathrm{len}(A_i)\geq2\text{且}\max(A_i)=i</math>。

<math>(3)</math>对每个<math>i\in\{1,\dots,n\}</math>，步长<math>l_i\in \N</math>。

<math>(4)</math>对每个<math>i\in\{1,\dots,n\}</math>，标记集合<math>M_i\subseteq A_i</math>

约定所有编号从 1 开始；<math>A_i[k]</math> 表示第 ''k'' 个元素，<math>A_i[-j]=A_i[\mathrm{len}(A_i)-j+1]</math>表示倒数第 ''j'' 个元素。

=== 定义2 （长行、中等行、短行） ===
行 <math>i</math> 称为长行若<math>\mathrm{len}(A_i)>2l_i</math>，称为中等行若<math>\mathrm{len}(A_i)=2l_i</math>，称为短行若 <math>\mathrm{len}(A_i)<2l_i</math>。

=== 定义3 （零图案、后继图案、极限图案） ===
若 ''n'' = 0，称 ''A'' 为零图案。若 <math>n>0\text{且}\mathrm{len}(A_n)=2\text{且}\min(A_n)=0</math>，称 ''A'' 为后继图案。否则称 ''A'' 为极限图案。

=== 定义4 （行比较键） ===
令<math>A_i=(A_1<a_2<\dots<a_m)\text{且}L=l_i</math>。定义保留序列

<math>K_i=\begin{cases}(a_1,a_2,\dots,a_m),&L\leq1;\\(a_1,a_{L+1},a_{L+2},\dots,a_m),&2\leq L\leq m;\\(a_1,a_2,\dots,a_m),&L\geq2\text{且}m<L.\end{cases}</math>

定义行键为<math>\overleftarrow{K_i}</math>（即<math>K_i
</math>逆序，从大到小）。

=== 定义5 （IBLP的大小比较） ===
给定两个 ''IBLP'' <math>A\text{、}B</math>，从 <math>i=1</math> 起逐行比较其

行键<math>\overleftarrow{K_i(A)}\text{与}\overleftarrow{K_i(B)}</math> 的字典序；第一处不同决定大小。若前<math>\min(n_a,n_b)</math>行都相等，则行数较小者更小。

=== 定义6 （一行的根<math>p(i)</math>） ===
对<math>i\in\{1,\dots,n\}</math>，定义<math>p(i)=A_i[-(l_i+1)]</math>.

=== 定义7 （传递序列<math>tr_i(j)</math>） ===
固定行 ''i''。若<math>j=A_i[k](1\leq k\leq\mathrm{len}(A_i))\text{且}k\geq l_i</math>，定义阈值 <math>\theta=A_i[k-l_i]</math>。令 <math>t_0=j</math>，并在<math>t_m>\theta\text{且}p(t_m)\text{有定义}</math>时令 <math>t_{m+1}=p(t_m)</math>。若存在最小 <math>m>0</math>使<math>t_m=\theta</math>，则定义<math>tr_i(j)=(t_0,t_1,\dots,t_m)</math>''，''否则称 <math>tr_i(j)</math> 无定义。若 <math>k\leq l_i</math>，亦称无定义。

=== 定义8 （部分函数<math>f_A</math>） ===
设 ''A'' 非零且有至少1行。令 <math>a_1=A_n[1]=\min(A_n)\text{，}L=l_n\text{，}p=p(n)=A_n[-(L+1)]</math>。定义部分函数 <math>f_A:\N\rightharpoonup\N</math>：

<math>(1)</math>若<math>x<a_1</math>，则<math>f_A(x)=x</math>；

<math>(2)</math>若<math>x=A_n[k]\text{且}x<p\text{且}k+L\leq\mathrm{len}(A_n)</math>，则<math>f_A(x)=A_n[k+L]</math>；

<math>(3)</math>若<math>x\geq p</math>，则<math>f_A(x)=x+n-p</math>；

<math>(4)</math>其余情形 <math>f_A(x)</math> 无定义。

=== 定义9 （copy 的行与步长） ===
设 ''A'' 行数为<math>n\geq1</math>，令 <math>p=p(n)</math>。若 copy 过程中出现 <math>f_A(x)</math> 无定义，则<math>copy(A)</math>无定义。否则定义 <math>A'=copy(A)</math> 行数为 <math>n'=2n-p</math>，满足：

<math>(1)</math>对<math>1\leq i\leq n-1\text{：}A_i'=A_i\text{，}l_i'=l_i\text{，}M_i'=M_i</math>；

<math>(2)</math>对每个<math>i\in\{1,\dots,n-p+1\}</math>，令源行<math>\sigma=p+i-1</math>，目标行<math>\tau=n-1+i</math>''i''，定义<math>A_\tau'=\mathrm{sort}(\{f_A(x)|x\in A_\sigma\})\text{，}l_\tau'=l_\sigma</math>，要求<math>\forall x\in A_\sigma\text{，}f_A(x)\text{有定义}</math>。

=== 定义10 （copy的标记过滤） ===
延续上一定义。对目标行<math>\tau</math>中元素<math>x\in A_\tau'</math>，令

<math>y\in A_\sigma</math>为其唯一来源（即 <math>f_A(y)=x</math>）。则 <math>x\in M_\tau'</math> 当且仅当：

<math>y\in M_\sigma</math>，并且满足下列之一：

* <math>tr_\sigma(y)</math>有定义且<math>tr_\sigma(y)[-2]\geq p</math>；
* 令<math>y_0</math>为<math>tr_\sigma(y)</math>中首次出现的<math><p</math>的元素（等价于“最大的
<math><p</math>的元素”）。要么<math>y_0<a_1</math>；要么存在 ''k'' 使<math>y_0=A_n[k]\text{且}k+L\leq\mathrm{len}(A_n)\text{且}A_n[k+L]\in M_n</math>，并且若 ''x'' 在 <math>A_\tau'</math>中的位置为 ''q''（从 1 开始），则当 <math>q+1-l_\sigma\geq1</math> 时需满足<math>A_\tau'[q+1-l_\sigma]\leq a_1.</math>

=== 定义11 （E(A,0)） ===
若 ''A'' 非零且 ''n ≥'' 1，则 ''E''(''A,'' 0) 为删除最后一行后的图案（行数变为 ''n −'' 1，其余行、步长、标记保持不变）。

=== 定义12 （''E''(''A, m'')的copy阶段 (''m≥1)''） ===
设A是极限图案。令<math>A^{(0)}=A</math>。若第一次<math>copy(A^{(0)})</math> 无定义，则称 ''A'' 为坏图案并定义<math>E(A,m)=E(A,0)</math>。否则定义

<math>A^{(1)}=copy(A^{(0)}),A^{(2)}=copy(A^{(1)}),\dots,A^{(m)}=copy(A^{(m-1)})</math>,

并令<math>B=E(A^{(m)},0)</math>

接下来对B做补全，初始行号 <math>r=n</math>（这里 ''n'' 为原始 ''A'' 的行数）。补全过程允许使用临时记录映射 <math>\rm Rec</math>（行号 <math>\mapsto</math> 有限序列），结束后丢弃。

=== 定义13 （标记补全） ===
固定当前行 ''r''。令<math>\mathcal{B}=\{b\in M_r|b\in A_r\}</math>并按升序枚举其元素<math>b_1<b_2<\dots<b_k</math>（该集合在本轮开始时冻结，新产生标记不加入本轮）。对每个 <math>b_i</math>依次：

<math>(1)</math>若 <math>tr_i(b_i)</math>无定义则跳过；

<math>(2)</math>令<math>t=tr_r(b_i)[-2]</math>。若<math>\mathrm{Rec}(t)</math>不存在或为空则跳过，否则记 <math>s=\mathrm{Rec}(t)</math>；

<math>(3)</math>若对所有<math>j=3,4,\dots,\mathrm{len}(tr_r(b_i))</math>都有<math>tr_r(b_i)[-j+1]+1\in A_{tr_r(b_i)[-j]}</math>，那么把s 及<math>b_i+1,b_i+2,\dots,b_i+\mathrm{len}(s)</math> 加入 <math>A_r</math>，并重新排序去重使

之严格递增。更新标记：''s'' 中元素不标记，<math>b_i+1,b_i+2,\dots,b_i+\mathrm{len}(s)</math> 全标

记，其余标记保留（按上述规则修正）。更新步长：<math>l_r=l_r+len(s)</math>。

=== 定义14 （原生补全） ===
固定当前行 ''r''。若<math>A_r</math>为长行，则原生补全不执行并返回 0。否则令<math>p_r=p(r)=A_r[-(l_r+1)]\text{，}a=A_r[-l_r]</math>.

构造序列 ''s''：令 <math>u_0=a</math>，并在<math>A_{u_m}[-2]</math> 存在且 <math>>p_r</math> 时令 <math>u_{m+1}=A_{u_m}[-2]</math>并把 <math>u_{m+1}</math> 追加到 ''s''，直至无法继续。令 <math>t=\mathrm{len}(s)</math>。若 <math>t=0</math> 返回 0；若<math>t>0</math>，令 <math>\mathrm{Rec}(r)=s</math> 并继续：

<math>(1)</math>在 ''r'' 后插入 ''t'' 行，使原本行号 <math>>r</math> 的行号整体加 ''t''；

<math>(2)</math> 仅对原本行号 <math>>r</math>的那些行，在其中把所有 <math>>r</math> 的元素加 ''t''，并同步

标记集合，步长不变；

<math>(3)</math>令旧行及旧步长为 <math>A_r^{old},l_r^{old}</math>。将旧行替换为 ''t'' + 1 行：

<math>A_{r+t}=\mathrm{sort}(A_r^{old}\cup s\cup\{r+1,r+2,\dots,r+t\})\text{，}l_{r+t}=l_r^{old}+t</math>.

标记规则：除s和r+t外均标记。

<math>(4)</math>对<math>i=t,t-1,\dots,1</math>，由<math>A_{r+i}</math>构造 <math>A_{r+i-1}</math>：删除元素<math>r+i</math>，并删除元素 <math>A_{r+i}[-l_{r+i}]</math>，去除<math>r+i-1</math> 的标记，并令 <math>l_{r+i-1}=l_{r+i}-1</math>。

<math>(5)</math>'''中等行例外：'''若<math>i=t</math> 且 ''<math>A_r^{old}</math>''为中等行，则在构造 <math>A_{r+i-1}</math> 时不删除 <math>A_{r+i}[-l_{r+i}]</math>且不减步长（令 <math>l_{r+i-1}=l_{r+i}</math>），但仍删除 <math>r+i</math> 并去除<math>r+i-1</math> 的标记。

原生补全返回t。

=== 定义15 （补全主循环(用于 ''E''(''A, m''))） ===
令初始<math>r=n</math>（''n'' 为原始 ''A'' 的行数）。当 ''r'' 不超过当前 ''B'' 的行数时循环：先对行 ''r'' 执行标记补全，再执行原生补全得到 ''t''，然后更新 <math>r=r+t+1</math>。当 ''r'' 越界时补全结束，丢弃 <math>\rm Rec</math>，所得 ''B'' 即为<math>E(A,m)</math>。

== 展开器 ==
iblp的展开器在[https://hypcos.github.io/notation-explorer/ NE]上可以找到，同时也可以使用如下Python代码直观地看到每个图案的行为。<syntaxhighlight lang="python3">
import bisect

def _clone_rows(rows):
return [row[:] for row in rows]

def _clone_mask(mask):
return [set(s) for s in mask]

def _find_index(sorted_row, val):
i = bisect.bisect_left(sorted_row, val)
if i < len(sorted_row) and sorted_row[i] == val:
return i
return None

def _shift_sorted_row_inplace(sorted_row, threshold, delta):
if delta == 0:
return
i = bisect.bisect_left(sorted_row, threshold)
for j in range(i, len(sorted_row)):
sorted_row[j] += delta

def _shift_mark_set(mark_set, threshold, delta):
if delta == 0 or not mark_set:
return mark_set
new = set()
for x in mark_set:
new.add(x + delta if x >= threshold else x)
return new

class ModifyUnpleasant(Exception):
pass

MSG_UNPLEASANT = (
"Something unpleasant happened. Please contact the author (E-mail: qwerasdfyh@126.com) "
"about the previous pattern so he can improve the rule design."
)

class BasicLaverPattern:
def __init__(self, rows, mask=None):
self.rows = _clone_rows(rows)
if mask is None:
self.mask = [set() for _ in self.rows]
else:
self.mask = _clone_mask(mask)
if self.mask:
self.mask[0] = set()
self._normalize_rows_inplace()

def _normalize_rows_inplace(self, start_row=1):
for r in range(max(1, start_row), len(self.rows)):
row = self.rows[r]
if row and row[-1] == r + 1:
row.pop()
self.mask[r].discard(r + 1)

def clone(self):
return BasicLaverPattern(self.rows, self.mask)

def is_zero(self):
return len(self.rows) == 1 and len(self.rows[0]) == 0

def is_successor(self):
if self.is_zero():
return False
last = self.rows[-1]
return len(last) == 2 and last[0] == 0

def draw(self):
if self.is_zero():
return
base_list = self.rows[0]
other_lists = self.rows[1:]
if not other_lists:
return
max_len = max((seq[-1] for seq in other_lists if seq), default=0) + 1
result = []
for i, seq in enumerate(other_lists, start=1):
line = [' '] * max_len
mset = self.mask[i]
for num in seq:
if 0 <= num < max_len:
line[num] = 'a' if num in mset else 'o'
if i <= len(base_list) and seq:
last_circle_index = seq[-1]
result.append(''.join(line[:last_circle_index + 1]) + f" {base_list[i-1]}")
for line in result:
print(line)

def to_string(self):
if self.is_zero():
return ""
base_list = self.rows[0]
out = []
for i in range(1, len(self.rows)):
seq = self.rows[i]
mset = self.mask[i]
parts = []
for x in reversed(seq):
parts.append(f"*{x}" if x in mset else str(x))
step = base_list[i - 1] if i - 1 < len(base_list) else 0
out.append("(" + ",".join(parts) + ")" + str(step))
return "".join(out)

def cut(self):
if self.is_zero():
return False
if len(self.rows) <= 1:
return False
if len(self.rows[0]) == 0:
self.rows = [[]]
self.mask = [set()]
return False
self.rows[0].pop()
self.rows.pop()
self.mask.pop()
if len(self.rows) == 1 and len(self.rows[0]) == 0:
self.mask = [set()]
self._normalize_rows_inplace()
return True

def _transmission_penultimate_and_terminal_checked(self, row_idx, n_value):
rows = self.rows
base = rows[0]
if n_value <= 0 or n_value >= len(rows):
return None
row = rows[row_idx]
l_m = base[row_idx - 1]
k = _find_index(row, n_value)
if k is None or k - l_m < 0:
return None
threshold = row[k - l_m]

cur = n_value
visited = {cur}
while True:
if cur <= 0 or cur >= len(rows):
return None
l_s = base[cur - 1]
if len(rows[cur]) < l_s + 1:
return None
nxt = rows[cur][-l_s - 1]
if nxt > threshold:
if nxt + 1 != cur + 1:
if _find_index(rows[cur], nxt + 1) is None:
return None
prev, cur = cur, nxt
if cur <= threshold:
return (prev, cur)
if cur in visited:
return None
visited.add(cur)

def _first_not_copied_in_transmission(self, orig_rows, orig_base, copied_set, row_idx, n_value):
row = orig_rows[row_idx]
l_m = orig_base[row_idx - 1]
k = _find_index(row, n_value)
if k is None or k - l_m < 0:
raise RuntimeError("Unpleasant.")
threshold = row[k - l_m]
cur = n_value
seq = [cur]
visited = {cur}
while True:
l_s = orig_base[cur - 1]
if len(orig_rows[cur]) < l_s + 1:
raise RuntimeError("Unpleasant.")
nxt = orig_rows[cur][-l_s - 1]
seq.append(nxt)
cur = nxt
if cur <= threshold:
break
if cur in visited:
raise RuntimeError("Unpleasant.")
visited.add(cur)
t = seq[-2]
terminal = seq[-1]
tprime = None
for x in seq:
if x not in copied_set:
tprime = x
break
return tprime, t, terminal

def _slice_right_block(self, row_idx, anchor, q):
row = self.rows[row_idx]
pos = _find_index(row, anchor)
if pos is None:
raise RuntimeError("Unpleasant.")
block = row[pos + 1: pos + 1 + q]
if len(block) != q:
raise RuntimeError("Unpleasant.")
return block

def _mark_completion_for_row(self, r, meta, native_done):
base = self.rows[0]
row0 = self.rows[r]
initial_marks = [x for x in row0 if x in self.mask[r]]
before = set(row0)
added_total = 0

for n in initial_marks:
if _find_index(self.rows[r], n) is None:
continue
if n <= 0 or n >= len(meta):
continue
info = meta[n]
if not info or not info.get("native_generated", False):
continue

tn = self._transmission_penultimate_and_terminal_checked(r, n)
if tn is None:
continue
t, n_terminal = tn
q = native_done.get(t, 0)
if q <= 0:
continue

target_row = t + q
left_block = self._slice_right_block(target_row, n_terminal, q)
right_block = list(range(n + 1, n + q + 1))

new_vals = set(left_block) | set(right_block)
truly_new = new_vals - before
if truly_new:
added_total += len(truly_new)
before |= truly_new

row_set = set(self.rows[r])
row_set.update(new_vals)
self.rows[r] = sorted(row_set)

self.mask[r].difference_update(left_block)
self.mask[r].update(right_block)

if added_total > 0:
base[r - 1] += (added_total // 2)

def _shift_values_ge(self, start_row_idx, threshold, delta):
for i in range(start_row_idx, len(self.rows)):
_shift_sorted_row_inplace(self.rows[i], threshold, delta)
self.mask[i] = _shift_mark_set(self.mask[i], threshold, delta)

def _native_completion_step(self, m, meta):
rows = self.rows
base = rows[0]
l = base[m - 1]
e = len(rows[m])

if e > 2 * l:
return False, 0

if l <= 0 or e < l:
return False, 0

s = [rows[m][-l]]
while True:
if s[-1] <= 0 or s[-1] >= len(rows):
return False, 0
if len(rows[s[-1]]) < 2:
return False, 0
s.append(rows[s[-1]][-2])
if len(rows[m]) < l + 1:
return False, 0
if s[-1] <= rows[m][-l - 1]:
break

k = len(s) - 1
if k == 1:
return False, 0
s.pop()
q = k - 1
if q <= 0:
return False, 0

marks_m_orig = set(self.mask[m])
self._shift_values_ge(m, m + 1, q)

if e == 2 * l:
c = rows[m][:]
else:
c = rows[m][:l - 1] + rows[m][l:]

ext = s[1:][::-1] + list(range(m + 1, m + q + 1))
rows[m].extend(ext)
rows[m].sort()
base[m - 1] += q

d = []
for i in range(q):
d_i = c + s[q - i:] + list(range(m + 1, m + i + 2))
d.append(sorted(d_i))

old_e = e + 1
base[:] = base[:m - 1] + list(range(old_e - l, old_e - l + q)) + base[m - 1:]
rows[:] = rows[:m] + d + rows[m:]
self.mask[:] = self.mask[:m] + [set() for _ in range(q)] + self.mask[m:]

meta_insert = [{"native_generated": True, "native_q": q} for _ in range(q)]
meta[:] = meta[:m] + meta_insert + meta[m:]

marks_to_propagate = {x + q if x >= m + 1 else x for x in marks_m_orig}
for row_idx in range(m, m + q + 1):
self.mask[row_idx].update(marks_to_propagate)
for j in range(1, q + 1):
self.mask[m + j].update(range(m, m + j))

self.mask[m + q].discard(m + 1 + q)
self._normalize_rows_inplace(start_row=m)
return True, q

def modify(self, copy_only=False, silent=False):
try:
orig_rows = _clone_rows(self.rows)
orig_mask = _clone_mask(self.mask)
orig_base = orig_rows[0][:]
orig_last_mask = set(orig_mask[-1]) if orig_mask else set()

rows = self.rows
base0 = rows[0]
n_before_cut = len(base0)
l_last = base0[n_before_cut - 1]
b = rows[-1][:]
b0 = b[0]
p_leftmost = b[0]

self.cut()
rows = self.rows
base0 = rows[0]

u = b[-l_last - 1]
v_copy = n_before_cut
base0.extend(orig_base[u - 1: v_copy])

b_map = {}
limit = len(b) - l_last
for i in range(limit):
key = b[i]
if key not in b_map:
b_map[key] = b[i + l_last]

def map_elem(x):
if x < b0:
return x
if x > u:
return x - u + n_before_cut
return b_map.get(x, -1)

copied_set = set(range(u, v_copy + 1))

for row_idx in range(u, v_copy + 1):
src_row = orig_rows[row_idx]
new_seq = []
for elem in src_row:
new_val = map_elem(elem)
if new_val == -1:
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
new_seq.append(new_val)
new_seq.sort()
rows.append(new_seq)

new_marks = set()
src_marks = orig_mask[row_idx]
if src_marks:
l_m = orig_base[row_idx - 1]
for marked_val in src_marks:
if _find_index(orig_rows[row_idx], marked_val) is None:
continue
tprime, t, _terminal = self._first_not_copied_in_transmission(
orig_rows, orig_base, copied_set, row_idx, marked_val
)
keep = False
if t in copied_set:
keep = True
else:
if tprime is not None and tprime < p_leftmost:
keep = True
elif tprime is not None:
u_img = b_map.get(tprime, None)
if u_img is not None and u_img in orig_last_mask:
mv_img = map_elem(marked_val)
if mv_img != -1:
pos_u = _find_index(new_seq, mv_img)
if pos_u is not None:
idx_check = pos_u - l_m + 1
if idx_check >= 0 and new_seq[idx_check] <= p_leftmost:
keep = True
if keep:
new_marks.add(map_elem(marked_val))
self.mask.append(new_marks)

if copy_only:
self._normalize_rows_inplace()
return self.clone()

meta = [None] * len(self.rows)
native_done = {}

m = n_before_cut
while True:
base0 = self.rows[0]
if m > len(base0):
break
self._mark_completion_for_row(m, meta, native_done)
did, q = self._native_completion_step(m, meta)
if did:
native_done[m] = q
m += q + 1
else:
m += 1

self._normalize_rows_inplace()
return self.clone()

except ModifyUnpleasant:
raise
except RuntimeError as e:
if str(e) == "Unpleasant.":
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
raise

initial_rows = [
[1, 1, 2, 2, 2],
[0, 1],
[0, 1, 2],
[0, 1, 2, 3],
[0, 1, 2, 3, 4],
[2, 3, 4, 5]
]
initial_mask = [set() for _ in initial_rows]
initial_mask[4] = {3}

def _encode_expr(pat: BasicLaverPattern):
base = pat.rows[0]
expr = []
for i in range(1, len(pat.rows)):
L = base[i - 1] if (i - 1) < len(base) else 0
vals_desc = list(reversed(pat.rows[i]))
mset = pat.mask[i]
row = [L] + [[v, (v in mset)] for v in vals_desc]
expr.append(row)
return expr

def _decode_expr(expr):
base = [row[0] for row in expr]
rows = [base]
mask = [set()]
for row in expr:
vals = [x[0] for x in row[1:]]
vals = sorted(set(vals))
rows.append(vals)
mask.append({x[0] for x in row[1:] if x[1]})
return BasicLaverPattern(rows, mask)

def _deepcopy_expr(expr):
return [[row[0]] + [[x[0], bool(x[1])] for x in row[1:]] for row in expr]

def _values(row):
return [row[0]] + [x[0] for x in row[1:]]

def _cut_expr(expr):
return _deepcopy_expr(expr[:-1])

def _pleasant_until(rows, t):
tv = _values(t)
L = t[0]
tcheck = tv[1 + L:]
if not tcheck:
return -1

tmax = tcheck[0]
tmin = tcheck[-1]
tset = set(tcheck)

for n, s in enumerate(rows):
scheck = _values(s)[1:]
i1 = -1
for idx, x in enumerate(scheck):
if x < tmax:
i1 = idx
break
i2 = -1
for idx in range(len(scheck) - 1, -1, -1):
if scheck[idx] > tmin:
i2 = idx
break

if i1 != -1 and i2 != -1 and i1 <= i2:
mid = scheck[i1:i2 + 1]
if any(x not in tset for x in mid):
return n
return -1

def _seq_from(expr, i, j):
row = expr[i]
val = row[j][0]
L = row[0]
threshold = row[j + L][0] if (j + L) < len(row) else 0

record = [[i + 1, j], [val]]
while val > threshold:
row = expr[val - 1]
idx = 1 + row[0]
record[-1].append(idx)
val = row[idx][0] if idx < len(row) else 0
record.append([val])

record.pop()
return record

def _apv(s_vals, t_vals):
L = t_vals[0]
t_last = t_vals[-1]
t_1 = t_vals[1]
t_1L = t_vals[1 + L] if (1 + L) < len(t_vals) else 0

out = []
for x in s_vals:
if x < t_last:
out.append(x)
elif x >= t_1L:
out.append(x - t_1L + t_1)
else:
k = -1
for idx in range(len(t_vals) - 1, -1, -1):
if t_vals[idx] == x:
k = idx
break
out.append(None if k == -1 else t_vals[k - L])
return out

def _ap(row_s, row_t):
svals = _values(row_s)[1:]
tvals = _values(row_t)
mapped = _apv(svals, tvals)
return [row_s[0]] + [[x, False] for x in mapped]

def _copy_block(raw, flag):
active = raw[-1]
expr = _cut_expr(raw)

begin = active[1 + active[0]][0]
end = (begin + flag) if (flag != -1) else (len(raw) + 1)
offset = len(raw) - begin

expr.extend([_ap(row, active) for row in raw[begin - 1:end - 1]])

active_min = active[-1][0]
begin_rowno = begin

for i in range(begin - 1, end - 1):
row = raw[i]
target_row = expr[i + offset]
for j in range(1, len(row)):
if not row[j][1]:
continue

seq = _seq_from(raw, i, j)

nomove = -1
for k, item in enumerate(seq):
if item[0] < begin_rowno:
nomove = k
break

if nomove == -1:
target_row[j][1] = True
continue

if seq[nomove][0] < active_min:
target_row[j][1] = True
continue

c = seq[nomove - 1][0] + offset
rowc = expr[c - 1]
b = rowc[seq[nomove - 1][1]][0]

idx_check = j + target_row[0] - 1
left_ok = (idx_check < len(target_row)) and (target_row[idx_check][0] <= active_min)
active_has_b_mark = any((x[0] == b and x[1]) for x in active[1:])

if left_ok and active_has_b_mark:
target_row[j][1] = True

return expr

def _comp_to(raw, r, already):
expr = _deepcopy_expr(raw)
for j in range(len(raw[r]) - 1, 0, -1):
if not raw[r][j][1]:
continue
n = raw[r][j][0]
seq = _seq_from(raw, r, j)
t = seq[-1][0]
T = already[t - 1] if (t - 1) < len(already) else None
if not T:
continue
q = len(T)
entries = (
[[x[0], bool(x[1])] for x in expr[r][1:]] +
[[x, False] for x in T] +
[[n + 1 + uu, True] for uu in range(q)]
)
entries.sort(key=lambda z: z[0], reverse=True)
expr[r] = [expr[r][0] + q] + entries
return expr

def _comp_from(raw, r, T):
q = len(T)

expr = [[row[0]] + [[x[0], bool(x[1])] for x in row[1:]] for row in raw[:r]]

if len(raw[r]) < raw[r][0] * 2 + 1:
lr = raw[r][0]
cr = raw[r][1:-raw[r][0]] + raw[r][1 + raw[r][0]:]
else:
lr = raw[r][0] + 1
cr = raw[r][1:]

need_len = r + q + 1
if len(expr) < need_len:
expr.extend([None] * (need_len - len(expr)))

for qq in range(q):
entries = (
[[x[0], bool(x[1])] for x in cr] +
[[x, False] for x in T[:1 + qq]] +
[[raw[r][1][0] + 1 + uu, False] for uu in range(qq)]
)
entries.sort(key=lambda z: z[0], reverse=True)
expr[r + qq] = [lr + qq] + entries

entries = (
[[x[0], bool(x[1])] for x in raw[r][1:]] +
[[x, False] for x in T] +
[[raw[r][1][0] + 1 + uu, False] for uu in range(q)]
)
entries.sort(key=lambda z: z[0], reverse=True)
expr[r + q] = [raw[r][0] + q] + entries

for qq in range(1, q + 1):
for uu in range(2, 1 + qq + 1):
expr[r + qq][uu][1] = True

threshold = raw[r][1][0]

def m(entry, idx):
if idx == 0:
return entry
vv = entry[0]
if vv <= threshold:
return [vv, bool(entry[1])]
return [vv + q, bool(entry[1])]

for row in raw[r + 1:]:
new_row = []
for idx, entry in enumerate(row):
new_row.append(m(entry, idx))
expr.append(new_row)

return expr

def _expand_pleasant_only(raw, FSterm, longer=False):
if FSterm < 0:
FSterm = 0

active = raw[-1]
L = active[0]
if (1 + L) >= len(active) or (active[1 + L][0] == 0):
return _cut_expr(raw)

begin = active[1 + L][0]
flag = _pleasant_until(raw[begin - 1:-1], active)
if flag != -1:
raise ModifyUnpleasant

expr = _deepcopy_expr(raw)
for _ in range(FSterm):
expr = _copy_block(expr, -1)

expr = _copy_block(expr, 1) if longer else _cut_expr(expr)

already = []
r = len(raw) - 1
while r < len(expr):
expr = _comp_to(expr, r, already)

if not (len(expr[r]) <= expr[r][0] * 2 + 1):
r += 1
continue

idx0 = expr[r][expr[r][0]][0]
T = [idx0]
bound = expr[r][expr[r][0] + 1][0]

while T[0] > bound:
rr = T[0] - 1
T.insert(0, expr[rr][2][0])

T = T[1:-1]
if len(T) < 1:
r += 1
continue

expr = _comp_from(expr, r, T)

while len(already) <= r:
already.append(None)
already[r] = T

r += len(T) + 1

return expr

def _expand_like_model(pattern: BasicLaverPattern, FSterm: int, longer: bool, silent: bool):
if pattern.is_zero():
return pattern.clone(), 0
if pattern.is_successor():
q = pattern.clone()
q.cut()
return q, 0

base0 = pattern.rows[0]
if not base0:
q = pattern.clone()
q.cut()
return q, 0

if FSterm <= 0:
q = pattern.clone()
q.cut()
return q, 0

try:
raw = _encode_expr(pattern)
res = _expand_pleasant_only(raw, FSterm=FSterm, longer=longer)
p2 = _decode_expr(res)
return p2.clone(), 1
except ModifyUnpleasant:
if not silent:
print(MSG_UNPLEASANT)
q = pattern.clone()
q.cut()
return q, 0

def _apply_special_one(pattern: BasicLaverPattern, silent=False):
if pattern.is_zero():
return pattern.clone(), 0
if pattern.is_successor():
p = pattern.clone()
p.cut()
return p, 0

p = pattern.clone()
try:
orig_rows = _clone_rows(p.rows)
orig_mask = _clone_mask(p.mask)
orig_base = orig_rows[0][:]
orig_last_mask = set(orig_mask[-1]) if orig_mask else set()

rows = p.rows
base0 = rows[0]
n_before_cut = len(base0)
if n_before_cut <= 0:
p2 = p.clone()
p2.cut()
return p2, 0

original_total_rows = len(rows)

l_last = base0[n_before_cut - 1]
b = rows[-1][:]
if not b:
p2 = p.clone()
p2.cut()
return p2, 0
b0 = b[0]
p_leftmost = b[0]

p.cut()
rows = p.rows
base0 = rows[0]

if l_last < 0 or len(b) < l_last + 1:
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
u = b[-l_last - 1]

if u - 1 < 0 or u - 1 >= len(orig_base):
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
base0.append(orig_base[u - 1])

b_map = {}
limit = len(b) - l_last
for i in range(limit):
key = b[i]
if key not in b_map:
b_map[key] = b[i + l_last]

def map_elem(x):
if x < b0:
return x
if x > u:
return x - u + n_before_cut
return b_map.get(x, -1)

copied_set = {u}

if u <= 0 or u >= len(orig_rows):
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant

src_row = orig_rows[u]
new_seq = []
for elem in src_row:
new_val = map_elem(elem)
if new_val == -1:
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
new_seq.append(new_val)
new_seq.sort()
rows.append(new_seq)

new_marks = set()
src_marks = orig_mask[u]
if src_marks:
l_m = orig_base[u - 1]
for marked_val in src_marks:
if _find_index(orig_rows[u], marked_val) is None:
continue
tprime, t, _terminal = p._first_not_copied_in_transmission(
orig_rows, orig_base, copied_set, u, marked_val
)
keep = False
if t in copied_set:
keep = True
else:
if tprime is not None and tprime < p_leftmost:
keep = True
elif tprime is not None:
u_img = b_map.get(tprime, None)
if u_img is not None and u_img in orig_last_mask:
mv_img = map_elem(marked_val)
if mv_img != -1:
pos_u = _find_index(new_seq, mv_img)
if pos_u is not None:
idx_check = pos_u - l_m + 1
if idx_check >= 0 and new_seq[idx_check] <= p_leftmost:
keep = True
if keep:
mv = map_elem(marked_val)
if mv != -1:
new_marks.add(mv)

p.mask.append(new_marks)
p._normalize_rows_inplace(start_row=len(p.rows) - 1)

meta = [None] * len(p.rows)
m = len(p.rows[0])
did, q = p._native_completion_step(m, meta)

if did and q > 0:
for _ in range(q):
p.cut()

while len(p.rows) > original_total_rows:
p.cut()

p._normalize_rows_inplace()
return p.clone(), 1

except ModifyUnpleasant:
q = pattern.clone()
q.cut()
return q, 0
except RuntimeError as e:
if str(e) == "Unpleasant.":
if not silent:
print(MSG_UNPLEASANT)
q = pattern.clone()
q.cut()
return q, 0
raise

def _apply_number(pattern, n, silent=False):
if pattern.is_zero():
return pattern.clone(), 0

if n == 0:
p = pattern.clone()
p.cut()
return p, 0

if pattern.is_successor():
p = pattern.clone()
p.cut()
return p, 0

if n == 1:
return _apply_special_one(pattern, silent=silent)

FSterm = n - 1
nxt, ok = _expand_like_model(pattern, FSterm=FSterm, longer=False, silent=silent)
if ok == 0:
return nxt, 0
return nxt, n

def reconstruct_pattern_list(op_numbers, silent=False):
pattern_list = [BasicLaverPattern(initial_rows, initial_mask)]
executed = []
for n in op_numbers:
cur = pattern_list[-1]
nxt, actual = _apply_number(cur, n, silent=silent)
executed.append(actual)
pattern_list.append(nxt)
return executed, pattern_list, None

def _cmp_lists(a, b):
la, lb = len(a), len(b)
m = la if la < lb else lb
for i in range(m):
if a[i] < b[i]:
return -1
if a[i] > b[i]:
return 1
if la < lb:
return -1
if la > lb:
return 1
return 0

def _row_key_for_compare(pat, row_idx):
base = pat.rows[0]
row = pat.rows[row_idx]
l = base[row_idx - 1] if row_idx - 1 < len(base) else 0
if l <= 1:
keep = row[:]
else:
if len(row) < l:
keep = row[:]
else:
keep = [row[0]] + row[l:]
keep = keep[::-1]
return keep

def compare_patterns(a, b):
ra = len(a.rows) - 1
rb = len(b.rows) - 1
m = ra if ra < rb else rb
for i in range(1, m + 1):
ka = _row_key_for_compare(a, i)
kb = _row_key_for_compare(b, i)
c = _cmp_lists(ka, kb)
if c != 0:
return c
if ra < rb:
return -1
if ra > rb:
return 1
return 0

def _is_prefix(seg, full):
if len(seg.rows) > len(full.rows):
return False
if seg.rows[0] != full.rows[0][:len(seg.rows[0])]:
return False
for i in range(1, len(seg.rows)):
if seg.rows[i] != full.rows[i]:
return False
return True

def _is_proper_prefix(seg, full):
return _is_prefix(seg, full) and (len(seg.rows) < len(full.rows))

def _pattern_equal(a: BasicLaverPattern, b: BasicLaverPattern):
return a.rows == b.rows and a.mask == b.mask

def _pattern_signature(p: BasicLaverPattern):
rows_sig = tuple(tuple(r) for r in p.rows)
mask_sig = tuple(tuple(sorted(s)) for s in p.mask)
return rows_sig, mask_sig

_EXPAND_COUNTS_CACHE = {}

def _expand_row_counts_from(start_pat: BasicLaverPattern, n: int):
if n < 0:
n = 0
key = (_pattern_signature(start_pat), n)
if key in _EXPAND_COUNTS_CACHE:
return _EXPAND_COUNTS_CACHE[key][:]

counts = [len(start_pat.rows)]
for k in range(1, n + 1):
res, _act = _apply_number(start_pat, k, silent=True)
counts.append(len(res.rows))

_EXPAND_COUNTS_CACHE[key] = counts[:]
return counts

def _simplify(op_numbers, pattern_list):
target = pattern_list[-1].clone()

s = op_numbers[:]
executed, pats, _ = reconstruct_pattern_list(s, silent=True)
s = executed
pattern_list = pats

i = len(s) - 1
while i >= 0:
if i >= len(s):
i = len(s) - 1
if i < 0:
break
if s[i] == 0:
i -= 1
continue

while True:
if i >= len(s):
break
n = s[i]

z = 0
j = i + 1
while j < len(s) and s[j] == 0:
z += 1
j += 1

candidate = None
need = None

if n == 1:
if z >= 1:
candidate = s[:i] + s[i + 1:]
else:
break
else:
start_pat = pattern_list[i]
counts = _expand_row_counts_from(start_pat, n)
need = counts[n] - counts[n - 1]
if need < 0:
need = 0

if z < need:
break

candidate = s[:]
candidate[i] = n - 1
if need > 0:
del candidate[i + 1: i + 1 + need]

cand_exec, cand_pats, _ = reconstruct_pattern_list(candidate, silent=True)
if not cand_pats or not _pattern_equal(cand_pats[-1], target):
break

s = cand_exec
pattern_list = cand_pats

if i >= len(s):
break
if s[i] == 0:
break

i = min(i, len(s) - 1)
i -= 1
while i >= 0 and s[i] == 0:
i -= 1

executed, pattern_list, _ = reconstruct_pattern_list(s, silent=True)
return executed, pattern_list

def _seq_str(nums):
return ",".join(str(x) for x in nums)

def _parse_o_string(s):
s = s.strip()
if s == "":
return BasicLaverPattern([[]], [set()]), None

pos = 0
rows_desc = []
steps = []
n = len(s)

while pos < n:
if s[pos] != "(":
return None, "error"
pos += 1
close = s.find(")", pos)
if close == -1:
return None, "error"
inside = s[pos:close].strip()
pos = close + 1

nums = []
if inside != "":
parts = inside.split(",")
for part in parts:
part = part.strip()
if part.startswith("*"):
part = part[1:].strip()
if part == "" or (not part.isdigit()):
return None, "error"
nums.append(int(part))

nums_asc = sorted(nums)
for i in range(1, len(nums_asc)):
if nums_asc[i] == nums_asc[i - 1]:
return None, "error"

if pos >= n or (not s[pos].isdigit()):
return None, "error"
j = pos
while j < n and s[j].isdigit():
j += 1
step = int(s[pos:j])
pos = j

rows_desc.append(nums_asc)
steps.append(step)

rows = [steps[:]] + rows_desc
mask = [set()] + [set() for _ in rows_desc]
return BasicLaverPattern(rows, mask), None

def _read_find_pattern(I):
initial = BasicLaverPattern(initial_rows, initial_mask)
C = initial.clone()

ops = []
pats = [C.clone()]

if compare_patterns(C, I) <= 0:
return C, ops, pats

MAX_OUTER = 50000
MAX_N = 20000
outer = 0

while outer < MAX_OUTER:
outer += 1

if compare_patterns(C, I) == 0:
return C, ops, pats

n = 0
while n <= MAX_N:
Cn, actual = _apply_number(C, n, silent=True)

if _is_proper_prefix(Cn, I):
n += 1
continue

if (compare_patterns(Cn, I) < 0) and (not _is_prefix(Cn, I)):
return C, ops, pats

if compare_patterns(Cn, I) >= 0:
if Cn.rows == C.rows and Cn.mask == C.mask:
return C, ops, pats
C = Cn
ops.append(actual)
pats.append(C.clone())
break

n += 1

else:
return C, ops, pats

return C, ops, pats

def main_program():
op_numbers = []
executed, pattern_list, _ = reconstruct_pattern_list(op_numbers, silent=True)
op_numbers = executed

while True:
cur = pattern_list[-1]
print("\nCurrent pattern:")
if cur.is_zero():
print("(empty)")
else:
cur.draw()

print(f"Operation sequence: {_seq_str(op_numbers)}")

if cur.is_zero():
pattern_type = "Zero"
elif cur.is_successor():
pattern_type = "Successor"
else:
pattern_type = "Limit"

msg = f"This is a {pattern_type} pattern."
msg += " Natural Number: Operation."
msg += " O: Output."
msg += " R: Read."
if len(pattern_list) > 1:
msg += " U: Undo."
msg += " S: Simplify."
msg += " I: Input operations."
print(msg)

user_input = input("Enter your operation: ").strip().upper()

if user_input.isdigit():
n_in = int(user_input)
nxt, actual = _apply_number(cur, n_in, silent=False)
pattern_list.append(nxt)
op_numbers.append(actual)
if actual == 0:
print("Applied cut operation.")
else:
print(f"Applied operation {actual}.")
continue

if user_input == 'O':
print(cur.to_string())
continue

if user_input == 'R':
raw = input("Input pattern string (from O): ").strip()
pat, err = _parse_o_string(raw)
if err:
print("error")
continue
found, ops, pats = _read_find_pattern(pat)
op_numbers = ops
pattern_list = pats
print(found.to_string())
continue

if user_input == 'U' and len(pattern_list) > 1:
op_numbers = op_numbers[:-1]
executed, pattern_list, _ = reconstruct_pattern_list(op_numbers, silent=True)
op_numbers = executed
print("Undo the last operation.")
continue

if user_input == 'S':
new_ops, new_patterns = _simplify(op_numbers, pattern_list)
if new_ops != op_numbers:
op_numbers = new_ops
pattern_list = new_patterns
print(f"Simplified operation sequence: {_seq_str(op_numbers)}")
else:
print("No further simplifications possible.")
continue

if user_input == 'I':
raw = input("Input the operation sequence (comma-separated natural numbers, e.g., 3,0,2,1): ").strip()
if raw == "":
parsed = []
else:
parts = [p.strip() for p in raw.split(",")]
if any(p == "" or (not p.isdigit()) for p in parts):
print("error")
continue
parsed = [int(p) for p in parts]
executed, pattern_list, _ = reconstruct_pattern_list(parsed, silent=True)
op_numbers = executed
continue

print("Invalid operation. Please try again.")

if __name__ == "__main__":
main_program()

</syntaxhighlight>

== 分析 ==
另见[[IBLP分析Part1]] [[IBLP分析Part2]] [[IBLP分析Part3]] [[IBLP分析Part4]]。

目前iBLP的分析已经到达ω-Y(1,4)，对应(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,3,2)2。
{| class="wikitable"
|+
!ω-Y序列
!iBLP
|-
|1,2
|(1,0)1(2,1)1
|-
|1,2,4
|(1,0)1(2,1,0)1
|-
|1,2,4,8
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3
|-
|1,2,4,8,16
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2,1,0)3(5,*4,3,2,1,0)3(6,4,2,1,0)3(7,*6,4,3,2,1,0)4(8,*7,*6,4,3,2,1,0)4
|-
|1,3
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1
|-
|1,3,4,3
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1
|-
|1,3,7
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*9,*8,5,4,3,2,1,0)5
|-
|1,3,9
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*10,*9,*8,5,4,3,2,1,0)5
|-
|1,3,10
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,4)1
|-
|1,4
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,3,2)2
|}

{{默认排序:序数记号}}
[[分类:记号]]

iBLP

2026-04-26T09:44:19Z

Baixie01000a7：

== 记号简介 ==
无限基本Laver图案(Infinite Basic Laver Pattern)是由test_alpha0的记号Basic Laver Pattern改造而来。IBLP目前尚不理想，还存在许多的坏图案。test_alpha0规定其极限表达式为(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,3,2)2(6,5,4)1，因为现在认为在该图案下方不存在坏图案，而其上方不远处就出现了很多坏图案。尽管如此，IBLP仍然被认为是目前最强的记号。本页面介绍的规则对应[https://hypcos.github.io/notation-explorer/ NE]上的DEN2。

== 定义 ==

=== 定义1 （IBLP） ===
一个IBLP是一个四元组<math>A=(n,(A_1,\dots,A_n),(l_1,\dots,l_n),(M_1,\dots,M_n))</math>，

其中：

<math>(1)n\in\N</math>。

<math>(2)</math>对每个<math>i\in\{1,\dots,n\}</math>，<math>A_i</math>是严格递增的非负整数序列，满足<math>\mathrm{len}(A_i)\geq2\text{且}\max(A_i)=i</math>。

<math>(3)</math>对每个<math>i\in\{1,\dots,n\}</math>，步长<math>l_i\in \N</math>。

<math>(4)</math>对每个<math>i\in\{1,\dots,n\}</math>，标记集合<math>M_i\subseteq A_i</math>

约定所有编号从 1 开始；<math>A_i[k]</math> 表示第 ''k'' 个元素，<math>A_i[-j]=A_i[\mathrm{len}(A_i)-j+1]</math>表示倒数第 ''j'' 个元素。

=== 定义2 （长行、中等行、短行） ===
行 <math>i</math> 称为长行若<math>\mathrm{len}(A_i)>2l_i</math>，称为中等行若<math>\mathrm{len}(A_i)=2l_i</math>，称为短行若 <math>\mathrm{len}(A_i)<2l_i</math>。

=== 定义3 （零图案、后继图案、极限图案） ===
若 ''n'' = 0，称 ''A'' 为零图案。若 <math>n>0\text{且}\mathrm{len}(A_n)=2\text{且}\min(A_n)=0</math>，称 ''A'' 为后继图案。否则称 ''A'' 为极限图案。

=== 定义4 （行比较键） ===
令<math>A_i=(A_1<a_2<\dots<a_m)\text{且}L=l_i</math>。定义保留序列

<math>K_i=\begin{cases}(a_1,a_2,\dots,a_m),&L\leq1;\\(a_1,a_{L+1},a_{L+2},\dots,a_m),&2\leq L\leq m;\\(a_1,a_2,\dots,a_m),&L\geq2\text{且}m<L.\end{cases}</math>

定义行键为<math>\overleftarrow{K_i}</math>（即<math>K_i
</math>逆序，从大到小）。

=== 定义5 （IBLP的大小比较） ===
给定两个 ''IBLP'' <math>A\text{、}B</math>，从 <math>i=1</math> 起逐行比较其

行键<math>\overleftarrow{K_i(A)}\text{与}\overleftarrow{K_i(B)}</math> 的字典序；第一处不同决定大小。若前<math>\min(n_a,n_b)</math>行都相等，则行数较小者更小。

=== 定义6 （一行的根<math>p(i)</math>） ===
对<math>i\in\{1,\dots,n\}</math>，定义<math>p(i)=A_i[-(l_i+1)]</math>.

=== 定义7 （传递序列<math>tr_i(j)</math>） ===
固定行 ''i''。若<math>j=A_i[k](1\leq k\leq\mathrm{len}(A_i))\text{且}k\geq l_i</math>，定义阈值 <math>\theta=A_i[k-l_i]</math>。令 <math>t_0=j</math>，并在<math>t_m>\theta\text{且}p(t_m)\text{有定义}</math>时令 <math>t_{m+1}=p(t_m)</math>。若存在最小 <math>m>0</math>使<math>t_m=\theta</math>，则定义<math>tr_i(j)=(t_0,t_1,\dots,t_m)</math>''，''否则称 <math>tr_i(j)</math> 无定义。若 <math>k\leq l_i</math>，亦称无定义。

=== 定义8 （部分函数<math>f_A</math>） ===
设 ''A'' 非零且有至少1行。令 <math>a_1=A_n[1]=\min(A_n)\text{，}L=l_n\text{，}p=p(n)=A_n[-(L+1)]</math>。定义部分函数 <math>f_A:\N\rightharpoonup\N</math>：

<math>(1)</math>若<math>x<a_1</math>，则<math>f_A(x)=x</math>；

<math>(2)</math>若<math>x=A_n[k]\text{且}x<p\text{且}k+L\leq\mathrm{len}(A_n)</math>，则<math>f_A(x)=A_n[k+L]</math>；

<math>(3)</math>若<math>x\geq p</math>，则<math>f_A(x)=x+n-p</math>；

<math>(4)</math>其余情形 <math>f_A(x)</math> 无定义。

=== 定义9 （copy 的行与步长） ===
设 ''A'' 行数为<math>n\geq1</math>，令 <math>p=p(n)</math>。若 copy 过程中出现 <math>f_A(x)</math> 无定义，则<math>copy(A)</math>无定义。否则定义 <math>A'=copy(A)</math> 行数为 <math>n'=2n-p</math>，满足：

<math>(1)</math>对<math>1\leq i\leq n-1\text{：}A_i'=A_i\text{，}l_i'=l_i\text{，}M_i'=M_i</math>；

<math>(2)</math>对每个<math>i\in\{1,\dots,n-p+1\}</math>，令源行<math>\sigma=p+i-1</math>，目标行<math>\tau=n-1+i</math>''i''，定义<math>A_\tau'=\mathrm{sort}(\{f_A(x)|x\in A_\sigma\})\text{，}l_\tau'=l_\sigma</math>，要求<math>\forall x\in A_\sigma\text{，}f_A(x)\text{有定义}</math>。

=== 定义10 （copy的标记过滤） ===
延续上一定义。对目标行<math>\tau</math>中元素<math>x\in A_\tau'</math>，令

<math>y\in A_\sigma</math>为其唯一来源（即 <math>f_A(y)=x</math>）。则 <math>x\in M_\tau'</math> 当且仅当：

<math>y\in M_\sigma</math>，并且满足下列之一：

* <math>tr_\sigma(y)</math>有定义且<math>tr_\sigma(y)[-2]\geq p</math>；
* 令<math>y_0</math>为<math>tr_\sigma(y)</math>中首次出现的<math><p</math>的元素（等价于“最大的
<math><p</math>的元素”）。要么<math>y_0<a_1</math>；要么存在 ''k'' 使<math>y_0=A_n[k]\text{且}k+L\leq\mathrm{len}(A_n)\text{且}A_n[k+L]\in M_n</math>，并且若 ''x'' 在 <math>A_\tau'</math>中的位置为 ''q''（从 1 开始），则当 <math>q+1-l_\sigma\geq1</math> 时需满足<math>A_\tau'[q+1-l_\sigma]\leq a_1.</math>

=== 定义11 （E(A,0)） ===
若 ''A'' 非零且 ''n ≥'' 1，则 ''E''(''A,'' 0) 为删除最后一行后的图案（行数变为 ''n −'' 1，其余行、步长、标记保持不变）。

=== 定义12 （''E''(''A, m'')的copy阶段 (''m≥1)''） ===
设A是极限图案。令<math>A^{(0)}=A</math>。若第一次<math>copy(A^{(0)})</math> 无定义，则称 ''A'' 为坏图案并定义<math>E(A,m)=E(A,0)</math>。否则定义

<math>A^{(1)}=copy(A^{(0)}),A^{(2)}=copy(A^{(1)}),\dots,A^{(m)}=copy(A^{(m-1)})</math>,

并令<math>B=E(A^{(m)},0)</math>

接下来对B做补全，初始行号 <math>r=n</math>（这里 ''n'' 为原始 ''A'' 的行数）。补全过程允许使用临时记录映射 <math>\rm Rec</math>（行号 <math>\mapsto</math> 有限序列），结束后丢弃。

=== 定义13 （标记补全） ===
固定当前行 ''r''。令<math>\mathcal{B}=\{b\in M_r|b\in A_r\}</math>并按升序枚举其元素<math>b_1<b_2<\dots<b_k</math>（该集合在本轮开始时冻结，新产生标记不加入本轮）。对每个 <math>b_i</math>依次：

<math>(1)</math>若 <math>tr_i(b_i)</math>无定义则跳过；

<math>(2)</math>令<math>t=tr_r(b_i)[-2]</math>。若<math>\mathrm{Rec}(t)</math>不存在或为空则跳过，否则记 <math>s=\mathrm{Rec}(t)</math>；

<math>(3)</math>若对所有<math>j=3,4,\dots,\mathrm{len}(tr_r(b_i))</math>都有<math>tr_r(b_i)[-j+1]+1\in A_{tr_r(b_i)[-j]}</math>，那么把s 及<math>b_i+1,b_i+2,\dots,b_i+\mathrm{len}(s)</math> 加入 <math>A_r</math>，并重新排序去重使

之严格递增。更新标记：''s'' 中元素不标记，<math>b_i+1,b_i+2,\dots,b_i+\mathrm{len}(s)</math> 全标

记，其余标记保留（按上述规则修正）。更新步长：<math>l_r=l_r+len(s)</math>。

=== 定义14 （原生补全） ===
固定当前行 ''r''。若<math>A_r</math>为长行，则原生补全不执行并返回 0。否则令<math>p_r=p(r)=A_r[-(l_r+1)]\text{，}a=A_r[-l_r]</math>.

构造序列 ''s''：令 <math>u_0=a</math>，并在<math>A_{u_m}[-2]</math> 存在且 <math>>p_r</math> 时令 <math>u_{m+1}=A_{u_m}[-2]</math>并把 <math>u_{m+1}</math> 追加到 ''s''，直至无法继续。令 <math>t=\mathrm{len}(s)</math>。若 <math>t=0</math> 返回 0；若<math>t>0</math>，令 <math>\mathrm{Rec}(r)=s</math> 并继续：

<math>(1)</math>在 ''r'' 后插入 ''t'' 行，使原本行号 <math>>r</math> 的行号整体加 ''t''；

<math>(2)</math> 仅对原本行号 <math>>r</math>的那些行，在其中把所有 <math>>r</math> 的元素加 ''t''，并同步

标记集合，步长不变；

<math>(3)</math>令旧行及旧步长为 <math>A_r^{old},l_r^{old}</math>。将旧行替换为 ''t'' + 1 行：

<math>A_{r+t}=\mathrm{sort}(A_r^{old}\cup s\cup\{r+1,r+2,\dots,r+t\})\text{，}l_{r+t}=l_r^{old}+t</math>.

标记规则：除s和r+t外均标记。

<math>(4)</math>对<math>i=t,t-1,\dots,1</math>，由<math>A_{r+i}</math>构造 <math>A_{r+i-1}</math>：删除元素<math>r+i</math>，并删除元素 <math>A_{r+i}[-l_{r+i}]</math>，去除<math>r+i-1</math> 的标记，并令 <math>l_{r+i-1}=l_{r+i}-1</math>。

<math>(5)</math>'''中等行例外：'''若<math>i=t</math> 且 ''<math>A_r^{old}</math>''为中等行，则在构造 <math>A_{r+i-1}</math> 时不删除 <math>A_{r+i}[-l_{r+i}]</math>且不减步长（令 <math>l_{r+i-1}=l_{r+i}</math>），但仍删除 <math>r+i</math> 并去除<math>r+i-1</math> 的标记。

原生补全返回t。

=== 定义15 （补全主循环(用于 ''E''(''A, m''))） ===
令初始<math>r=n</math>（''n'' 为原始 ''A'' 的行数）。当 ''r'' 不超过当前 ''B'' 的行数时循环：先对行 ''r'' 执行标记补全，再执行原生补全得到 ''t''，然后更新 <math>r=r+t+1</math>。当 ''r'' 越界时补全结束，丢弃 <math>\rm Rec</math>，所得 ''B'' 即为<math>E(A,m)</math>。

== 展开器 ==
iblp的展开器在[https://hypcos.github.io/notation-explorer/ NE]上可以找到，同时也可以使用如下Python代码直观地看到每个图案的行为。<syntaxhighlight lang="python3">
import bisect

def _clone_rows(rows):
return [row[:] for row in rows]

def _clone_mask(mask):
return [set(s) for s in mask]

def _find_index(sorted_row, val):
i = bisect.bisect_left(sorted_row, val)
if i < len(sorted_row) and sorted_row[i] == val:
return i
return None

def _shift_sorted_row_inplace(sorted_row, threshold, delta):
if delta == 0:
return
i = bisect.bisect_left(sorted_row, threshold)
for j in range(i, len(sorted_row)):
sorted_row[j] += delta

def _shift_mark_set(mark_set, threshold, delta):
if delta == 0 or not mark_set:
return mark_set
new = set()
for x in mark_set:
new.add(x + delta if x >= threshold else x)
return new

class ModifyUnpleasant(Exception):
pass

MSG_UNPLEASANT = (
"Something unpleasant happened. Please contact the author (E-mail: qwerasdfyh@126.com) "
"about the previous pattern so he can improve the rule design."
)

class BasicLaverPattern:
def __init__(self, rows, mask=None):
self.rows = _clone_rows(rows)
if mask is None:
self.mask = [set() for _ in self.rows]
else:
self.mask = _clone_mask(mask)
if self.mask:
self.mask[0] = set()
self._normalize_rows_inplace()

def _normalize_rows_inplace(self, start_row=1):
for r in range(max(1, start_row), len(self.rows)):
row = self.rows[r]
if row and row[-1] == r + 1:
row.pop()
self.mask[r].discard(r + 1)

def clone(self):
return BasicLaverPattern(self.rows, self.mask)

def is_zero(self):
return len(self.rows) == 1 and len(self.rows[0]) == 0

def is_successor(self):
if self.is_zero():
return False
last = self.rows[-1]
return len(last) == 2 and last[0] == 0

def draw(self):
if self.is_zero():
return
base_list = self.rows[0]
other_lists = self.rows[1:]
if not other_lists:
return
max_len = max((seq[-1] for seq in other_lists if seq), default=0) + 1
result = []
for i, seq in enumerate(other_lists, start=1):
line = [' '] * max_len
mset = self.mask[i]
for num in seq:
if 0 <= num < max_len:
line[num] = 'a' if num in mset else 'o'
if i <= len(base_list) and seq:
last_circle_index = seq[-1]
result.append(''.join(line[:last_circle_index + 1]) + f" {base_list[i-1]}")
for line in result:
print(line)

def to_string(self):
if self.is_zero():
return ""
base_list = self.rows[0]
out = []
for i in range(1, len(self.rows)):
seq = self.rows[i]
mset = self.mask[i]
parts = []
for x in reversed(seq):
parts.append(f"*{x}" if x in mset else str(x))
step = base_list[i - 1] if i - 1 < len(base_list) else 0
out.append("(" + ",".join(parts) + ")" + str(step))
return "".join(out)

def cut(self):
if self.is_zero():
return False
if len(self.rows) <= 1:
return False
if len(self.rows[0]) == 0:
self.rows = [[]]
self.mask = [set()]
return False
self.rows[0].pop()
self.rows.pop()
self.mask.pop()
if len(self.rows) == 1 and len(self.rows[0]) == 0:
self.mask = [set()]
self._normalize_rows_inplace()
return True

def _transmission_penultimate_and_terminal_checked(self, row_idx, n_value):
rows = self.rows
base = rows[0]
if n_value <= 0 or n_value >= len(rows):
return None
row = rows[row_idx]
l_m = base[row_idx - 1]
k = _find_index(row, n_value)
if k is None or k - l_m < 0:
return None
threshold = row[k - l_m]

cur = n_value
visited = {cur}
while True:
if cur <= 0 or cur >= len(rows):
return None
l_s = base[cur - 1]
if len(rows[cur]) < l_s + 1:
return None
nxt = rows[cur][-l_s - 1]
if nxt > threshold:
if nxt + 1 != cur + 1:
if _find_index(rows[cur], nxt + 1) is None:
return None
prev, cur = cur, nxt
if cur <= threshold:
return (prev, cur)
if cur in visited:
return None
visited.add(cur)

def _first_not_copied_in_transmission(self, orig_rows, orig_base, copied_set, row_idx, n_value):
row = orig_rows[row_idx]
l_m = orig_base[row_idx - 1]
k = _find_index(row, n_value)
if k is None or k - l_m < 0:
raise RuntimeError("Unpleasant.")
threshold = row[k - l_m]
cur = n_value
seq = [cur]
visited = {cur}
while True:
l_s = orig_base[cur - 1]
if len(orig_rows[cur]) < l_s + 1:
raise RuntimeError("Unpleasant.")
nxt = orig_rows[cur][-l_s - 1]
seq.append(nxt)
cur = nxt
if cur <= threshold:
break
if cur in visited:
raise RuntimeError("Unpleasant.")
visited.add(cur)
t = seq[-2]
terminal = seq[-1]
tprime = None
for x in seq:
if x not in copied_set:
tprime = x
break
return tprime, t, terminal

def _slice_right_block(self, row_idx, anchor, q):
row = self.rows[row_idx]
pos = _find_index(row, anchor)
if pos is None:
raise RuntimeError("Unpleasant.")
block = row[pos + 1: pos + 1 + q]
if len(block) != q:
raise RuntimeError("Unpleasant.")
return block

def _mark_completion_for_row(self, r, meta, native_done):
base = self.rows[0]
row0 = self.rows[r]
initial_marks = [x for x in row0 if x in self.mask[r]]
before = set(row0)
added_total = 0

for n in initial_marks:
if _find_index(self.rows[r], n) is None:
continue
if n <= 0 or n >= len(meta):
continue
info = meta[n]
if not info or not info.get("native_generated", False):
continue

tn = self._transmission_penultimate_and_terminal_checked(r, n)
if tn is None:
continue
t, n_terminal = tn
q = native_done.get(t, 0)
if q <= 0:
continue

target_row = t + q
left_block = self._slice_right_block(target_row, n_terminal, q)
right_block = list(range(n + 1, n + q + 1))

new_vals = set(left_block) | set(right_block)
truly_new = new_vals - before
if truly_new:
added_total += len(truly_new)
before |= truly_new

row_set = set(self.rows[r])
row_set.update(new_vals)
self.rows[r] = sorted(row_set)

self.mask[r].difference_update(left_block)
self.mask[r].update(right_block)

if added_total > 0:
base[r - 1] += (added_total // 2)

def _shift_values_ge(self, start_row_idx, threshold, delta):
for i in range(start_row_idx, len(self.rows)):
_shift_sorted_row_inplace(self.rows[i], threshold, delta)
self.mask[i] = _shift_mark_set(self.mask[i], threshold, delta)

def _native_completion_step(self, m, meta):
rows = self.rows
base = rows[0]
l = base[m - 1]
e = len(rows[m])

if e > 2 * l:
return False, 0

if l <= 0 or e < l:
return False, 0

s = [rows[m][-l]]
while True:
if s[-1] <= 0 or s[-1] >= len(rows):
return False, 0
if len(rows[s[-1]]) < 2:
return False, 0
s.append(rows[s[-1]][-2])
if len(rows[m]) < l + 1:
return False, 0
if s[-1] <= rows[m][-l - 1]:
break

k = len(s) - 1
if k == 1:
return False, 0
s.pop()
q = k - 1
if q <= 0:
return False, 0

marks_m_orig = set(self.mask[m])
self._shift_values_ge(m, m + 1, q)

if e == 2 * l:
c = rows[m][:]
else:
c = rows[m][:l - 1] + rows[m][l:]

ext = s[1:][::-1] + list(range(m + 1, m + q + 1))
rows[m].extend(ext)
rows[m].sort()
base[m - 1] += q

d = []
for i in range(q):
d_i = c + s[q - i:] + list(range(m + 1, m + i + 2))
d.append(sorted(d_i))

old_e = e + 1
base[:] = base[:m - 1] + list(range(old_e - l, old_e - l + q)) + base[m - 1:]
rows[:] = rows[:m] + d + rows[m:]
self.mask[:] = self.mask[:m] + [set() for _ in range(q)] + self.mask[m:]

meta_insert = [{"native_generated": True, "native_q": q} for _ in range(q)]
meta[:] = meta[:m] + meta_insert + meta[m:]

marks_to_propagate = {x + q if x >= m + 1 else x for x in marks_m_orig}
for row_idx in range(m, m + q + 1):
self.mask[row_idx].update(marks_to_propagate)
for j in range(1, q + 1):
self.mask[m + j].update(range(m, m + j))

self.mask[m + q].discard(m + 1 + q)
self._normalize_rows_inplace(start_row=m)
return True, q

def modify(self, copy_only=False, silent=False):
try:
orig_rows = _clone_rows(self.rows)
orig_mask = _clone_mask(self.mask)
orig_base = orig_rows[0][:]
orig_last_mask = set(orig_mask[-1]) if orig_mask else set()

rows = self.rows
base0 = rows[0]
n_before_cut = len(base0)
l_last = base0[n_before_cut - 1]
b = rows[-1][:]
b0 = b[0]
p_leftmost = b[0]

self.cut()
rows = self.rows
base0 = rows[0]

u = b[-l_last - 1]
v_copy = n_before_cut
base0.extend(orig_base[u - 1: v_copy])

b_map = {}
limit = len(b) - l_last
for i in range(limit):
key = b[i]
if key not in b_map:
b_map[key] = b[i + l_last]

def map_elem(x):
if x < b0:
return x
if x > u:
return x - u + n_before_cut
return b_map.get(x, -1)

copied_set = set(range(u, v_copy + 1))

for row_idx in range(u, v_copy + 1):
src_row = orig_rows[row_idx]
new_seq = []
for elem in src_row:
new_val = map_elem(elem)
if new_val == -1:
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
new_seq.append(new_val)
new_seq.sort()
rows.append(new_seq)

new_marks = set()
src_marks = orig_mask[row_idx]
if src_marks:
l_m = orig_base[row_idx - 1]
for marked_val in src_marks:
if _find_index(orig_rows[row_idx], marked_val) is None:
continue
tprime, t, _terminal = self._first_not_copied_in_transmission(
orig_rows, orig_base, copied_set, row_idx, marked_val
)
keep = False
if t in copied_set:
keep = True
else:
if tprime is not None and tprime < p_leftmost:
keep = True
elif tprime is not None:
u_img = b_map.get(tprime, None)
if u_img is not None and u_img in orig_last_mask:
mv_img = map_elem(marked_val)
if mv_img != -1:
pos_u = _find_index(new_seq, mv_img)
if pos_u is not None:
idx_check = pos_u - l_m + 1
if idx_check >= 0 and new_seq[idx_check] <= p_leftmost:
keep = True
if keep:
new_marks.add(map_elem(marked_val))
self.mask.append(new_marks)

if copy_only:
self._normalize_rows_inplace()
return self.clone()

meta = [None] * len(self.rows)
native_done = {}

m = n_before_cut
while True:
base0 = self.rows[0]
if m > len(base0):
break
self._mark_completion_for_row(m, meta, native_done)
did, q = self._native_completion_step(m, meta)
if did:
native_done[m] = q
m += q + 1
else:
m += 1

self._normalize_rows_inplace()
return self.clone()

except ModifyUnpleasant:
raise
except RuntimeError as e:
if str(e) == "Unpleasant.":
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
raise

initial_rows = [
[1, 1, 2, 2, 2],
[0, 1],
[0, 1, 2],
[0, 1, 2, 3],
[0, 1, 2, 3, 4],
[2, 3, 4, 5]
]
initial_mask = [set() for _ in initial_rows]
initial_mask[4] = {3}

def _encode_expr(pat: BasicLaverPattern):
base = pat.rows[0]
expr = []
for i in range(1, len(pat.rows)):
L = base[i - 1] if (i - 1) < len(base) else 0
vals_desc = list(reversed(pat.rows[i]))
mset = pat.mask[i]
row = [L] + [[v, (v in mset)] for v in vals_desc]
expr.append(row)
return expr

def _decode_expr(expr):
base = [row[0] for row in expr]
rows = [base]
mask = [set()]
for row in expr:
vals = [x[0] for x in row[1:]]
vals = sorted(set(vals))
rows.append(vals)
mask.append({x[0] for x in row[1:] if x[1]})
return BasicLaverPattern(rows, mask)

def _deepcopy_expr(expr):
return [[row[0]] + [[x[0], bool(x[1])] for x in row[1:]] for row in expr]

def _values(row):
return [row[0]] + [x[0] for x in row[1:]]

def _cut_expr(expr):
return _deepcopy_expr(expr[:-1])

def _pleasant_until(rows, t):
tv = _values(t)
L = t[0]
tcheck = tv[1 + L:]
if not tcheck:
return -1

tmax = tcheck[0]
tmin = tcheck[-1]
tset = set(tcheck)

for n, s in enumerate(rows):
scheck = _values(s)[1:]
i1 = -1
for idx, x in enumerate(scheck):
if x < tmax:
i1 = idx
break
i2 = -1
for idx in range(len(scheck) - 1, -1, -1):
if scheck[idx] > tmin:
i2 = idx
break

if i1 != -1 and i2 != -1 and i1 <= i2:
mid = scheck[i1:i2 + 1]
if any(x not in tset for x in mid):
return n
return -1

def _seq_from(expr, i, j):
row = expr[i]
val = row[j][0]
L = row[0]
threshold = row[j + L][0] if (j + L) < len(row) else 0

record = [[i + 1, j], [val]]
while val > threshold:
row = expr[val - 1]
idx = 1 + row[0]
record[-1].append(idx)
val = row[idx][0] if idx < len(row) else 0
record.append([val])

record.pop()
return record

def _apv(s_vals, t_vals):
L = t_vals[0]
t_last = t_vals[-1]
t_1 = t_vals[1]
t_1L = t_vals[1 + L] if (1 + L) < len(t_vals) else 0

out = []
for x in s_vals:
if x < t_last:
out.append(x)
elif x >= t_1L:
out.append(x - t_1L + t_1)
else:
k = -1
for idx in range(len(t_vals) - 1, -1, -1):
if t_vals[idx] == x:
k = idx
break
out.append(None if k == -1 else t_vals[k - L])
return out

def _ap(row_s, row_t):
svals = _values(row_s)[1:]
tvals = _values(row_t)
mapped = _apv(svals, tvals)
return [row_s[0]] + [[x, False] for x in mapped]

def _copy_block(raw, flag):
active = raw[-1]
expr = _cut_expr(raw)

begin = active[1 + active[0]][0]
end = (begin + flag) if (flag != -1) else (len(raw) + 1)
offset = len(raw) - begin

expr.extend([_ap(row, active) for row in raw[begin - 1:end - 1]])

active_min = active[-1][0]
begin_rowno = begin

for i in range(begin - 1, end - 1):
row = raw[i]
target_row = expr[i + offset]
for j in range(1, len(row)):
if not row[j][1]:
continue

seq = _seq_from(raw, i, j)

nomove = -1
for k, item in enumerate(seq):
if item[0] < begin_rowno:
nomove = k
break

if nomove == -1:
target_row[j][1] = True
continue

if seq[nomove][0] < active_min:
target_row[j][1] = True
continue

c = seq[nomove - 1][0] + offset
rowc = expr[c - 1]
b = rowc[seq[nomove - 1][1]][0]

idx_check = j + target_row[0] - 1
left_ok = (idx_check < len(target_row)) and (target_row[idx_check][0] <= active_min)
active_has_b_mark = any((x[0] == b and x[1]) for x in active[1:])

if left_ok and active_has_b_mark:
target_row[j][1] = True

return expr

def _comp_to(raw, r, already):
expr = _deepcopy_expr(raw)
for j in range(len(raw[r]) - 1, 0, -1):
if not raw[r][j][1]:
continue
n = raw[r][j][0]
seq = _seq_from(raw, r, j)
t = seq[-1][0]
T = already[t - 1] if (t - 1) < len(already) else None
if not T:
continue
q = len(T)
entries = (
[[x[0], bool(x[1])] for x in expr[r][1:]] +
[[x, False] for x in T] +
[[n + 1 + uu, True] for uu in range(q)]
)
entries.sort(key=lambda z: z[0], reverse=True)
expr[r] = [expr[r][0] + q] + entries
return expr

def _comp_from(raw, r, T):
q = len(T)

expr = [[row[0]] + [[x[0], bool(x[1])] for x in row[1:]] for row in raw[:r]]

if len(raw[r]) < raw[r][0] * 2 + 1:
lr = raw[r][0]
cr = raw[r][1:-raw[r][0]] + raw[r][1 + raw[r][0]:]
else:
lr = raw[r][0] + 1
cr = raw[r][1:]

need_len = r + q + 1
if len(expr) < need_len:
expr.extend([None] * (need_len - len(expr)))

for qq in range(q):
entries = (
[[x[0], bool(x[1])] for x in cr] +
[[x, False] for x in T[:1 + qq]] +
[[raw[r][1][0] + 1 + uu, False] for uu in range(qq)]
)
entries.sort(key=lambda z: z[0], reverse=True)
expr[r + qq] = [lr + qq] + entries

entries = (
[[x[0], bool(x[1])] for x in raw[r][1:]] +
[[x, False] for x in T] +
[[raw[r][1][0] + 1 + uu, False] for uu in range(q)]
)
entries.sort(key=lambda z: z[0], reverse=True)
expr[r + q] = [raw[r][0] + q] + entries

for qq in range(1, q + 1):
for uu in range(2, 1 + qq + 1):
expr[r + qq][uu][1] = True

threshold = raw[r][1][0]

def m(entry, idx):
if idx == 0:
return entry
vv = entry[0]
if vv <= threshold:
return [vv, bool(entry[1])]
return [vv + q, bool(entry[1])]

for row in raw[r + 1:]:
new_row = []
for idx, entry in enumerate(row):
new_row.append(m(entry, idx))
expr.append(new_row)

return expr

def _expand_pleasant_only(raw, FSterm, longer=False):
if FSterm < 0:
FSterm = 0

active = raw[-1]
L = active[0]
if (1 + L) >= len(active) or (active[1 + L][0] == 0):
return _cut_expr(raw)

begin = active[1 + L][0]
flag = _pleasant_until(raw[begin - 1:-1], active)
if flag != -1:
raise ModifyUnpleasant

expr = _deepcopy_expr(raw)
for _ in range(FSterm):
expr = _copy_block(expr, -1)

expr = _copy_block(expr, 1) if longer else _cut_expr(expr)

already = []
r = len(raw) - 1
while r < len(expr):
expr = _comp_to(expr, r, already)

if not (len(expr[r]) <= expr[r][0] * 2 + 1):
r += 1
continue

idx0 = expr[r][expr[r][0]][0]
T = [idx0]
bound = expr[r][expr[r][0] + 1][0]

while T[0] > bound:
rr = T[0] - 1
T.insert(0, expr[rr][2][0])

T = T[1:-1]
if len(T) < 1:
r += 1
continue

expr = _comp_from(expr, r, T)

while len(already) <= r:
already.append(None)
already[r] = T

r += len(T) + 1

return expr

def _expand_like_model(pattern: BasicLaverPattern, FSterm: int, longer: bool, silent: bool):
if pattern.is_zero():
return pattern.clone(), 0
if pattern.is_successor():
q = pattern.clone()
q.cut()
return q, 0

base0 = pattern.rows[0]
if not base0:
q = pattern.clone()
q.cut()
return q, 0

if FSterm <= 0:
q = pattern.clone()
q.cut()
return q, 0

try:
raw = _encode_expr(pattern)
res = _expand_pleasant_only(raw, FSterm=FSterm, longer=longer)
p2 = _decode_expr(res)
return p2.clone(), 1
except ModifyUnpleasant:
if not silent:
print(MSG_UNPLEASANT)
q = pattern.clone()
q.cut()
return q, 0

def _apply_special_one(pattern: BasicLaverPattern, silent=False):
if pattern.is_zero():
return pattern.clone(), 0
if pattern.is_successor():
p = pattern.clone()
p.cut()
return p, 0

p = pattern.clone()
try:
orig_rows = _clone_rows(p.rows)
orig_mask = _clone_mask(p.mask)
orig_base = orig_rows[0][:]
orig_last_mask = set(orig_mask[-1]) if orig_mask else set()

rows = p.rows
base0 = rows[0]
n_before_cut = len(base0)
if n_before_cut <= 0:
p2 = p.clone()
p2.cut()
return p2, 0

original_total_rows = len(rows)

l_last = base0[n_before_cut - 1]
b = rows[-1][:]
if not b:
p2 = p.clone()
p2.cut()
return p2, 0
b0 = b[0]
p_leftmost = b[0]

p.cut()
rows = p.rows
base0 = rows[0]

if l_last < 0 or len(b) < l_last + 1:
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
u = b[-l_last - 1]

if u - 1 < 0 or u - 1 >= len(orig_base):
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
base0.append(orig_base[u - 1])

b_map = {}
limit = len(b) - l_last
for i in range(limit):
key = b[i]
if key not in b_map:
b_map[key] = b[i + l_last]

def map_elem(x):
if x < b0:
return x
if x > u:
return x - u + n_before_cut
return b_map.get(x, -1)

copied_set = {u}

if u <= 0 or u >= len(orig_rows):
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant

src_row = orig_rows[u]
new_seq = []
for elem in src_row:
new_val = map_elem(elem)
if new_val == -1:
if not silent:
print(MSG_UNPLEASANT)
raise ModifyUnpleasant
new_seq.append(new_val)
new_seq.sort()
rows.append(new_seq)

new_marks = set()
src_marks = orig_mask[u]
if src_marks:
l_m = orig_base[u - 1]
for marked_val in src_marks:
if _find_index(orig_rows[u], marked_val) is None:
continue
tprime, t, _terminal = p._first_not_copied_in_transmission(
orig_rows, orig_base, copied_set, u, marked_val
)
keep = False
if t in copied_set:
keep = True
else:
if tprime is not None and tprime < p_leftmost:
keep = True
elif tprime is not None:
u_img = b_map.get(tprime, None)
if u_img is not None and u_img in orig_last_mask:
mv_img = map_elem(marked_val)
if mv_img != -1:
pos_u = _find_index(new_seq, mv_img)
if pos_u is not None:
idx_check = pos_u - l_m + 1
if idx_check >= 0 and new_seq[idx_check] <= p_leftmost:
keep = True
if keep:
mv = map_elem(marked_val)
if mv != -1:
new_marks.add(mv)

p.mask.append(new_marks)
p._normalize_rows_inplace(start_row=len(p.rows) - 1)

meta = [None] * len(p.rows)
m = len(p.rows[0])
did, q = p._native_completion_step(m, meta)

if did and q > 0:
for _ in range(q):
p.cut()

while len(p.rows) > original_total_rows:
p.cut()

p._normalize_rows_inplace()
return p.clone(), 1

except ModifyUnpleasant:
q = pattern.clone()
q.cut()
return q, 0
except RuntimeError as e:
if str(e) == "Unpleasant.":
if not silent:
print(MSG_UNPLEASANT)
q = pattern.clone()
q.cut()
return q, 0
raise

def _apply_number(pattern, n, silent=False):
if pattern.is_zero():
return pattern.clone(), 0

if n == 0:
p = pattern.clone()
p.cut()
return p, 0

if pattern.is_successor():
p = pattern.clone()
p.cut()
return p, 0

if n == 1:
return _apply_special_one(pattern, silent=silent)

FSterm = n - 1
nxt, ok = _expand_like_model(pattern, FSterm=FSterm, longer=False, silent=silent)
if ok == 0:
return nxt, 0
return nxt, n

def reconstruct_pattern_list(op_numbers, silent=False):
pattern_list = [BasicLaverPattern(initial_rows, initial_mask)]
executed = []
for n in op_numbers:
cur = pattern_list[-1]
nxt, actual = _apply_number(cur, n, silent=silent)
executed.append(actual)
pattern_list.append(nxt)
return executed, pattern_list, None

def _cmp_lists(a, b):
la, lb = len(a), len(b)
m = la if la < lb else lb
for i in range(m):
if a[i] < b[i]:
return -1
if a[i] > b[i]:
return 1
if la < lb:
return -1
if la > lb:
return 1
return 0

def _row_key_for_compare(pat, row_idx):
base = pat.rows[0]
row = pat.rows[row_idx]
l = base[row_idx - 1] if row_idx - 1 < len(base) else 0
if l <= 1:
keep = row[:]
else:
if len(row) < l:
keep = row[:]
else:
keep = [row[0]] + row[l:]
keep = keep[::-1]
return keep

def compare_patterns(a, b):
ra = len(a.rows) - 1
rb = len(b.rows) - 1
m = ra if ra < rb else rb
for i in range(1, m + 1):
ka = _row_key_for_compare(a, i)
kb = _row_key_for_compare(b, i)
c = _cmp_lists(ka, kb)
if c != 0:
return c
if ra < rb:
return -1
if ra > rb:
return 1
return 0

def _is_prefix(seg, full):
if len(seg.rows) > len(full.rows):
return False
if seg.rows[0] != full.rows[0][:len(seg.rows[0])]:
return False
for i in range(1, len(seg.rows)):
if seg.rows[i] != full.rows[i]:
return False
return True

def _is_proper_prefix(seg, full):
return _is_prefix(seg, full) and (len(seg.rows) < len(full.rows))

def _pattern_equal(a: BasicLaverPattern, b: BasicLaverPattern):
return a.rows == b.rows and a.mask == b.mask

def _pattern_signature(p: BasicLaverPattern):
rows_sig = tuple(tuple(r) for r in p.rows)
mask_sig = tuple(tuple(sorted(s)) for s in p.mask)
return rows_sig, mask_sig

_EXPAND_COUNTS_CACHE = {}

def _expand_row_counts_from(start_pat: BasicLaverPattern, n: int):
if n < 0:
n = 0
key = (_pattern_signature(start_pat), n)
if key in _EXPAND_COUNTS_CACHE:
return _EXPAND_COUNTS_CACHE[key][:]

counts = [len(start_pat.rows)]
for k in range(1, n + 1):
res, _act = _apply_number(start_pat, k, silent=True)
counts.append(len(res.rows))

_EXPAND_COUNTS_CACHE[key] = counts[:]
return counts

def _simplify(op_numbers, pattern_list):
target = pattern_list[-1].clone()

s = op_numbers[:]
executed, pats, _ = reconstruct_pattern_list(s, silent=True)
s = executed
pattern_list = pats

i = len(s) - 1
while i >= 0:
if i >= len(s):
i = len(s) - 1
if i < 0:
break
if s[i] == 0:
i -= 1
continue

while True:
if i >= len(s):
break
n = s[i]

z = 0
j = i + 1
while j < len(s) and s[j] == 0:
z += 1
j += 1

candidate = None
need = None

if n == 1:
if z >= 1:
candidate = s[:i] + s[i + 1:]
else:
break
else:
start_pat = pattern_list[i]
counts = _expand_row_counts_from(start_pat, n)
need = counts[n] - counts[n - 1]
if need < 0:
need = 0

if z < need:
break

candidate = s[:]
candidate[i] = n - 1
if need > 0:
del candidate[i + 1: i + 1 + need]

cand_exec, cand_pats, _ = reconstruct_pattern_list(candidate, silent=True)
if not cand_pats or not _pattern_equal(cand_pats[-1], target):
break

s = cand_exec
pattern_list = cand_pats

if i >= len(s):
break
if s[i] == 0:
break

i = min(i, len(s) - 1)
i -= 1
while i >= 0 and s[i] == 0:
i -= 1

executed, pattern_list, _ = reconstruct_pattern_list(s, silent=True)
return executed, pattern_list

def _seq_str(nums):
return ",".join(str(x) for x in nums)

def _parse_o_string(s):
s = s.strip()
if s == "":
return BasicLaverPattern([[]], [set()]), None

pos = 0
rows_desc = []
steps = []
n = len(s)

while pos < n:
if s[pos] != "(":
return None, "error"
pos += 1
close = s.find(")", pos)
if close == -1:
return None, "error"
inside = s[pos:close].strip()
pos = close + 1

nums = []
if inside != "":
parts = inside.split(",")
for part in parts:
part = part.strip()
if part.startswith("*"):
part = part[1:].strip()
if part == "" or (not part.isdigit()):
return None, "error"
nums.append(int(part))

nums_asc = sorted(nums)
for i in range(1, len(nums_asc)):
if nums_asc[i] == nums_asc[i - 1]:
return None, "error"

if pos >= n or (not s[pos].isdigit()):
return None, "error"
j = pos
while j < n and s[j].isdigit():
j += 1
step = int(s[pos:j])
pos = j

rows_desc.append(nums_asc)
steps.append(step)

rows = [steps[:]] + rows_desc
mask = [set()] + [set() for _ in rows_desc]
return BasicLaverPattern(rows, mask), None

def _read_find_pattern(I):
initial = BasicLaverPattern(initial_rows, initial_mask)
C = initial.clone()

ops = []
pats = [C.clone()]

if compare_patterns(C, I) <= 0:
return C, ops, pats

MAX_OUTER = 50000
MAX_N = 20000
outer = 0

while outer < MAX_OUTER:
outer += 1

if compare_patterns(C, I) == 0:
return C, ops, pats

n = 0
while n <= MAX_N:
Cn, actual = _apply_number(C, n, silent=True)

if _is_proper_prefix(Cn, I):
n += 1
continue

if (compare_patterns(Cn, I) < 0) and (not _is_prefix(Cn, I)):
return C, ops, pats

if compare_patterns(Cn, I) >= 0:
if Cn.rows == C.rows and Cn.mask == C.mask:
return C, ops, pats
C = Cn
ops.append(actual)
pats.append(C.clone())
break

n += 1

else:
return C, ops, pats

return C, ops, pats

def main_program():
op_numbers = []
executed, pattern_list, _ = reconstruct_pattern_list(op_numbers, silent=True)
op_numbers = executed

while True:
cur = pattern_list[-1]
print("\nCurrent pattern:")
if cur.is_zero():
print("(empty)")
else:
cur.draw()

print(f"Operation sequence: {_seq_str(op_numbers)}")

if cur.is_zero():
pattern_type = "Zero"
elif cur.is_successor():
pattern_type = "Successor"
else:
pattern_type = "Limit"

msg = f"This is a {pattern_type} pattern."
msg += " Natural Number: Operation."
msg += " O: Output."
msg += " R: Read."
if len(pattern_list) > 1:
msg += " U: Undo."
msg += " S: Simplify."
msg += " I: Input operations."
print(msg)

user_input = input("Enter your operation: ").strip().upper()

if user_input.isdigit():
n_in = int(user_input)
nxt, actual = _apply_number(cur, n_in, silent=False)
pattern_list.append(nxt)
op_numbers.append(actual)
if actual == 0:
print("Applied cut operation.")
else:
print(f"Applied operation {actual}.")
continue

if user_input == 'O':
print(cur.to_string())
continue

if user_input == 'R':
raw = input("Input pattern string (from O): ").strip()
pat, err = _parse_o_string(raw)
if err:
print("error")
continue
found, ops, pats = _read_find_pattern(pat)
op_numbers = ops
pattern_list = pats
print(found.to_string())
continue

if user_input == 'U' and len(pattern_list) > 1:
op_numbers = op_numbers[:-1]
executed, pattern_list, _ = reconstruct_pattern_list(op_numbers, silent=True)
op_numbers = executed
print("Undo the last operation.")
continue

if user_input == 'S':
new_ops, new_patterns = _simplify(op_numbers, pattern_list)
if new_ops != op_numbers:
op_numbers = new_ops
pattern_list = new_patterns
print(f"Simplified operation sequence: {_seq_str(op_numbers)}")
else:
print("No further simplifications possible.")
continue

if user_input == 'I':
raw = input("Input the operation sequence (comma-separated natural numbers, e.g., 3,0,2,1): ").strip()
if raw == "":
parsed = []
else:
parts = [p.strip() for p in raw.split(",")]
if any(p == "" or (not p.isdigit()) for p in parts):
print("error")
continue
parsed = [int(p) for p in parts]
executed, pattern_list, _ = reconstruct_pattern_list(parsed, silent=True)
op_numbers = executed
continue

print("Invalid operation. Please try again.")

if __name__ == "__main__":
main_program()

</syntaxhighlight>

== 分析 ==
另见[[IBLP分析Part1]] [[IBLP分析Part2]] [[IBLP分析Part3]] [[IBLP分析Part4]]。

目前iBLP的分析已经到达1-Y(1,3,8)，对应(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,10,9)1。

{{默认排序:序数记号}}
[[分类:记号]]

IBLP分析Part4

2026-04-25T14:37:16Z

Baixie01000a7：创建页面，内容为“{| class="wikitable" |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1 |1,3,4,3 |- |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,3,2)1 |1,3,4,3,3 |- |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,…”

{| class="wikitable"
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1
|1,3,4,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,3,2)1
|1,3,4,3,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12)1
|1,3,4,3,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12)1(14,3,2,1,0)3(15,*14,3,2,1,0)3(16,14,3)1(17,16,2,1,0)3(18,*17,16,3,2,1,0)4(19,*18,*17,16,14,3,2,1,0)5(20,*19,*18,*17,16,14,3,2,1,0)5(21,17,2,1,0)3(22,*21,17,3,2,1,0)4(23,*22,*21,17,14,3,2,1,0)5(24,*23,*22,*21,17,16,14,3,2,1,0)6(25,*22,*21,17,14,3,2,1,0)5(26,14,3)1
|1,3,4,3,4,2,5,9,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12)1(14,3,2,1,0)3(15,*14,3,2,1,0)3(16,14,3)1(17,16,2,1,0)3(18,*17,16,3,2,1,0)4(19,*18,*17,16,14,3,2,1,0)5(20,*19,*18,*17,16,14,3,2,1,0)5(21,17,2,1,0)3(22,*21,17,3,2,1,0)4(23,*22,*21,17,14,3,2,1,0)5(24,*23,*22,*21,17,16,14,3,2,1,0)6(25,*22,*21,17,14,3,2,1,0)5(26,14,3)1(27,26)1
|1,3,4,3,4,2,5,9,5,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12)1(14,3,2)1
|1,3,4,3,4,2,5,9,5,6,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3
|1,3,4,3,4,2,5,9,5,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,3,2)1
|1,3,4,3,4,2,5,9,5,7,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,13,2,1,0)3(15,3,2)1
|1,3,4,3,4,2,5,9,5,7,9,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,13,12)1
|1,3,4,3,4,2,5,9,5,7,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,3,2)1
|1,3,4,3,4,2,5,9,5,7,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,14,13,12)2
|1,3,4,3,4,2,5,9,5,7,10,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,16,15)1
|1,3,4,3,4,2,5,9,5,7,10,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3
|1,3,4,3,4,2,5,9,5,7,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14)1
|1,3,4,3,4,2,5,9,5,7,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14)1(17,16,14,13,12)3(18,*17,16,15,14,13,12)4(19,18,17,16)2(20,19,18)1
|1,3,4,3,4,2,5,9,5,7,12,16,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14)1(17,16,14,13,12)3(18,*17,16,15,14,13,12)4(19,*18,*17,16,15,14,13,12)4
|1,3,4,3,4,2,5,9,5,7,12,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14)1(17,16,14,13,12)3(18,*17,16,15,14,13,12)4(19,*18,*17,16,15,14,13,12)4(20,17,14,13,12)3(21,*20,17,15,14,13,12)4(22,*21,*20,17,16,15,14,13,12)5
|1,3,4,3,4,2,5,9,5,7,12,17,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14)1(17,16,14,13,12)3(18,*17,16,15,14,13,12)4(19,*18,*17,16,15,14,13,12)4(20,17,14,13,12)3(21,*20,17,15,14,13,12)4(22,*21,*20,17,16,15,14,13,12)5(23,20,17)1
|1,3,4,3,4,2,5,9,5,7,12,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14)1(17,16,14,13,12)3(18,*17,16,15,14,13,12)4(19,*18,*17,16,15,14,13,12)4(20,17,14,13,12)3(21,*20,17,15,14,13,12)4(22,*21,*20,17,16,15,14,13,12)5(23,*20,17,3,2,1,0)4(24,3,2)1
|1,3,4,3,4,2,5,9,5,7,12,18,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14)1(17,16,14,13,12)3(18,*17,16,15,14,13,12)4(19,*18,*17,16,15,14,13,12)4(20,17,14,13,12)3(21,*20,17,15,14,13,12)4(22,*21,*20,17,16,15,14,13,12)5(23,*20,17,15,14,13,12)4
|1,3,4,3,4,2,5,9,5,7,12,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14)1(17,16,14,13,12)3(18,*17,16,15,14,13,12)4(19,*18,*17,16,15,14,13,12)4(20,17,14,13,12)3(21,*20,17,15,14,13,12)4(22,*21,*20,17,16,15,14,13,12)5(23,*20,17,15,14,13,12)4(24,15,14)1
|1,3,4,3,4,2,5,9,5,7,12,21,12
|-
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|1,3,4,3,4,2,5,9,5,8
|-
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|1,3,4,3,4,2,5,9,5,8,11
|-
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|1,3,4,3,4,2,5,9,5,9
|-
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|1,3,4,3,4,2,5,9,5,9,4,9,18,9,16
|-
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|1,3,4,3,4,3
|-
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|1,3,4,4
|-
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|1,3,4,4,2,5,9,5
|-
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|1,3,4,4,2,5,9,6
|-
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|1,3,4,4,2,5,9,6,5
|-
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|1,3,4,4,2,5,9,7
|-
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|1,3,4,4,2,5,9,7,10,5
|-
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|1,3,4,4,2,5,9,7,11
|-
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|1,3,4,4,2,5,9,7,12
|-
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|1,3,4,4,2,5,9,8
|-
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|1,3,4,4,2,5,9,8,11
|-
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|1,3,4,4,2,5,9,8,12
|-
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|1,3,4,4,2,5,9,8,12,4,9
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,9
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,19
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,20
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,20,8,17
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,20,9
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,20,20
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,20,26
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,20,29
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,21
|-
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|1,3,4,4,2,5,9,8,12,4,9,18,14,23
|-
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|1,3,4,4,2,5,9,8,12,5
|-
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|1,3,4,4,2,5,9,8,12,8
|-
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|1,3,4,4,2,5,9,8,12,8,12,5
|-
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|1,3,4,4,2,5,9,8,12,9
|-
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|1,3,4,4,2,5,9,8,12,10
|-
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|1,3,4,4,2,5,9,8,12,11
|-
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|1,3,4,4,2,5,9,8,12,11,15
|-
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|1,3,4,4,2,5,9,8,12,11,15,5
|-
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|1,3,4,4,2,5,9,8,12,11,15,12
|-
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|1,3,4,4,2,5,9,8,12,11,15,14,18
|-
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|1,3,4,4,2,5,9,9
|-
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|1,3,4,4,2,5,9,9,4,9,18,15
|-
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|1,3,4,4,2,5,9,9,4,9,18,15,9
|-
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|1,3,4,4,2,5,9,9,4,9,18,16
|-
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|1,3,4,4,2,5,9,9,4,9,18,18
|-
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|1,3,4,4,3
|-
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|1,3,4,4,3,4,4,3
|-
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|1,3,4,4,4
|-
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|1,3,4,4,4,2,5,9,9,6,5
|-
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|1,3,4,4,4,2,5,9,9,9
|-
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|1,3,4,4,4,2,5,9,9,9,4,9,18,18,16
|-
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|1,3,4,4,4,3
|-
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|1,3,4,5
|-
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|1,3,4,5,2,5,9,10
|-
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|1,3,4,5,2,5,9,10,5
|-
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|1,3,4,5,2,5,9,10,7
|-
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|1,3,4,5,2,5,9,10,8
|-
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|1,3,4,5,2,5,9,10,8,12,5
|-
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|1,3,4,5,2,5,9,10,8,12,12,5
|-
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|1,3,4,5,2,5,9,10,8,12,13
|-
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|1,3,4,5,2,5,9,10,8,12,13,11,15,16,14,18,19
|-
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|1,3,4,5,2,5,9,10,9
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|1,3,4,5,2,5,9,10,9,5
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|1,3,4,5,2,5,9,10,13
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|1,3,4,5,2,5,9,11,16,25,16
|-
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|1,3,4,5,2,5,9,11,16,25,27
|-
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|1,3,4,5,2,5,9,11,16,25,29
|-
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|1,3,4,5,2,5,9,12
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|1,3,4,5,2,5,9,12,15
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|1,3,4,5,2,5,9,12,16
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|1,3,4,5,2,5,9,12,16,5
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|1,3,4,5,2,5,9,12,16,16
|-
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|1,3,4,5,2,5,9,12,16,16,5
|-
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|1,3,4,5,2,5,9,12,16,19
|-
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|1,3,4,5,2,5,9,12,16,19,23,5
|-
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|1,3,4,5,2,5,9,13
|-
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|1,3,4,5,2,5,9,13,17
|-
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|1,3,4,5,2,5,9,14
|-
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|1,3,4,5,2,5,9,14,4,9,18,28
|-
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|1,3,4,5,2,5,9,14,4,9,18,28,9
|-
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|1,3,4,5,2,5,9,14,4,9,18,29
|-
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|1,3,4,5,3
|-
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|1,3,4,5,4
|-
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|1,3,4,5,4,2,5,9,14,6,5
|-
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|1,3,4,5,4,2,5,9,14,9
|-
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|1,3,4,5,4,2,5,9,14,9,4,9,18,32,16
|-
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|1,3,4,5,4,3
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|1,3,4,5,4,5
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|1,3,4,5,4,5,2,5,9,14,9,10,5
|-
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|1,3,4,5,4,5,2,5,9,14,9,13
|-
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|1,3,4,5,4,5,2,5,9,14,9,14
|-
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|1,3,4,5,4,5,2,5,9,14,9,14,4,9,18,32,18,28
|-
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|1,3,4,5,4,5,3
|-
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|1,3,4,5,5
|-
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|1,3,4,5,5,2,5,9,14,10,5
|-
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|1,3,4,5,5,2,5,9,14,11
|-
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|1,3,4,5,5,2,5,9,14,13
|-
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|1,3,4,5,5,2,5,9,14,13,18
|-
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|1,3,4,5,5,2,5,9,14,13,18,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,12,11,8,5)3
|1,3,4,5,5,2,5,9,14,13,18,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,3,2,1,0)4(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,3,2)1
|1,3,4,5,5,2,5,9,14,13,18,17,22,5
|-
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|1,3,4,5,5,2,5,9,14,13,18,17,22,21,26,5
|-
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|1,3,4,5,5,2,5,9,14,14
|-
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|1,3,4,5,5,3
|-
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|1,3,4,5,6
|-
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|1,3,4,5,6,2,5,9,14,15,5
|-
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|1,3,4,5,6,2,5,9,14,16
|-
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|1,3,4,5,6,2,5,9,14,17
|-
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|1,3,4,5,6,2,5,9,14,18
|-
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|1,3,4,5,6,2,5,9,14,19
|-
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|1,3,4,5,6,2,5,9,14,20
|-
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|1,3,4,5,6,3
|-
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|1,3,4,6
|-
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|1,3,4,6,3
|-
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|1,3,4,6,4,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,*8,5,3,2,1,0)4(16,15,8,5)2(17,16,15,8,5)3(18,*17,16,15,8,5)3
|1,3,4,6,4,6
|-
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|1,3,4,6,5
|-
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|1,3,4,6,5,2,5,9,15,10,5
|-
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|1,3,4,6,5,2,5,9,15,13
|-
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|1,3,4,6,5,2,5,9,15,13,18
|-
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|1,3,4,6,5,2,5,9,15,13,18,5
|-
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|1,3,4,6,5,2,5,9,15,13,18,18,5
|-
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|1,3,4,6,5,2,5,9,15,13,18,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17,16,15)3(20,*19,18,17,16,15)3
|1,3,4,6,5,2,5,9,15,13,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17,16,15)3(20,*19,18,17,16,15)3(21,17,16,15)2
|1,3,4,6,5,2,5,9,15,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17,16,15)3(20,*19,18,17,16,15)3(21,17,16,15)2(22,21,17,16,15)3(23,*22,21,3,2,1,0)4(24,3,2)1
|1,3,4,6,5,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,3,2,1,0)4(18,17,16,15)2(19,18,17,16,15)3(20,*19,18,17,16,15)3(21,17,16,15)2(22,21,17,16,15)3(23,*22,21,3,2,1,0)4(24,23,22,21)2(25,24,23,22,21)3(26,*25,24,23,22,21)3
|1,3,4,6,5,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,11,8,5)2(16,15,11,8,5)3(17,*16,15,11,8,5)3
|1,3,4,6,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12)1
|1,3,4,6,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12)1(16,3,2)1
|1,3,4,6,7,2,5,9,15,16,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12,2,1,0)3
|1,3,4,6,7,2,5,9,15,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12,2,1,0)3(16,*15,12,3,2,1,0)4(17,*16,*15,12,4,3,2,1,0)5
|1,3,4,6,7,2,5,9,15,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12,11,8,5)3
|1,3,4,6,7,2,5,9,15,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3
|1,3,4,6,7,2,5,9,15,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3
|1,3,4,6,7,2,5,9,15,21,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,15,13)1
|1,3,4,6,7,2,5,9,15,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,*15,13,3,2,1,0)4(18,3,2)1
|1,3,4,6,7,3
|-
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|1,3,4,6,7,8,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,*15,13,3,2,1,0)4(18,17,15,13)2(19,18,17,15,13)3(20,*19,18,17,15,13)3
|1,3,4,6,7,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,*15,13,12,11,8,5)4
|1,3,4,6,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,16,15,13)2(18,17,16,15,13)3(19,*18,17,16,15,13)3
|1,3,4,6,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11,8,5)3(14,*13,12,11,8,5)3(15,13,11,8,5)3(16,*15,13,12,11,8,5)3(17,*16,*15,13,12,11,8,5)4
|1,3,4,6,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1
|1,3,4,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,12,11)1
|1,3,4,7,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13)1
|1,3,4,7,8
|-
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|1,3,4,7,8,2,5,9,16,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13)1(15,3,2)1
|1,3,4,7,8,2,5,9,16,17,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,2,1,0)3
|1,3,4,7,8,2,5,9,16,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,2,1,0)3(15,*14,13,3,2,1,0)4(16,*15,*14,13,4,3,2,1,0)5
|1,3,4,7,8,2,5,9,16,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3
|1,3,4,7,8,2,5,9,16,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,2,1,0)2(16,15,2)1
|1,3,4,7,8,2,5,9,16,20,4,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,2,1,0)2(16,15,2)1(17,16,2,1,0)3(18,*17,16,15,2,1,0)4(19,*18,*17,16,15,2,1,0)4(20,17,2,1,0)3(21,*20,17,15,2,1,0)4(22,*21,*20,17,16,15,2,1,0)5(23,*20,17,15,2,1,0)4(24,23,20,17)2(25,24,23)1
|1,3,4,7,8,2,5,9,16,20,4,9,18,34
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,39
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,40
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,40,8,17,35,69,79
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,40,9
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,41
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,42
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,42,54,73
|-
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|1,3,4,7,8,2,5,9,16,20,4,9,18,34,43
|-
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|1,3,4,7,8,2,5,9,16,20,5
|-
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|1,3,4,7,8,2,5,9,16,20,9
|-
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|1,3,4,7,8,2,5,9,16,20,9,4,9,18,34,43,16
|-
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|1,3,4,7,8,2,5,9,16,20,9,5
|-
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|1,3,4,7,8,2,5,9,16,20,9,16,20
|-
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|1,3,4,7,8,2,5,9,16,20,12
|-
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|1,3,4,7,8,2,5,9,16,20,13
|-
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|1,3,4,7,8,2,5,9,16,20,13,18
|-
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|1,3,4,7,8,2,5,9,16,20,13,18,5
|-
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|1,3,4,7,8,2,5,9,16,20,13,20
|-
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|1,3,4,7,8,2,5,9,16,20,13,20,24
|-
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|1,3,4,7,8,2,5,9,16,20,13,20,24,17,24,28
|-
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|1,3,4,7,8,2,5,9,16,20,14
|-
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|1,3,4,7,8,2,5,9,16,20,15,26,30
|-
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|1,3,4,7,8,2,5,9,16,20,16
|-
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|1,3,4,7,8,2,5,9,16,20,25
|-
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|1,3,4,7,8,2,5,9,16,20,27
|-
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|1,3,4,7,8,2,5,9,16,21
|-
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|1,3,4,7,8,2,5,9,16,21,14,22,28
|-
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|1,3,4,7,8,2,5,9,16,21,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11)1
|1,3,4,7,8,2,5,9,16,21,15,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11)1(17,16,11,8,5)3
|1,3,4,7,8,2,5,9,16,21,15,26,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,11,8,5)2(16,15,11)1(17,16,11,8,5)3(18,11,8,5)2(19,18,11)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,15,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3
|1,3,4,7,8,2,5,9,16,21,15,26,31,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,11,8,5)2(17,16,11)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,15,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,16,15,12)2(18,17,16)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,16,15,12)2(18,17,16)1(19,18,11,8,5)3(20,19,18)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,28,33,39
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,16,15,12)2(18,17,16)1(19,18,11,8,5)3(20,*19,18,3,2,1,0)4(21,20,19,18)2(22,21,20)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,28,33,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,16,15,12)2(18,17,16)1(19,18,16,15,12)3
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,28,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,3,2,1,0)4(17,16,15,12)2(18,17,16)1(19,18,16,15,12)3(20,16,15,12)2(21,20,16)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,20,28,34,27,39
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3
|1,3,4,7,8,2,5,9,16,21,15,26,31,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,12,11,8,5)3(18,*17,12,11,8,5)3
|1,3,4,7,8,2,5,9,16,21,15,26,31,21,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,*17,15,3,2,1,0)4(20,19,17,15)2(21,20,19)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,21,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,*17,15,3,2,1,0)4(20,19,17,15)2(21,20,19)1(22,21,11,8,5)3(23,11,8,5)2(24,23,11)1
|1,3,4,7,8,2,5,9,16,21,15,26,31,21,32,37,15,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,*17,15,3,2,1,0)4(20,19,17,15)2(21,20,19)1(22,21,11,8,5)3(23,*22,21,12,11,8,5)4
|1,3,4,7,8,2,5,9,16,21,15,26,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,*17,15,3,2,1,0)4(20,19,17,15)2(21,20,19)1(22,21,19,17,15)3
|1,3,4,7,8,2,5,9,16,21,15,26,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,*17,15,12,11,8,5)4
|1,3,4,7,8,2,5,9,16,21,15,26,33,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,18,17,15)2(20,19,18)1
|1,3,4,7,8,2,5,9,16,21,15,26,33,23,36
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,11,8,5)3(18,*17,15,12,11,8,5)4(19,*18,*17,15,12,11,8,5)4
|1,3,4,7,8,2,5,9,16,21,15,26,33,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,12)1
|1,3,4,7,8,2,5,9,16,21,15,26,33,25,44
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,12)1(18,17,11,8,5)3
|1,3,4,7,8,2,5,9,16,21,15,26,33,25,44
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,12)1(18,17,11,8,5)3(19,15,11,8,5)3(20,*19,15,12,11,8,5)4(21,*20,*19,15,12,11,8,5)4(22,19,15)1
|1,3,4,7,8,2,5,9,16,21,15,26,33,25,44,55,25,44
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,12)1(18,17,11,8,5)3(19,15,12)1
|1,3,4,7,8,2,5,9,16,21,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,12)1(18,17,11,8,5)3(19,*18,17,3,2,1,0)4(20,19,18,17)2(21,20,19)1
|1,3,4,7,8,2,5,9,16,21,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11,8,5)3(16,*15,12,11,8,5)3(17,15,12)1(18,17,11,8,5)3(19,*18,17,12,11,8,5)4
|1,3,4,7,8,2,5,9,16,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,12,11)1
|1,3,4,7,8,2,5,9,16,22,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,14,13)1
|1,3,4,7,8,2,5,9,16,22,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,3,2,1,0)4(16,3,2)1
|1,3,4,7,8,2,5,9,16,22,29,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,3,2,1,0)4(16,12,11)1
|1,3,4,7,8,2,5,9,16,22,29,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,3,2,1,0)4(16,15,14,13)2(17,16,15)1
|1,3,4,7,8,2,5,9,16,22,29,39
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4
|1,3,4,7,8,2,5,9,16,22,30
|-
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|1,3,4,7,8,2,5,9,16,22,31,16
|-
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|1,3,4,7,8,2,5,9,16,22,33
|-
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|1,3,4,7,8,2,5,9,16,22,33,39
|-
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|1,3,4,7,8,2,5,9,16,22,33,43,33
|-
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|1,3,4,7,8,2,5,9,16,23
|-
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|1,3,4,7,8,2,5,9,16,23,30
|-
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|1,3,4,7,8,2,5,9,16,24
|-
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|1,3,4,7,8,3
|-
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|1,3,4,7,8,4,3
|-
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|1,3,4,7,8,6,11
|-
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|1,3,4,7,8,6,11,12,3
|-
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|1,3,4,7,8,7
|-
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|1,3,4,7,8,7,8,3
|-
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|1,3,4,7,8,8,3
|-
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|1,3,4,7,8,9
|-
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|1,3,4,7,8,9,2,5,9,16,24,28
|-
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|1,3,4,7,8,9,2,5,9,16,24,31
|-
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|1,3,4,7,8,9,2,5,9,16,24,32
|-
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|1,3,4,7,8,9,2,5,9,16,24,33
|-
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|1,3,4,7,8,9,3
|-
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|1,3,4,7,8,10
|-
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|1,3,4,7,8,11
|-
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|1,3,4,7,8,11,12,2,5,9,16,24,35,43
|-
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|1,3,4,7,8,11,12,3
|-
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|1,3,4,7,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,12,11,8,5)3(22,*21,12,11,8,5)4(23,21,12)1(24,23,11,8,5)3(25,*24,23,12,11,8,5)4(26,*25,*24,23,21,12,11,8,5)5(27,*26,*25,*24,23,21,12,11,8,5)5(28,24,11,8,5)3(29,*28,24,12,11,8,5)4(30,*29,*28,24,21,12,11,8,5)5(31,*30,*29,*28,24,23,21,12,11,8,5)6(32,*29,*28,24,21,12,11,8,5)5
|1,3,4,7,9,6,11,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,12,11)1
|1,3,4,7,9,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,*17,14,12,11,8,5)4
|1,3,4,7,9,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,11,8,5)3(22,*21,20,12,11,8,5)4(23,*22,*21,20,13,12,11,8,5)5
|1,3,4,7,9,10,2,5,9,16,25,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,11,8,5)3(22,*21,20,12,11,8,5)4(23,*22,*21,20,13,12,11,8,5)5(24,*21,20,3,2,1,0)4(25,3,2)1
|1,3,4,7,9,10,2,5,9,16,25,32,40,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,11,8,5)3(22,*21,20,12,11,8,5)4(23,*22,*21,20,13,12,11,8,5)5(24,*21,20,12,11,8,5)4
|1,3,4,7,9,10,2,5,9,16,25,32,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2
|1,3,4,7,9,10,2,5,9,16,25,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,12,11)1
|1,3,4,7,9,10,2,5,9,16,25,34,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20,17,14)3(23,22,21)1
|1,3,4,7,9,10,2,5,9,16,25,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20,17,14)3(23,*22,21,3,2,1,0)4(24,3,2)1
|1,3,4,7,9,10,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20,17,14)3(23,*22,21,12,11,8,5)4
|1,3,4,7,9,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20,17,14)3(23,*22,21,20,17,14)3
|1,3,4,7,9,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1
|1,3,4,7,9,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,21,20)1
|1,3,4,7,9,14,18,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4
|1,3,4,7,9,14,18,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,24,23,22)2(26,25,24)1
|1,3,4,7,9,14,18,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4
|1,3,4,7,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4(26,23,20,17,14)3(27,*26,23,21,20,17,14)4(28,*27,*26,23,22,21,20,17,14)5
|1,3,4,7,10,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4(26,23,20,17,14)3(27,*26,23,21,20,17,14)4(28,*27,*26,23,22,21,20,17,14)5(29,26,23)1
|1,3,4,7,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4(26,23,20,17,14)3(27,*26,23,21,20,17,14)4(28,*27,*26,23,22,21,20,17,14)5(29,*26,23,3,2,1,0)4(30,3,2)1
|1,3,4,7,11,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4(26,23,20,17,14)3(27,*26,23,21,20,17,14)4(28,*27,*26,23,22,21,20,17,14)5(29,*26,23,12,11,8,5)4(30,12,11)1
|1,3,4,7,11,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,11,8,5)2(13,12,11)1(14,13,11,8,5)3(15,*14,13,12,11,8,5)4(16,*15,*14,13,12,11,8,5)4(17,14,11,8,5)3(18,*17,14,12,11,8,5)4(19,*18,*17,14,13,12,11,8,5)5(20,*17,14,12,11,8,5)4(21,20,17,14)2(22,21,20)1(23,22,20,17,14)3(24,*23,22,21,20,17,14)4(25,*24,*23,22,21,20,17,14)4(26,23,20,17,14)3(27,*26,23,21,20,17,14)4(28,*27,*26,23,22,21,20,17,14)5(29,*26,23,12,11,8,5)4(30,29,26,23)2(31,30,29)1
|1,3,4,7,11,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,*11,*8,5,4,3,2,1,0)5
|1,3,5
|}

IBLP分析Part3

2026-04-25T14:36:45Z

Baixie01000a7：创建页面，内容为“{| class="wikitable" |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1 |1,3 |- |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,1)1(6,5,1)1(7,6,5,1)2(8,7,6)1 |1,3,2,5 |- |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,1,0)1 |1,3,2,5,4 |- |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,1,0)1(6,5,1,0)2(7,6,5)1 |1,3,2,5,4,9 |- |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2 |1,3,2,5,4,9,6 |- |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1 |1,3,2,5,4,9,6,9 |- |(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,…”

{| class="wikitable"
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1
|1,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,1)1(6,5,1)1(7,6,5,1)2(8,7,6)1
|1,3,2,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,1,0)1
|1,3,2,5,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,1,0)1(6,5,1,0)2(7,6,5)1
|1,3,2,5,4,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2
|1,3,2,5,4,9,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1
|1,3,2,5,4,9,6,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7,6,5)3(10,9,8)1
|1,3,2,5,4,9,6,9,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7,6,5)3(10,*9,8,7,6,5)3
|1,3,2,5,4,9,6,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1
|1,3,2,5,4,9,6,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,2,1,0)3(11,10,6)1(12,11,10,6)2(13,12,11)1
|1,3,2,5,4,9,6,11,8,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,5)1
|1,3,2,5,4,9,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,5)1(11,10,6,5)2(12,11,10)1
|1,3,2,5,4,9,7,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,5)1(11,10,6,5)2(12,11,10)1(10,7,6,5)2
|1,3,2,5,4,9,7,13,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,5)1(11,10,6,5)2(12,11,10)1(10,7,6,5)2(11,10,7,6,5)2(12,11,10)1(13,12,11,10)2(14,13,12)1
|1,3,2,5,4,9,7,13,10,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,6,5)1(8,7,6,5)2(9,8,7)1(10,6,5)1(11,10,6,5)2(12,11,10)1(10,7,6,5)2(11,10,7,6,5)2(12,11,10)1(13,12,11,10)2(14,13,12)1(15,11,10)1
|1,3,2,5,4,9,7,13,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,*6,5,2,1,0)3
|1,3,2,5,4,9,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2,1,0)3(7,*6,5,2,1,0)3(8,6,2,1,0)3(9,*8,6,5,2,1,0)3(10,*9,*8,6,5,2,1,0)4
|1,3,2,5,4,9,8,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,2,1,0)2(6,5,2)1
|1,3,2,5,4,9,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3
|1,3,2,5,4,9,8,17,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,2,1,0)2(7,6,2)1
|1,3,2,5,4,9,8,17,11,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,2,1,0)3
|1,3,2,5,4,9,8,17,11,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1
|1,3,2,5,4,9,8,17,11,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6,5,3)3(9,*8,7,6,5,3)3
|1,3,2,5,4,9,8,17,11,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1
|1,3,2,5,4,9,8,17,11,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,5,3)1
|1,3,2,5,4,9,8,17,11,17,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,5,3)1(10,9,5,3)2(11,10,9)1
|1,3,2,5,4,9,8,17,11,17,15,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,6,5,3)2
|1,3,2,5,4,9,8,17,11,17,15,22,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,6,5,3)2(10,9,6,5,3)3(11,10,9)1
|1,3,2,5,4,9,8,17,11,17,15,22,19,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,6,5,3)2(10,9,6,5,3)3(11,*10,9,6,5,3)3
|1,3,2,5,4,9,8,17,11,17,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,5,3)1(7,6,5,3)2(8,7,6)1(9,6,5,3)2(10,9,6,)1
|1,3,2,5,4,9,8,17,11,17,16,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3
|1,3,2,5,4,9,8,17,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4
|1,3,2,5,4,9,8,17,12,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1
|1,3,2,5,4,9,8,17,12,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1
|1,3,2,5,4,9,8,17,12,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,9,8)1
|1,3,2,5,4,9,8,17,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,9,8)1(15,14,9,8)2(16,15,14)1
|1,3,2,5,4,9,8,17,13,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,2,1,0)3
|1,3,2,5,4,9,8,17,13,21,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,2,1,0)3(15,*14,11,3,2,1,0)4
|1,3,2,5,4,9,8,17,13,21,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,2,1,0)3(15,*14,11,3,2,1,0)4(16,14,11)1
|1,3,2,5,4,9,8,17,13,21,17,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,2,1,0)3(15,*14,11,3,2,1,0)4(16,14,11)1(17,16,14,11)2(18,17,16)1
|1,3,2,5,4,9,8,17,13,21,17,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,9,8)2
|1,3,2,5,4,9,8,17,13,21,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,11,9,8)2(15,14,11)1
|1,3,2,5,4,9,8,17,13,21,18,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,12,11,9,8)3
|1,3,2,5,4,9,8,17,13,21,18,26,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,12,11,9,8)3(15,14,12)1(16,15,14,12)2(17,16,15)1
|1,3,2,5,4,9,8,17,13,21,18,26,23,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,12,11,9,8)3(15,14,12)1(16,15,14,12)2(17,16,15)1(18,14,12)1
|1,3,2,5,4,9,8,17,13,21,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,9,8)1(12,11,9,8)2(13,12,11)1(14,12,11,9,8)3(15,*14,12,11,9,8)3
|1,3,2,5,4,9,8,17,13,21,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,*9,8,3,2,1,0)4
|1,3,2,5,4,9,8,17,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,7,5)2
|1,3,2,5,4,9,8,17,14,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,7,5)2(10,9,8)1
|1,3,2,5,4,9,8,17,14,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,7,5)2(10,9,8)1(11,9,8,7,5)2(12,*11,9,8,7,5)3
|1,3,2,5,4,9,8,17,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,8,7,5)2(10,9,8)1(11,9,8,7,5)2(12,*11,9,8,7,5)3(13,11,8,7,5)3(14,*13,11,9,8,7,5)4(15,14,13,11,)2(16,15,14)1
|1,3,2,5,4,9,8,17,15,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4
|1,3,2,5,4,9,8,17,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,2,1,0)3(13,*12,10,3,2,1,0)4(14,*13,*12,10,3,2,1,0)4
|1,3,2,5,4,9,8,17,16,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,5,2,1,0)3
|1,3,2,5,4,9,8,17,16,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,5,2,1,0)3(11,*10,5,3,2,1,0)4
|1,3,2,5,4,9,8,17,16,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,5,2,1,0)3(11,*10,5,3,2,1,0)4(12,*11,*10,5,3,2,1,0)4
|1,3,2,5,4,9,8,17,16,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,7,2,1,0)3(11,*10,7,3,2,1,0)4(12,*11,*10,7,5,3,2,1,0)5
|1,3,2,5,4,9,8,17,16,24,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,7,2,1,0)3(11,*10,7,3,2,1,0)4(12,*11,*10,7,5,3,2,1,0)5(13,10,7)1
|1,3,2,5,4,9,8,17,16,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,7,2,1,0)3(11,*10,7,3,2,1,0)4(12,*11,*10,7,5,3,2,1,0)5(13,*10,7,3,2,1,0)4(14,*13,*10,7,5,3,2,1,0)5
|1,3,2,5,4,9,8,17,16,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,2,1,0)3(8,*7,5,3,2,1,0)4(9,*8,*7,5,3,2,1,0)4(10,7,2,1,0)3(11,*10,7,3,2,1,0)4(12,*11,*10,7,5,3,2,1,0)5(13,*12,*11,*10,7,5,3,2,1,0)5
|1,3,2,5,4,9,8,17,16,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,3)1
|1,3,2,5,4,9,8,17,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,3)1(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,3,2,1,0)4(11,8,2,1,0)3(12,*11,8,3,2,1,0)4(13,*12,*11,8,5,3,2,1,0)5(14,*13,*12,*11,8,5,3,2,1,0)5
|1,3,2,5,4,9,8,17,16,33,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2,1,0)3(6,*5,3,2,1,0)3(7,5,3)1(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,3,2,1,0)4(11,8,5)1
|1,3,2,5,4,9,8,17,16,33,32,65
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2)1
|1,3,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,3,2)1(6,3,2)1
|1,3,3,3
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1
|1,3,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,1)1(7,6,1)1(8,7,6,1)2(9,8,7)1(10,9)1
|1,3,4,2,5,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,1,0)1
|1,3,4,2,5,6,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,1,0)1(7,6,1,0)2(8,7,6)1(9,8)1
|1,3,4,2,5,6,4,9,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,2,1,0)2(7,6,2,1,0)3(8,*7,6,2,1,0)3
|1,3,4,2,5,6,4,9,10,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,2,1,0)2(7,6,2)1(8,7)1
|1,3,4,2,5,6,4,9,10,8,17,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,3,2,1,0)2(7,*6,3,2,1,0)3(8,6,3)1(9,8)1
|1,3,4,2,5,6,4,9,10,8,17,18,16,33,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,3,2)1
|1,3,4,2,5,6,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,5,4)1
|1,3,4,2,5,6,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4)1(6,5,4)1(7,6,5,4)2(8,7,6)1
|1,3,4,2,5,6,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3
|1,3,4,2,5,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,1)1(7,6,1,)2(8,7,6,1)2(9,8,7)1(10,9,8,6,1)3
|1,3,4,2,5,7,2,5,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,1,0)1
|1,3,4,2,5,7,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,1,0)1(7,6,1,0)2(8,7,6)1(9,8,6,1,0)3
|1,3,4,2,5,7,4,9,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2
|1,3,4,2,5,7,4,9,11,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1
|1,3,4,2,5,7,4,9,11,6,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,2,1,0)3
|1,3,4,2,5,7,4,9,11,6,11,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,2,1,0)3(12,7,6)1
|1,3,4,2,5,7,4,9,11,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,2,1,0)3(12,7,6)1(13,12,7,6)2(14,13,12)1(15,14,2,1,0)3
|1,3,4,2,5,7,4,9,11,7,13,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,2,1,0)3(12,9,8,7,6)3(13,*12,9,8,7,6)3
|1,3,4,2,5,7,4,9,11,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,2,1,0)3(12,9,8)1
|1,3,4,2,5,7,4,9,11,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,8,7,6)3
|1,3,4,2,5,7,4,9,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,7,6)1(9,8,7,6)2(10,9,8)1(11,10,8,7,6)3(12,8,7,6)2(13,12,8,7,6)3(14,13,12)1(15,14,13,12)2(16,15,14)1(17,16,14,13,12)3
|1,3,4,2,5,7,4,9,12,7,13,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,*7,6,2,1,0)3
|1,3,4,2,5,7,4,9,12,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2,1,0)3(8,*7,6,2,1,0)3(9,7,2,1,0)3(10,*9,7,6,2,1,0)4(11,*10,*9,7,6,2,1,0)4
|1,3,4,2,5,7,4,9,12,8,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2)1
|1,3,4,2,5,7,4,9,12,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,2,1,0)2(7,6,2)1(8,7,2,1,0)3
|1,3,4,2,5,7,4,9,12,8,17,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3
|1,3,4,2,5,7,4,9,12,8,17,20,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,2,1,0)3(9,*8,6,3,2,1,0)4(10,*9,*8,6,3,2,1,0)4
|1,3,4,2,5,7,4,9,12,8,17,22,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1
|1,3,4,2,5,7,4,9,12,8,17,22,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3
|1,3,4,2,5,7,4,9,12,8,17,22,16,33,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,6,2,1,0)3(11,*10,6,3,2,1,0)4(12,*11,*10,6,3,2,1,0)4(13,10,2,1,0)3(14,*13,10,3,2,1,0)4(15,*14,*13,10,6,3,2,1,0)5(16,*15,*14,*13,10,6,3,2,1,0)5
|1,3,4,2,5,7,4,9,12,8,17,22,16,33,42,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,6,3)
|1,3,4,2,5,7,4,9,12,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,9,2,1,0)3
|1,3,4,2,5,7,4,9,12,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,9,8)1
|1,3,4,2,5,7,4,9,12,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,10,9,8)3
|1,3,4,2,5,7,4,9,12,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1
|1,3,4,2,5,7,4,9,12,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,*9,8,3,2,1,0)4
|1,3,4,2,5,7,4,9,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,2,1,0)2(12,11,2)1(13,12,2,1,0)3(14,11,2,1,0)3(15,*14,11,2,1,0)3(16,14,11)1(17,16,2,1,0)3(18,*17,16,11,2,1,0)4
|1,3,4,2,5,7,4,9,13,8,17,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,6,2,1,0)3(12,*11,6,3,2,1,0)4(13,*12,*11,6,3,2,1,0)4(14,11,6)1
|1,3,4,2,5,7,4,9,13,8,17,21,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2,1,0)3(7,*6,3,2,1,0)3(8,6,3)1(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,6,2,1,0)3(12,*11,6,3,2,1,0)4(13,*12,*11,6,3,2,1,0)4(14,11,6)1(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,6,3,2,1,0)5
|1,3,4,2,5,7,4,9,13,8,17,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2)1
|1,3,4,2,5,7,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2)1(7,3,2)1
|1,3,4,2,5,7,5,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2)1(7,6,2,1,0)3
|1,3,4,2,5,7,5,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,3,2)1(7,6,2,1,0)3(8,3,2)1
|1,3,4,2,5,7,5,7,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,4,2,1,0)3
|1,3,4,2,5,7,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,2,1,0)3
|1,3,4,2,5,7,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1
|1,3,4,2,5,7,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,1,0)1
|1,3,4,2,5,7,10,4
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,1,0)1(8,7,1,0)2(9,8,7)1(10,9,7,1,0)3(11,8,7)1
|1,3,4,2,5,7,10,4,9,13,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,1,0)1(8,7,1,0)2(9,8,7)1(10,9,7,1,0)3(11,10,9)1
|1,3,4,2,5,7,10,4,9,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2
|1,3,4,2,5,7,10,4,9,13,18,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,12,11)1
|1,3,4,2,5,7,10,4,9,13,18,6,11,15,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,12,11)1(14,8,7)1
|1,3,4,2,5,7,10,4,9,13,18,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2,1,0)3(9,*8,7,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,18,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2,1,0)3(9,*8,7,2,1,0)3(10,8,2,1,0)3(11,*10,8,7,2,1,0)4(12,*11,*10,8,7,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,18,8,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2)1
|1,3,4,2,5,7,10,4,9,13,18,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,2,1,0)2(8,7,2)1(9,8,2,1,0)3(10,9,8)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,12,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,12,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,2,1,0)3(15,*14,13,3,2,1,0)4(16,14,13)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,12,21,29,37
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*9,7,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*10,*9,7,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,10,9)1(13,7,2,1,0)3(14,*13,7,3,2,1,0)4(15,*14,*13,7,3,2,1,0)4(16,13,2,1,0)3(17,*16,13,3,2,1,0)4(18,*17,*16,13,7,3,2,1,0)5(19,16,13)1
|1,3,4,2,5,7,10,4,9,13,18,8,17,25,34,16,33,49,66
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,3,2)1(8,7,2,1,0)3(9,8,7)1
|1,3,4,2,5,7,10,4,9,13,18,9,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,4,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,18,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,4,2,1,0)3(8,2,1,0)2(9,8,2)1
|1,3,4,2,5,7,10,4,9,13,18,12,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,4,2,1,0)3(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,18,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,4,2,1,0)3(8,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,13,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,4,2,1,0)3(8,7,4)1
|1,3,4,2,5,7,10,4,9,13,18,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,5,4)1
|1,3,4,2,5,7,10,4,9,13,18,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2
|1,3,4,2,5,7,10,4,9,13,18,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1
|1,3,4,2,5,7,10,4,9,13,18,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,18,26,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,5,4)1(11,10,5,4)2(12,11,10)1(13,12,2,1,0)3(14,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,18,26,30,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,6,5,4)2(11,10,6)1(12,11,2,1,0)3(13,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,23,31,35,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6,5,4)3(11,10,7)1(12,11,10,7)2(13,12,11)1(14,13,2,1,0)3(15,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,23,31,35,28,36,40,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6,5,4)3(11,10,7)1(12,11,10,7)2(13,12,11)1(14,13,2,1,0)3(15,10,7)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6,5,4)3(11,*10,7,6,5,4)3
|1,3,4,2,5,7,10,4,9,13,18,26,30,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,9,8)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,35,43
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,2,1,0)3(14,3,2)1
|1,3,4,2,5,7,10,4,9,13,18,26,30,35,43,47,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3
|1,3,4,2,5,7,10,4,9,13,18,26,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3
|1,3,4,2,5,7,10,4,9,13,18,26,31,23,31,36,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3(11,10,7)1(12,11,10,7)2(13,12,11)1(14,13,6,5,4)3
|1,3,4,2,5,7,10,4,9,13,18,26,31,23,31,36,28,36,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3(11,10,7)1(12,11,10,7)2(13,12,11)1(14,13,11,10,7)3
|1,3,4,2,5,7,10,4,9,13,18,26,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3(11,*10,7,6,5,4)3
|1,3,4,2,5,7,10,4,9,13,18,26,32,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3(11,*10,7,6,5,4)3(12,10,7)1(13,12,6,5,4)3(14,*13,12,7,6,5,4)4
|1,3,4,2,5,7,10,4,9,13,18,26,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6)1
|1,3,4,2,5,7,10,4,9,13,18,26,33,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6)1(10,9,8)1
|1,3,4,2,5,7,10,4,9,13,18,26,33,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,5,4)1(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6)1(10,9,8)1(11,10,9,8)2(12,11,10)1
|1,3,4,2,5,7,10,4,9,13,18,26,33,41,52
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,1,0)1(8,7,1,0)2(9,8,7)1(10,9,7,1,0)3(11,*10,9,8,7,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,4,9,13,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2
|1,3,4,2,5,7,10,4,9,13,19,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1
|1,3,4,2,5,7,10,4,9,13,19,6,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3
|1,3,4,2,5,7,10,4,9,13,19,6,11,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,10,9)1
|1,3,4,2,5,7,10,4,9,13,19,6,11,15,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,*12,11,10,9,8,7)4
|1,3,4,2,5,7,10,4,9,13,19,6,11,15,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,*12,11,10,9,8,7)4(14,7,2,1,0)3(15,14,7)1(16,15,14,7)2(17,16,15)1(18,17,15,14,7)3(19,*18,17,16,15,14,7)4
|1,3,4,2,5,7,10,4,9,13,19,6,11,15,21,8,13,17,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,*12,11,10,9,8,7)4(14,8,7)1
|1,3,4,2,5,7,10,4,9,13,19,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,8,7)1(10,9,8,7)2(11,10,9)1(12,11,9,8,7)3(13,*12,11,10,9,8,7)4(14,8,7)1(15,14,8,7)2(16,15,14)1(17,16,14,8,7)3(18,*17,16,15,14,8,7)4
|1,3,4,2,5,7,10,4,9,13,19,7,13,18,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2,1,0)3(9,*8,7,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2)1
|1,3,4,2,5,7,10,4,9,13,19,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2)1(9,8,2,1,0)3(10,7,2)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2)1(9,8,2,1,0)3(10,9,8)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,34
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,2,1,0)2(8,7,2)1(9,8,2,1,0)3(10,*9,8,7,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,2,1,0)3(15,12,11)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,23,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,12,11)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,29,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,14,13)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,29,38
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,29,39
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,9,2,1,0)3(17,*16,9,3,2,1,0)4(18,16,9)1(19,18,16,9)2(20,19,18)1(21,20,18,16,9)3(22,*21,20,19,18,16,9)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,12,21,29,39,16,25,33,43
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,9,7)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,9,7)1(17,16,9,7)2(18,17,16)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,9,7)1(17,16,9,7)2(18,17,16)1(19,18,16,9,7)3(20,*19,18,17,16,9,7)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,11,2,1,0)3(17,*16,11,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,37,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,11,9,7)2(17,16,11)1(18,17,11,9,7)3(19,*18,17,16,11,9,7)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,18,26,33,42
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,18,26,33,42,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3(17,16,12)1(18,17,16,12)2(19,18,17)1(20,19,17,16,12)3(21,*20,19,18,17,16,12)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,18,26,33,42,23,31,38,47
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3(17,16,12)1(18,17,16,12)2(19,18,17)1(20,19,17,16,12)3(21,*20,19,18,17,16,12)4(22,16,12)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3(17,*16,12,11,9,7)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3(17,*16,12,11,9,7)3(18,16,11,9,7)3(19,18,16)1(20,19,18,16)2(21,20,19)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,20,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,9,7)1(12,11,9,7)2(13,12,11)1(14,13,11,9,7)3(15,*14,13,12,11,9,7)4(16,12,11,9,7)3(17,*16,12,11,9,7)3(18,16,11,9,7)3(19,18,16)1(20,19,18,16)2(21,20,19)1(22,21,19,18,16)3(23,*22,21,20,19,18,16)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,13,21,28,38,20,32,43,56
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*9,7,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*9,7,3,2,1,0)4(12,9,7)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*9,7,3,2,1,0)4(12,*9,7,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25,35,47
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,10,9,7)2
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25,35,47,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25,35,47,19,27,34,43
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,3,2,1,0)4(20,15,11)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25,35,47,19,27,34,43,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,3,2,1,0)4(20,*18,17,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,14,25,35,47,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,11,10,9,7)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,11,10,9,7)4(20,18,17)1(21,20,18,17)2(22,21,20)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,15,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10,9,7)3(16,*15,11,1,0,9,7)3(17,15,11)1(18,17,10,9,7)3(19,*18,17,11,10,9,7)4(20,18,17)1(21,20,18,17)2(22,21,20)1(23,22,20,18,17)3(24,*23,22,21,20,18,17)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,15,28,40,54
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,3,2,1,0)4(15,11,10)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,35,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,11,10,9,7)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,10,9,7)2(12,11,10)1(13,12,10,9,7)3(14,*13,12,11,10,9,7)4(15,11,10,9,7)3(16,*15,11,10,9,7)3(17,15,10,9,7)3(18,*17,15,11,10,9,7)4(19,18,17,15)2(20,19,18)1(21,20,18,17,15)3(22,*21,20,19,18,17,15)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,15,28,40,56
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,2,1,0)3(10,*9,7,3,2,1,0)4(11,*10,*9,7,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,35
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,2,1,0)2(12,11,2,1,0)3(13,*12,11,2,1,0)3
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,36,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,3,2,1,0)2(12,*11,3,2,1,0)3(13,11,2,1,0)3(14,*13,11,3,2,1,0)4(15,*14,*13,11,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,38,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,3,2,1,0)2(12,*11,3,2,1,0)3(13,11,3)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,38,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,7,2,1,0)2(12,*11,7,3,2,1,0)3(13,*12,*11,7,3,2,1,0)4(14,11,7)1(15,14,2,1,0)3(16,11,2,1,0)3(17,*16,11,3,2,1,0)4(18,*17,*16,11,7,3,2,1,0)5(19,*18,*17,*16,11,7,3,2,1,0)5
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,42,32
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,7,3)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,42,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,42,53
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,7,3)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,49,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,9,2,1,0)3(13,*12,9,3,2,1,0)4(14,7,3)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,49,49,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,10,9)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,49,66
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,*10,9,3,2,1,0)4
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,49,67
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,*10,9,3,2,1,0)4(13,7,2,1,0)3(14,*13,7,3,2,1,0)4(15,*14,*13,7,3,2,1,0)4(16,13,7)1
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,36,16,33,49,67,24,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,*10,9,3,2,1,0)4(13,7,2,1,0)3(14,*13,7,3,2,1,0)4(15,*14,*13,7,3,2,1,0)4(16,13,7)1(17,16,2,1,0)3(18,*17,16,3,2,1,0)4(19,*18,*17,16,7,3,2,1,0)5(20,*17,16,3,2,1,0)4(21,*20,*17,16,7,3,2,1,0)5
|1,3,4,2,5,7,10,4,9,13,19,8,17,25,37
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,*10,9,3,2,1,0)4(13,7,3)1
|1,3,4,2,5,7,10,4,9,13,19,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,11,10,9)2(13,12,11)1(14,13,11,10,9)3(15,*14,13,12,11,10,9)4(16,12,11,10,9)3(17,*16,12,11,10,9)3(18,16,12)1(19,18,11,10,9)3(20,*19,18,12,11,10,9)4
|1,3,4,2,5,7,10,4,9,13,20
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2,1,0)3(8,*7,3,2,1,0)3(9,7,3)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,*11,*10,9,7,3,2,1,0)5
|1,3,4,2,5,7,10,4,9,13,20,8,17,25,39
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2)1
|1,3,4,2,5,7,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2)1(8,7,2,1,0)3(9,8,7)1
|1,3,4,2,5,7,10,5,7,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2)1(8,7,2,1,0)3(9,*8,7,3,2,1,0)4
|1,3,4,2,5,7,10,5,7,10,4,9,13,20,9,13,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,3,2)1(8,7,2,1,0)3(9,*8,7,3,2,1,0)4(10,3,2)1
|1,3,4,2,5,7,10,5,7,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,4,2,1,0)3(8,3,2)1
|1,3,4,2,5,7,10,7,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,4,2,1,0)3(8,*7,4,3,2,1,0)4(9,3,2)1
|1,3,4,2,5,7,10,7,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,5,4)1
|1,3,4,2,5,7,10,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*5,4,3,2,1,0)4(8,3,2)1
|1,3,4,2,5,7,10,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,2,1,0)3(8,7,6)1
|1,3,4,2,5,7,10,12,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,2,1,0)3(8,*7,6,3,2,1,0)4(9,3,2)1
|1,3,4,2,5,7,10,12,15,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2
|1,3,4,2,5,7,10,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,11,10)1
|1,3,4,2,5,7,10,13,4,9,13,20,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,14,10,9,8)3(16,11,10)1
|1,3,4,2,5,7,10,13,4,9,13,20,24,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,14,13,12)2
|1,3,4,2,5,7,10,13,4,9,13,20,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,2,1,0)2(9,8,2,1,0)3(10,*9,8,2,1,0)3
|1,3,4,2,5,7,10,13,4,9,13,20,25,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,2,1,0)2(9,8,2)1
|1,3,4,2,5,7,10,13,4,9,13,20,25,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3
|1,3,4,2,5,7,10,13,4,9,13,20,25,8,17,25,40,49,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1
|1,3,4,2,5,7,10,13,4,9,13,20,25,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,8,3)1
|1,3,4,2,5,7,10,13,4,9,13,20,25,9,13,20,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,10,2,1,0)3(14,*13,10,3,2,1,0)4(15,8,3)1
|1,3,4,2,5,7,10,13,4,9,13,20,25,9,13,20,24,31,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,11,10)1
|1,3,4,2,5,7,10,13,4,9,13,20,25,9,13,20,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,*11,10,3,2,1,0)4
|1,3,4,2,5,7,10,13,4,9,13,20,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,12,11,10)2
|1,3,4,2,5,7,10,13,4,9,13,20,26,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,12,11,10)2(14,13,12)1(15,14,12,11,10)3(16,*15,14,13,12,11,10)4
|1,3,4,2,5,7,10,13,4,9,13,20,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,*12,*11,10,8,3,2,1,0)5
|1,3,4,2,5,7,10,13,4,9,13,20,27,8,17,25,40,52
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,3,2)1
|1,3,4,2,5,7,10,13,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,4,2,1,0)3
|1,3,4,2,5,7,10,13,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,5,4)1
|1,3,4,2,5,7,10,13,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,*5,4,3,2,1,0)4(9,3,2)1
|1,3,4,2,5,7,10,13,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,6,5,4)2
|1,3,4,2,5,7,10,13,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3
|1,3,4,2,5,7,10,13,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,2,1,0)2(10,9,2)1(11,10,2,1,0)3(12,*11,10,9,2,1,0)4(13,12,11,10)2(14,13,12,11,10)3
|1,3,4,2,5,7,10,13,16,4,9,13,20,27,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,3,2)1
|1,3,4,2,5,7,10,13,16,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,8,7)1
|1,3,4,2,5,7,10,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,8,7)1(10,2,1,0)2(11,10,2)1(12,11,2,1,0)3(13,*12,11,10,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,15,14)1
|1,3,4,2,5,7,10,14,4,9,13,20,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,8,7)1(10,3,2)1
|1,3,4,2,5,7,10,14,4,9,13,20,28,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4
|1,3,4,2,5,7,10,14,4,9,13,20,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,1,0)1(11,10,1,0)2(12,11,10)1
|1,3,4,2,5,7,10,14,4,9,13,20,29,4,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,1,0)1(11,10,1,0)2(12,11,10)1(13,12,10,1,0)3(14,*13,12,11,10,1,0)4(15,11,10)1
|1,3,4,2,5,7,10,14,4,9,13,20,29,4,9,13,20,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,1,0)1(11,10,1,0)2(12,11,10)1(13,12,10,1,0)3(14,*13,12,11,10,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,16,15)1
|1,3,4,2,5,7,10,14,4,9,13,20,29,4,9,13,20,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,1,0)1(11,10,1,0)2(12,11,10)1(13,12,10,1,0)3(14,*13,12,11,10,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,11,10,1,0)4
|1,3,4,2,5,7,10,14,4,9,13,20,29,4,9,13,20,29
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,2,1,0)2
|1,3,4,2,5,7,10,14,4,9,13,20,29,6
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,2,1,0)2(11,10,2)1
|1,3,4,2,5,7,10,14,4,9,13,20,29,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,2,1,0)2(11,10,2)1(12,11,2,1,0)3(13,*12,11,10,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,10,2,1,0)4
|1,3,4,2,5,7,10,14,4,9,13,20,29,8,17,25,40,57
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,3,2,1,0)3(11,*10,3,2,1,0)3
|1,3,4,2,5,7,10,14,4,9,13,20,29,8,17,25,40,58,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,3)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,10,3,2,1,0)5(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,16,14,13,12)3(19,*18,16,15,14,13,12)4(20,*18,16,15,14,13,12)4(21,10,3)1
|1,3,4,2,5,7,10,14,4,9,13,20,29,8,17,25,40,58,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,3)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,10,3,2,1,0)5(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,16,14,13,12)3(19,*18,16,15,14,13,12)4(20,19,18,16)2(21,20,19)1(22,21,19,18,16)3(23,*22,21,20,19,18,16)4(24,23,22,21)2(25,24,23,22,21)3(26,*25,24,20,19,18,16)4(27,20,19,18,16)3(28,*27,20,19,18,16)3(29,27,20)1(30,29,19,18,16)3(31,*30,29,20,19,18,16)4(32,*31,*30,29,27,20,19,18,16)5(33,32,31,30,29)3(34,*33,32,31,30,29)3(35,33,31,30,29)3(36,*35,33,32,31,30,29)4
|1,3,4,2,5,7,10,14,4,9,13,20,31
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,3)1(13,12,2,1,0)3(14,*13,12,3,2,1,0)4(15,*14,*13,12,10,3,2,1,0)5(16,15,14,13,12)3(17,*16,15,14,13,12)3(18,16,14,13,12)3(19,*18,16,15,14,13,12)4(20,*19,*18,16,10,3,2,1,0)5
|1,3,4,2,5,7,10,14,4,9,13,20,31,8,17,25,40,64
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,3,2)1
|1,3,4,2,5,7,10,14,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,*8,7,3,2,1,0)4(11,3,2)1
|1,3,4,2,5,7,10,14,14,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,2,1,0)4(11,3,2)1
|1,3,4,2,5,7,10,14,16,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,6,5,4)4(11,3,2)1
|1,3,4,2,5,7,10,14,17,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,6,5,4)4(11,*10,9,3,2,1,0)4(12,3,2)1
|1,3,4,2,5,7,10,14,17,21,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,8,7)2
|1,3,4,2,5,7,10,14,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,8,7)2(11,3,2)1
|1,3,4,2,5,7,10,14,18,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,8,7)2(11,10,9,8,7)3
|1,3,4,2,5,7,10,14,18,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,8,7)2(11,10,9,8,7)3(12,11,10)1
|1,3,4,2,5,7,10,14,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,3,2,1,0)4(10,9,8,7)2(11,10,9,8,7)3(12,*11,10,3,2,1,0)4(13,3,2)1
|1,3,4,2,5,7,10,14,19,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3
|1,3,4,2,5,7,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,1,0)1(11,10,1,0)2(12,11,10)1
|1,3,4,2,5,7,11,4,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,1,0)1(11,10,1,0)2(12,11,10)1(13,12,10,1,0)3(14,*13,12,11,10,1,0)4(15,14,13,12)2(16,15,14,13,12)3(17,*16,15,14,13,12)3
|1,3,4,2,5,7,11,4,9,13,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,2,1,0)2(11,10,2)1
|1,3,4,2,5,7,11,4,9,13,21,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,2,1,0)2(11,10,2)1(12,11,2,1,0)3(13,*12,11,10,2,1,0)4(14,13,12,11)2(15,14,13,12,11)3(16,*15,14,13,12,11)3
|1,3,4,2,5,7,11,4,9,13,21,8,17,25,41
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,3,2,1,0)3(11,*10,3,2,1,0)3(12,10,3)1
|1,3,4,2,5,7,11,4,9,13,21,8,17,25,41,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,3,2)1
|1,3,4,2,5,7,11,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,3,2)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,12,11,10)2(14,13,12,11,10)3(15,*14,13,12,11,10)3
|1,3,4,2,5,7,11,5,7,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,4,2,1,0)3(11,*10,4,3,2,1,0)4(12,11,10,4)2(13,12,11,10,4)3(14,*13,12,11,10,4)3
|1,3,4,2,5,7,11,7,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,5,2,1,0)3(11,*10,5,3,2,1,0)4(12,11,10,5)2(13,12,11,10,5)3(14,*13,12,11,10,5)3
|1,3,4,2,5,7,11,9,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,5,4)1
|1,3,4,2,5,7,11,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,*5,4,3,2,1,0)4(11,3,2)1
|1,3,4,2,5,7,11,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,*5,4,3,2,1,0)4(11,10,5,4)2(12,11,10,5,4)3(13,*12,11,10,5,4)3
|1,3,4,2,5,7,11,10,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,6,5,4)2
|1,3,4,2,5,7,11,10,15,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,6,5,4)2(11,10,6,5,4)3(12,*11,10,3,2,1,0)4(13,12,11,10)2(14,13,12,11,10)3(15,*14,13,12,11,10)3
|1,3,4,2,5,7,11,10,15,13,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,6,5,4)2(11,10,6,5,4)3(12,*11,10,3,2,1,0)4(13,12,11,10)2(14,13,12,11,10)3(15,*14,13,12,11,10)3(16,12,11,10)2
|1,3,4,2,5,7,11,10,15,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,6,5,4)2(11,10,6,5,4)3(12,*11,10,6,5,4)3
|1,3,4,2,5,7,11,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,7,2,1,0)3
|1,3,4,2,5,7,11,13
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,7,2,1,0)3(11,*10,7,3,2,1,0)4(12,11,10,7)2(13,12,11,10,7)3(14,*13,12,11,10,7)3
|1,3,4,2,5,7,11,13,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,7,6,5,4)3
|1,3,4,2,5,7,11,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,7,6,5,4)3(11,*10,7,6,5,4)3
|1,3,4,2,5,7,11,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3
|1,3,4,2,5,7,11,15,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3(12,10,8)1
|1,3,4,2,5,7,11,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3(12,*10,8,3,2,1,0)4(13,3,2)1
|1,3,4,2,5,7,11,16,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3(12,*10,8,7,6,5,4)4
|1,3,4,2,5,7,11,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3(12,11,10,8)2(13,12,11,10,8)3(14,*13,12,11,10,8)3(15,13,11,10,8)3(16,*15,13,12,11,10,8)4
|1,3,4,2,5,7,11,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6,5,4)3(9,*8,7,6,5,4)3(10,8,6,5,4)3(11,*10,8,6,5,4)3(12,*11,*10,8,7,6,5,4)4
|1,3,4,2,5,7,11,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1
|1,3,4,2,5,7,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,7,6)1
|1,3,4,2,5,7,12,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3
|1,3,4,2,5,7,12,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,3,2)1
|1,3,4,2,5,7,12,14,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6,5,4)3(11,*10,7,6,5,4)3(12,10,7)1(13,12,2,1,0)3
|1,3,4,2,5,7,12,14,11,20,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,2,1,0)3(10,7,6)1
|1,3,4,2,5,7,12,14,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3
|1,3,4,2,5,7,12,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6,5,4)3(11,*10,7,6,5,4)3(12,10,7)1(13,12,6,5,4)3(14,*13,12,7,6,5,4)4
|1,3,4,2,5,7,12,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,7,6)1
|1,3,4,2,5,7,12,16,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,9,8)1
|1,3,4,2,5,7,12,16,21
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,3,2,1,0)4(11,3,2)1
|1,3,4,2,5,7,12,16,21,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4
|1,3,4,2,5,7,12,16,22
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,10,9,8)3
|1,3,4,2,5,7,12,16,23
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4(11,10,9,8)2(12,11,10,9,8)3(13,*12,11,10,9,8)3(14,12,10,9,8)3(15,*14,12,11,10,9,8)4(16,*15,*14,12,11,10,9,8)4
|1,3,4,2,5,7,12,16,24
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4(11,10,9,8)2(12,11,10)1
|1,3,4,2,5,7,12,16,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,11,10)1
|1,3,4,2,5,7,12,16,25,33,25
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,6,5,4)2(8,7,6)1(9,8,6,5,4)3(10,*9,8,7,6,5,4)4(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,3,2,1,0)4(15,14,13,12)2(16,15,14)1
|1,3,4,2,5,7,12,16,25,33,50
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4
|1,3,4,2,5,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,1,0)1(9,8,1,0)2(10,9,8)1(11,10,8,1,0)3(12,*11,10,9,8,1,0)4(13,*12,*11,10,9,8,1,0)4
|1,3,4,2,5,8,4,9,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1
|1,3,4,2,5,8,4,9,14,6,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,*14,*13,12,11,10,9,8)4
|1,3,4,2,5,8,4,9,14,6,11,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,*14,*13,12,11,10,9,8)4(16,9,8)1
|1,3,4,2,5,8,4,9,14,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2,1,0)3(10,9,8)1(11,10,9,8)2(12,11,10)1(13,12,10,9,8)3(14,*13,12,11,10,9,8)4(15,*14,*13,12,11,10,9,8)4(16,9,8)1(17,16,9,8)2(18,17,16)1(1918,16,9,8)3(20,*19,18,17,16,9,8)4(21,*20,*19,*18,17,16,9,8)4
|1,3,4,2,5,8,4,9,14,7,13,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2,1,0)3(10,*9,8,2,1,0)3
|1,3,4,2,5,8,4,9,14,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2)1
|1,3,4,2,5,8,4,9,14,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,2,1,0)2(9,8,2)1(10,9,2,1,0)3(11,*10,9,8,2,1,0)3(12,*11,*10,9,8,2,1,0)4
|1,3,4,2,5,8,4,9,14,8,17,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1
|1,3,4,2,5,8,4,9,14,8,17,26,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,8,3)1
|1,3,4,2,5,8,4,9,14,8,17,26,16,33,49,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,12,11,10)2(14,13,12)1
|1,3,4,2,5,8,4,9,14,8,17,26,16,33,49,72
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,3,2,1,0)3(9,*8,3,2,1,0)3(10,8,3)1(11,10,2,1,0)3(12,*11,10,3,2,1,0)4(13,*12,*11,10,8,3,2,1,0)5
|1,3,4,2,5,8,4,9,14,8,17,26,16,33,50
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,3,2)1
|1,3,4,2,5,8,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,3,2)1(9,8,2,1,0)3(10,*9,8,3,2,1,0)4(11,*10,*9,8,3,2,1,0)4
|1,3,4,2,5,8,5,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3
|1,3,4,2,5,8,7
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,3,2)1
|1,3,4,2,5,8,7,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,3,2)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,11,10,9)2(13,12,11)1
|1,3,4,2,5,8,7,5,7,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,3,2)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,11,10,9)2(13,12,11)1(14,13,11,10,9)3(15,*14,13,12,11,10,9)4(16,*15,*14,13,12,11,10,9)4
|1,3,4,2,5,8,7,5,7,12,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,3,2)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,11,10,9)2(13,12,11)1(14,13,11,10,9)3(15,*14,13,12,11,10,9)4(16,*15,*14,13,12,11,10,9)4(17,13,11,10,9)3(18,12,11)1
|1,3,4,2,5,8,7,5,7,12,17,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,3,2)1(10,9,2,1,0)3(11,*10,9,3,2,1,0)4(12,*11,*10,9,3,2,1,0)4
|1,3,4,2,5,8,7,5,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,8,4)1
|1,3,4,2,5,8,7,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,*8,4,3,2,1,0)4(10,3,2)1
|1,3,4,2,5,8,7,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,*8,4,3,2,1,0)4(10,9,8,4)2(11,10,9,8,4)3(12,*11,10,9,8,4)3
|1,3,4,2,5,8,7,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,*8,4,3,2,1,0)4(10,9,8,4)2(11,10,9)1
|1,3,4,2,5,8,7,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,*8,4,3,2,1,0)4(10,9,8,4)2(11,10,9)1(12,11,9,8,4)3(13,*12,11,10,9,8,4)4(14,*13,*12,11,10,9,8,4)4
|1,3,4,2,5,8,7,12,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,*8,4,3,2,1,0)4(10,9,8,4)2(11,10,9)1(12,11,9,8,4)3(13,*12,11,10,9,8,4)4(14,*13,*12,11,10,9,8,4)4(15,11,9,8,4)3(16,*15,11,10,9,8,4)4
|1,3,4,2,5,8,7,12,17,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,4,2,1,0)3(9,*8,4,3,2,1,0)4(10,*9,*8,4,3,2,1,0)4
|1,3,4,2,5,8,8
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3
|1,3,4,2,5,8,10
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(6,3,2)1
|1,3,4,2,5,8,10,5
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5
|1,3,4,2,5,8,11
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,8,2,1,0)3(12,*11,8,3,2,1,0)4(13,*12,*11,8,4,3,2,1,0)5
|1,3,4,2,5,8,11,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,8,5)1
|1,3,4,2,5,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,8,5)1(12,1,0)1(13,12,1,0)2(14,13,12)1(15,14,12,1,0)3(16,*15,14,13,12,1,0)4(17,*16,*15,14,13,12,1,0)4
|1,3,4,2,5,9,4,9,14
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,8,5)1(12,1,0)1(13,12,1,0)2(14,13,12)1(15,14,12,1,0)3(16,*15,14,13,12,1,0)4(17,*16,*15,14,13,12,1,0)4(18,15,12,1,0)3(19,*18,15,13,12,1,0)4(20,*19,*18,15,14,13,12,1,0)5
|1,3,4,2,5,9,4,9,14,19
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,8,5)1(12,1,0)1(13,12,1,0)2(14,13,12)1(15,14,12,1,0)3(16,*15,14,13,12,1,0)4(17,*16,*15,14,13,12,1,0)4(18,15,12,1,0)3(19,*18,15,13,12,1,0)4(20,*19,*18,15,14,13,12,1,0)5(21,18,15)1
|1,3,4,2,5,9,4,9,15
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,8,5)1(12,2,1,0)2(13,12,2)1
|1,3,4,2,5,9,4,9,15,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,8,5)1(12,3,2)1
|1,3,4,2,5,9,4,9,15,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4
|1,3,4,2,5,9,4,9,16
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,2,1,0)2(13,12,2)1
|1,3,4,2,5,9,4,9,16,8,17
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,2,1,0)2(13,12,2)1(14,13,2,1,0)3(15,*14,13,12,2,1,0)4(16,*15,*14,13,12,2,1,0)4(17,14,2,1,0)3(18,*17,14,12,2,1,0)4(19,*18,*17,14,13,12,2,1,0)5
|1,3,4,2,5,9,4,9,16,8,17,26
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,2,1,0)2(13,12,2)1(14,13,2,1,0)3(15,*14,13,12,2,1,0)4(16,*15,*14,13,12,2,1,0)4(17,14,2,1,0)3(18,*17,14,12,2,1,0)4(19,*18,*17,14,13,12,2,1,0)5(20,17,14)1
|1,3,4,2,5,9,4,9,16,8,17,27
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,2,1,0)2(13,12,2)1(14,13,2,1,0)3(15,*14,13,12,2,1,0)4(16,*15,*14,13,12,2,1,0)4(17,14,2,1,0)3(18,*17,14,12,2,1,0)4(19,*18,*17,14,13,12,2,1,0)5(20,*17,14,12,2,1,0)4
|1,3,4,2,5,9,4,9,16,8,17,28
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2,1,0)3(13,*12,3,2,1,0)3
|1,3,4,2,5,9,4,9,16,8,17,28,12
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2,1,0)3(13,*12,3,2,1,0)3(14,12,3)1
|1,3,4,2,5,9,4,9,16,8,17,29,16,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2,1,0)3(13,*12,3,2,1,0)3(14,12,3)1(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,12,3,2,1,0)5(18,*17,*16,*15,14,12,3,2,1,0)5
|1,3,4,2,5,9,4,9,16,8,17,29,16,33,50
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2,1,0)3(13,*12,3,2,1,0)3(14,12,3)1(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,12,3,2,1,0)5(18,*17,*16,*15,14,12,3,2,1,0)5(19,15,2,1,0)3(20,*19,15,3,2,1,0)4(21,*20,*19,15,12,3,2,1,0)5(22,*21,*20,*19,15,14,12,3,2,1,0)6
|1,3,4,2,5,9,4,9,16,8,17,29,16,33,50,67
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2,1,0)3(13,*12,3,2,1,0)3(14,12,3)1(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,12,3,2,1,0)5(18,*17,*16,*15,14,12,3,2,1,0)5(19,15,2,1,0)3(20,*19,15,3,2,1,0)4(21,*20,*19,15,12,3,2,1,0)5(22,*21,*20,*19,15,14,12,3,2,1,0)6(23,19,15)1
|1,3,4,2,5,9,4,9,16,8,17,29,16,33,51
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2,1,0)3(13,*12,3,2,1,0)3(14,12,3)1(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,12,3,2,1,0)5(18,*17,*16,*15,14,12,3,2,1,0)5(19,15,2,1,0)3(20,*19,15,3,2,1,0)4(21,*20,*19,15,12,3,2,1,0)5(22,*21,*20,*19,15,14,12,3,2,1,0)6(23,*19,15,3,2,1,0)4
|1,3,4,2,5,9,4,9,16,8,17,29,16,33,52
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2,1,0)3(13,*12,3,2,1,0)3(14,12,3)1(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,12,3,2,1,0)5(18,*17,*16,*15,14,12,3,2,1,0)5(19,15,2,1,0)3(20,*19,15,3,2,1,0)4(21,*20,*19,15,12,3,2,1,0)5(22,*21,*20,*19,15,14,12,3,2,1,0)6(23,*19,15,3,2,1,0)4(24,12,3)1
|1,3,4,2,5,9,4,9,16,8,17,29,16,33,55,33
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2,1,0)3(13,*12,3,2,1,0)3(14,12,3)1(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,12,3,2,1,0)5(18,*17,*16,*15,14,12,3,2,1,0)5(19,15,2,1,0)3(20,*19,15,3,2,1,0)4(21,*20,*19,15,12,3,2,1,0)5(22,*21,*20,*19,15,14,12,3,2,1,0)6(23,*19,15,3,2,1,0)4(24,*10,15,3,2,1,0)4
|1,3,4,2,5,9,4,9,16,8,17,30
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2,1,0)3(13,*12,3,2,1,0)3(14,12,3)1(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,12,3,2,1,0)5(18,*17,*16,*15,14,12,3,2,1,0)5(19,15,2,1,0)3(20,*19,15,3,2,1,0)4(21,*20,*19,15,12,3,2,1,0)5(22,*21,*20,*19,15,14,12,3,2,1,0)6(23,*19,15,3,2,1,0)4(24,*10,15,3,2,1,0)4(25,12,3)1
|1,3,4,2,5,9,4,9,16,9
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2,1,0)3(13,*12,3,2,1,0)3(14,12,3)1(15,14,2,1,0)3(16,*15,14,3,2,1,0)4(17,*16,*15,14,12,3,2,1,0)5(18,*17,*16,*15,14,12,3,2,1,0)5(19,15,2,1,0)3(20,*19,15,3,2,1,0)4(21,*20,*19,15,12,3,2,1,0)5(22,*21,*20,*19,15,14,12,3,2,1,0)6(23,*19,15,3,2,1,0)4(24,*23,*19,15,12,3,2,1,0)5
|1,3,4,2,5,9,4,9,18
|-
|(1,0)1(2,1,0)1(3,2,1,0)2(4,3,2)1(5,4,2,1,0)3(6,*5,4,3,2,1,0)4(7,*6,*5,4,3,2,1,0)4(8,5,2,1,0)3(9,*8,5,3,2,1,0)4(10,*9,*8,5,4,3,2,1,0)5(11,*8,5,3,2,1,0)4(12,3,2)1
|1,3,4,3
|}

iBLP

2026-04-25T14:24:07Z

Baixie01000a7：

BHM分析Part5：ψ(I)~SRO

2026-02-27T07:02:43Z

Baixie01000a7：

本条目展示[[BHM]]分析的第五部分。使用<math>MOCF</math>进行对照

<nowiki>\begin{align}\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)=\psi(I+\psi_I(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)=\psi(I+\psi_I(1))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(4,0)=\psi(I+\psi_I(\omega))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,0)(5,1)(5,0)(6,0)(5,1)=\psi(I+\psi_I(\psi_I(0)))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)=\psi(I+\psi_I(I))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)(1,0)(2,0)(3,0)=\psi(I+\psi_{\Omega_{\psi_I(I)+1}}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)(1,0)(2,0)(3,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)=\psi(I+\psi_{\Omega_{\psi_I(I)+1}}(I))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)(1,0)(2,0)(3,0)(2,0)(3,0)=\psi(I+\Omega_{\psi_I(I)+1})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)(2,0)(2,1)=\psi(I+\Omega_{\psi_I(I)+1}^{\Omega_{\psi_I(I)+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,0)(5,1)(5,0)(6,0)(5,1)(5,0)(5,0)(6,1)(6,0)(7,0)(6,1)(4,0)(4,1)=\psi(I+\Omega_{\Omega_{\psi_I(I)+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I+\psi_I(I+1))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)=\psi(I+\psi_I(I+2))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)=\psi(I+\psi_I(I+\psi_I(0)))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)=\psi(I+\psi_I(I+\psi_I(I)))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I\times2)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I\times3)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)=\psi(I\times\omega)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)=\psi(I\times\psi_I(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I^2)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I^3)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)=\psi(I^\omega)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)=\psi(I^{\psi_I(0)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I^I)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I^{I+1})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I^{I\times2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I^{I^2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(2,0)=\psi(I^{I^\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I^{I^I})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I^{I^{I^I}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(3,0)=\psi(\psi_{\Omega_{I+1}}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(3,0)(1,0)(2,0)(3,0)=\psi(\psi_{\Omega_{I+1}}(1))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(3,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\psi_{\Omega_{I+1}}(I))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(3,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\psi_{\Omega_{I+1}}(I^2))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(3,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\psi_{\Omega_{I+1}}(I^I))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(3,0)(2,0)(2,0)(3,0)=\psi(\psi_{\Omega_{I+1}}(\psi_{\Omega_{I+1}}(0)))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(3,0)(2,0)(3,0)=\psi(\Omega_{I+1})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,1)=\psi(\Omega_{I+1}^\Omega)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)=\psi(\Omega_{I+1}^{\psi_I(0)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\Omega_{I+1}^I)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)=\psi(\Omega_{I+1}^{I}\times\omega)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\Omega_{I+1}^{I}\times\omega+\Omega_{I+1}^I)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)=\psi(\Omega_{I+1}^{I}\times\omega\times2)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)=\psi(\Omega_{I+1}^{I}\times\omega^2)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)=\psi(\Omega_{I+1}^{I}\times\omega^\omega)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)(3,0)=\psi(\Omega_{I+1}^{I}\times\psi(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)(3,1)=\psi(\Omega_{I+1}^{I}\times\Omega)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)(3,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)=\psi(\Omega_{I+1}^{I}\times\psi_I(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)(3,1)(3,0)(4,0)(3,1)=\psi(\Omega_{I+1}^{I}\times I)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,0)(3,1)(3,0)(4,0)(3,1)=\psi(\Omega_{I+1}^I\times\psi_{\Omega_{I+1}}(\Omega_{I+1}^{I}\times I))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)(3,1)(3,0)(4,0)(3,1)(2,0)(3,0)=\psi(\Omega_{I+1}^{I+1})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)=\psi(\Omega_{I+1}^{\Omega_{I+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)=\psi(\Omega_{I+1}^{\Omega_{I+1}}\times2)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(1,0)(2,0)(3,0)=\psi(\psi_{\Omega_{I+2}}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(1,1)=\psi(\Omega_{I+2}^{\Omega_{I+2}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)=\psi(\Omega_{I+\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(1,1)(1,0)(2,0)=\psi(\Omega_{I+\omega\times2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,0)=\psi(\Omega_{I+\omega^2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)=\psi(\Omega_{I+\Omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)=\psi(\Omega_{I+\Omega_\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)=\psi(\Omega_{I+\psi_I(0)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\Omega_{I\times2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\Omega_{I\times3})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)=\psi(\Omega_{I\times\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\Omega_{I^2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(3,0)=\psi(\Omega_{\psi_{\Omega_{I+1}}(0)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\Omega_{\psi_{\Omega_{I+1}}(\Omega_{I+1}^I)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\Omega_{\psi_{\Omega_{I+1}}(\Omega_{I+1}^I\times2)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)=\psi(\Omega_{\psi_{\Omega_{I+1}}(\Omega_{I+1}^I\times\omega)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(3,0)(4,0)=\psi(\Omega_{\psi_{\Omega_{I+1}}(\Omega_{I+1}^{I+1})})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)=\psi(\Omega_{\psi_{\Omega_{I+1}}(\Omega_{I+1}^{\Omega_{I+1}})})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)=\psi(\Omega_{\psi_{\Omega_{I+1}}(\Omega_{I+\omega})})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)(3,0)(4,1)=\psi(\Omega_{\psi_{\Omega_{I+1}}(\Omega_{I+\Omega})})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)(4,0)(4,0)(5,1)(5,0)(6,0)(5,1)(5,0)(5,1)(5,0)(6,0)=\psi(\Omega_{\psi_{\Omega_{I+1}}(\Omega_{\psi_{\Omega_{I+1}}(\Omega_{I+\Omega})})})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)=\psi(\Omega_{\Omega_{I+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(2,1)=\psi(\Omega_{\Omega_{I+2}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)=\psi(\Omega_{\Omega_{I+\omega}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)=\psi(\Omega_{\Omega_{I+\Omega}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)=\psi(\Omega_{\Omega_{I\times2}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(2,0)(3,0)=\psi(\Omega_{\Omega_{I\times\omega}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(2,0)(3,0)(4,0)=\psi(\Omega_{\Omega_{\psi_{\Omega_{I+1}}}(0)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)=\psi(\Omega_{\Omega_{\Omega_{I+1}}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I_2}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,1)(3,1)=\psi(\psi_{I_2}(0)+\psi_I(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\psi_{I_2}(0)+I)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)=\psi(\psi_{I_2}(0)+\Omega_{I+\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)(3,1)=\psi(\psi_{I_2}(0)\times2)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)(3,1)(1,0)(2,0)=\psi(\psi_{I_2}(0)\times\omega)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)(3,1)(1,0)(2,0)(3,0)(2,0)(3,0)=\psi(\Omega_{\psi_{I_2}(0)+1})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,1)=\psi(\Omega_{\psi_{I_2}(0)+1}^{\Omega_{\psi_{I_2}(0)+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)(3,1)=\psi(\Omega_{\psi_{I_2}(0)\times2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)(3,1)(2,0)(3,0)(4,0)=\psi(\Omega_{\psi_{\Omega_{\psi_{I_2}(0)+1}}(0)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(4,0)(4,1)(4,0)(5,0)(4,0)(5,1)(5,0)(6,0)(5,1)(5,0)(5,1)(5,0)(6,0)(5,0)(6,1)(5,1)(4,0)(4,1)=\psi(\Omega_{\Omega_{\psi_{I_2}(0)+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)=\psi(\psi_{I_2}(1))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)=\psi(\psi_{I_2}(2))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)=\psi(\psi_{I_2}(\omega))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)=\psi(\psi_{I_2}(I))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)=\psi(I_2)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)=\psi(I_2^{I_2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(3,0)=\psi(\psi_{\Omega_{I_2+1}}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)=\psi(\Omega_{I_2+1}^{\Omega_{I_2+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)=\psi(\Omega_{I_2+\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)=\psi(\Omega_{I_2+\Omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(\Omega_{I_2+I})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)=\psi(\Omega_{I_2\times2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)=\psi(\Omega_{\Omega_{I_2+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,1)(3,0)(4,0)(3,1)=\psi(\Omega_{\Omega_{\Omega_{I_2+1}}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I_3}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I_4}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)=\psi(I_\omega)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I_\omega+I)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)=\psi(I_\omega\times2)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(1,0)(2,0)=\psi(I_\omega\times\omega)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)=\psi(I_\omega^2)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)=\psi(I_\omega^{I_\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(1,0)(2,0)(3,0)=\psi(\psi_{\Omega_{I_\omega+1}}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(1,1)=\psi(\Omega_{I_{\omega}+1}^{\Omega_{I_{\omega}+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I_{\omega+1}}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)=\psi(I_{\omega\times2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,0)=\psi(I_{\omega^2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,0)(2,0)=\psi(I_{\omega^\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,0)(3,0)=\psi(I_{\psi(0)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,1)=\psi(I_{\Omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)=\psi(I_{\Omega_\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,1)(3,1)=\psi(I_{\psi_I(0)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I_I)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,1)(2,1)=\psi(I_{I_2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)=\psi(I_{I_\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)=\psi(I_{I_\Omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)=\psi(I_{I_I})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I(1,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)=\psi(\psi_{I(1,0)}(0)\times2)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(1,0)(2,0)(3,0)(2,0)(3,0)=\psi(\Omega_{\psi_{I(1,0)}(0)+1})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,1)=\psi(\Omega_{\psi_{I(1,0)}(0)+1}^{\Omega_{\psi_{I(1,0)}(0)+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,1)(2,0)(3,0)=\psi(\Omega_{\psi_{I(1,0)}(0)+\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)(4,0)(5,0)(4,1)=\psi(\Omega_{\psi_{I(1,0)}(0)\times2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)(4,0)(5,0)(4,1)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)(4,0)(5,0)(4,1)=\psi(\Omega_{\psi_{\Omega_{\psi_{I(1,0)}(0)+1}}(\Omega_{\psi_{I(1,0)}(0)+1}^{\psi_{I(1,0)}(0)})})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)(4,0)(5,0)(4,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(4,0)(5,0)(4,0)(5,1)(5,0)(6,0)(5,1)(5,0)(6,0)(5,1)(3,0)(4,0)=\psi(\Omega_{\psi_{\Omega_{\psi_{I(1,0)}(0)+1}}(\Omega_{\psi_{I(1,0)}(0)+1}^{\psi_{I(1,0)}(0)+1})})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,0)(4,1)(4,0)(5,0)(4,1)(4,0)(5,0)(4,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(4,0)(5,0)(4,0)(5,1)(5,0)(6,0)(5,1)(5,0)(6,0)(5,1)(4,0)(4,1)=\psi(\Omega_{\Omega_{\psi_{I(1,0)}(0)+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,1)(2,0)(3,0)(2,1)=\psi(\psi_{I_{\psi_{I(1,0)}(0)+1}}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)=\psi(I_{\psi_{I(1,0)}(0)+\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(2,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)=\psi(I_{\psi_{I(1,0)}(0)\times2})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(2,0)(3,0)=\psi(I_{\psi_{I(1,0)}(0)\times\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(2,0)(3,1)(3,0)(4,0)(3,1)=\psi(I_{\psi_{\Omega_{\psi_{I(1,0)}(0)+1}}(\Omega_{\psi_{I(1,0)}(0)+1}^{I})})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(4,0)(5,0)(4,0)(5,1)(5,0)(6,0)(5,1)(5,0)(6,0)(5,1)(4,0)(4,1)=\psi(I_{\Omega_{\psi_{I(1,0)}(0)+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)(3,0)(3,0)(4,1)(4,0)(5,0)(4,1)(4,0)(5,0)(4,0)(5,1)(5,0)(6,0)(5,1)(5,0)(6,0)(5,1)(4,0)(4,1)(4,0)(5,0)(4,1)=\psi(I_{I_{\psi_{I(1,0)}(0)+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)=\psi(\psi_{I(1,0)}(1))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)=\psi(\psi_{I(1,0)}(2))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)=\psi(\psi_{I(1,0)}(\omega))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,0)(3,1)(3,0)(4,0)(3,1)(3,0)(4,0)(3,1)=\psi(\psi_{I(1,0)}(\psi_{I(1,0)}(0)))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)=\psi(I(1,0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)=\psi(I(1,0)^2)\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)=\psi(I(1,0)^{\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)=\psi(I(1,0)^{I(1,0)})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)(1,0)(2,0)(3,0)(2,0)(3,0)=\psi(\Omega_{I(1,0)+1})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)=\psi(\Omega_{I(1,0)+1}^{\Omega_{I(1,0)+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)=\psi(\Omega_{I(1,0)+\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I_{I(1,0)+1}}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I_{I(1,0)+2}}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)=\psi(I_{I(1,0)+\omega})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I_{I(1,0)+I})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)(2,0)(2,1)(2,0)(3,0)(2,1)=\psi(I_{I_{I(1,0)+1}})\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I(1,1)}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I(1,2)}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)=\psi(I(1,\omega))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I(2,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I(3,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)=\psi(I(\omega,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(1,1)=\psi(\Omega_{I(\omega,0)+1}^{\Omega_{I(1,0)+1}})\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I_{I(\omega,0)+1}}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I(1,I(\omega,0)+1)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(1,1)(1,0)(2,0)(2,0)=\psi(I(\omega,1))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(1,1)(1,0)(2,0)(2,0)(1,0)(1,1)(1,0)(2,0)(2,0)=\psi(I(\omega,2))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)=\psi(I(\omega,\omega))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(1,1)=\psi(\psi_{I(\omega+1,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(2,0)=\psi(I(\omega,I(\omega+1,0)+1))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(1,1)=\psi(\psi_{I(\omega+1,1)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(1,1)(1,0)(2,0)=\psi(I(\omega+1,\omega))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I(\omega+2,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(1,1)(1,0)(2,0)(2,0)=\psi(I(\omega\times2,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(1,1)(1,0)(2,0)(2,0)=\psi(I(\omega\times3,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)=\psi(I(\omega^2,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)(1,0)(1,1)(1,0)(2,0)(2,0)=\psi(I(\omega^2+\omega,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)(1,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)=\psi(I(\omega^2\times2,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)(1,0)(2,0)=\psi(I(\omega^3,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)(1,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)(1,0)(2,0)=\psi(I(\omega^3\times2,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)=\psi(I(\omega^4,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)(2,0)=\psi(I(\omega^\omega,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)(2,0)(2,0)=\psi(I(\omega^{\omega^\omega},0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,0)(3,0)=\psi(I(\psi(0),0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,1)=\psi(I(\Omega,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)=\psi(I(\Omega_\omega,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I(I,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)(2,0)(3,0)(2,1)=\psi(I(I(1,0),0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(3,0)=\psi(I(I(\omega,0),0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(3,0)(2,0)(3,1)(3,0)(4,0)(4,0)=\psi(I(I(I(\omega,0),0),0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(1,0,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(1,0)(2,1)(2,0)(3,0)(3,0)(2,1)=\psi(\psi_{I(1,0,0)}(1))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(1,1)=\psi(\Omega_{I(1,0,0)+1}^{\Omega_{I(1,0,0)+1}})\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)=\psi(\Omega_{I(1,0,0)+\omega})\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I_{I(1,0,0)+1}}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(2,0)=\psi(I(\omega,I(1,0,0)+1))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(2,0)(1,1)=\psi(I(1,0,1))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)=\psi(I(1,0,\omega))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I(1,1,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(2,0)=\psi(I(1,\omega,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(2,0,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(3,0,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)=\psi(I(\omega,0,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(1,0,0,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)=\psi(\Omega_{I(1,0,0,0)+\omega})\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I_{I(1,0,0,0)+1}}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(1,0,I(1,0,0,0)+1)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(2,0,I(1,0,0,0)+1)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(1,0,0,1)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(1,1)=\psi(\psi_{I(1,0,1,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(1,1,0,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(2,0,0,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)=\psi(I(\omega,0,0,0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)(1,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(1,0,0,0,0)}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(2,0)=\psi(I(1@\omega))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(2,1)=\psi(I(1@I))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(2,0)(1,0)(2,1)(2,0)(3,0)(3,0)(3,0)=\psi(I(1@I(1@\omega)))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(1@(1,0))}(0))\\&(0,0)(1,1)(1,0)(2,0)(2,0)(2,0)(2,0)(1,1)=\psi(\psi_{I(1@(1@(1,0)))}(0))\\&(0,0)(1,1)(1,0)(2,0)(3,0)=\psi(\psi_{\Omega_{M+1}}(0))\end{align}</nowiki>
[[分类:分析]]

DEN

2026-02-25T15:49:43Z

Baixie01000a7：已将重定向目标从iblp更改为iBLP

#REDIRECT [[iBLP]]

Googolism - Part 6

2026-02-25T15:23:31Z

Baixie01000a7：

【[[Googolism - Part 5|更小]] | [[Googolism|主页]] | 更大】

== Binary phi level ==

=== Part 6.1: <math>f_{\zeta_0}^2(10)</math> ~ <math>f_{\varepsilon_{\zeta_0+1}}^2(10)</math> ===

* Grand tethracross, E100#^^##100#2
* Grand Berlin Wall, E100#^^##100,000,000#2
* '''Fish number 6''', <math>\approx f_{\zeta_0+1}(63)</math>
* Grangol-carta-tethracross, E100#^^##100#100
* Godgahlah-carta-tethracross, E100#^^##100#^#100
* Tethrathoth-carta-tethracross, E100#^^##100#^^#100
* Tethriterator-carta-tethracross, E100#^^##100#^^#>#100
* Tethracross-by-deuteron, E100#^^##100#^^##100
* Tethracross-by-triton, E100#^^##100#^^##100#^^##100
* Tethracross-by-teterton, E100#^^##*#5
* Tethracross-by-pepton, E100#^^##*#6
* Tethracross-by-exton, E100#^^##*#7
* Tethracross-by-epton, E100#^^##*#8
* Tethracross-by-ogdon, E100#^^##*#9
* Tethracross-by-enton, E100#^^##*#10
* Tethracross-by-dekaton, E100#^^##*#11
* Deutero-tethrinoocross, {100,100[1\1\2]1[1\1\2]2}
* Deutero-tethracross, E100#^^##*#^^##100
* Trito-tethracross, E100#^^##*#^^##*#^^##100
* Teterto-tethracross, E100#^^##*#^^##*#^^##*#^^##100
* Pepto-tethracross, E100(#^^##)^#5
* Exto-tethracross, E100(#^^##)^#6
* Epto-tethracross, E100(#^^##)^#7
* Ogdo-tethracross, E100(#^^##)^#8
* Ento-tethracross, E100(#^^##)^#9
* Dekato-tethracross, E100(#^^##)^#10
* Isosto-tethracross, E100(#^^##)^#20
* Trianto-tethracross, E100(#^^##)^#30
* Saranto-tethracross, E100(#^^##)^#40
* Peninto-tethracross, E100(#^^##)^#50
* Exinto-tethracross, E100(#^^##)^#60
* Ebdominto-tethracross, E100(#^^##)^#70
* Ogdonto-tethracross, E100(#^^##)^#80
* Eneninto-tethracross, E100(#^^##)^#90
* Tethrinoocruxifact, {100,100[2\1\2]2}
* Tethracruxifact / hecato-tethracross, E100(#^^##)^#100
* Grideutertethrinoocross, {100,100[3\1\2]2}
* Grideutertethracross, E100(#^^##)^##100
* Kubicutethracross, E100(#^^##)^###100
* Quarticutethracross, E100(#^^##)^####100
* Quinticutethracross, E100(#^^##)^#^#5
* Sexticutethracross, E100(#^^##)^#^#6
* Septicutethracross, E100(#^^##)^#^#7
* Octicutethracross, E100(#^^##)^#^#8
* Nonicutethracross, E100(#^^##)^#^#9
* Decicutethracross, E100(#^^##)^#^#10
* Centicutethracross / Tethracruxigodgathor, E100(#^^##)^#^#100
* Tethracross-ad-gridgahlahium, E100(#^^##)^#^##100
* Tethracross-ad-kubikahlahium, E100(#^^##)^#^###100
* Tethracross-ad-quarticahlahium, E100(#^^##)^#^####100
* Tethracross-ad-godgathorium, E100(#^^##)^#^#^#100
* Tethracross-ad-godtotholium, E100(#^^##)^#^#^#^#100
* Tethracross-ad-godtertolium, E100(#^^##)^#^#^#^#^#100
* Tethracross-ad-godtopolium, E100(#^^##)^#^^#6
* Tethracross-ad-godhathorium, E100(#^^##)^#^^#7
* Tethracross-ad-godheptolium, E100(#^^##)^#^^#8
* Tethracross-ad-godoctolium, E100(#^^##)^#^^#9
* Tethracross-ad-godentolium, E100(#^^##)^#^^#10
* Tethracross-ad-goddekatholium, E100(#^^##)^#^^#11
* Tethracross-ad-tethrathothium / Tethracruxitethrathoth, E100(#^^##)^#^^#100
* Tethracross-ad-Monster-Giantium, E100(#^^##)^(#^^#)^(#^^#)^#100
* Tethracross-ad-terrible-tethrathothium, E100(#^^##)^(#^^#)^^#100
* Tethracross-ad-terrible-terrible-tethrathothium, E100(#^^##)^((#^^#)^^#)^^#100
* Tethracross-ad-tethriteratorium, E100(#^^##)^#^^#>#100
* Tethracross-ad-tethriditeratorium, E100(#^^##)^#^^#>(#+#)100
* Tethracross-ad-tethraspatialatorium, E100(#^^##)^#^^#>#^#100
* Tethracross-ad-dustaculated-tethrathothium, E100(#^^##)^#^^#>#^^#100
* Tethracross-ad-tristaculated-tethrathothium, E100(#^^##)^#^^#>#^^#>#^^#100
* Tethracross-ad-tetrastaculated-tethrathothium, E100(#^^##)^#^^#>#^^#>#^^#>#^^#100
* Tethracross-ad-pentastaculated-tethrathothium, E100(#^^##)^#^^##5
* Tethracross-ad-hexastaculated-tethrathothium, E100(#^^##)^#^^##6
* Tethracross-ad-heptastaculated-tethrathothium, E100(#^^##)^#^^##7
* Tethracross-ad-octastaculated-tethrathothium, E100(#^^##)^#^^##8
* Tethracross-ad-ennastaculated-tethrathothium, E100(#^^##)^#^^##9
* Tethracross-ad-dekastaculated-tethrathothium, E100(#^^##)^#^^##10
* Dutetrated-tethracross, E100(#^^##)^(#^^##)100
* Tritetrated-tethracross, E100(#^^##)^(#^^##)^(#^^##)100
* Quadratetrated-tethracross, E100(#^^##)^(#^^##)^(#^^##)^(#^^##)100
* Quinquatetrated-tethracross, E100(#^^##)^^#5
* Sexatetrated-tethracross, E100(#^^##)^^#6
* Septatetrated-tethracross, E100(#^^##)^^#7
* Octatetrated-tethracross, E100(#^^##)^^#8
* Nonatetrated-tethracross, E100(#^^##)^^#9
* Decatetrated-tethracross, E100(#^^##)^^#10
* Terrible tethracross, E100(#^^##)^^#100

=== Part 6.2: <math>f_{\varepsilon_{\zeta_0+1}}^2(10)</math> ~ <math>f_{\zeta_1}^2(10)</math> ===

* Dutetrated-terrible-tethracross, E100((#^^##)^^#)^((#^^##)^^#)100
* Terrible terrible tethracross, E100((#^^##)^^#)^^#100
* Terrible terrible terrible tethracross, E100(((#^^##)^^#)^^#)^^#100
* Quadruple-terrible tethracross, E100((((#^^##)^^#)^^#)^^#)^^#100
* Quintuple-terrible tethracross, E100(#^^##)^^#>#5
* Tethriterated-tethracross / hundred-ex-terrible tethracross, E100(#^^##)^^#>#100
* Hundred-ex-terrible territethracross, E100(#^^##)^^#>#101
* Tethrathoth-ex-terrible tethracross, E100(#^^##)^^#>#(E100#^^#100)
* Tethracross-ex-terrible tethracross, E100(#^^##)^^#>#(E100#^^##100)
* Grand tethriterated-tethracross, E100(#^^##)^^#>#100#2
* Deutero-tethriterated-tethracross, E100(#^^##)^^#>#*(#^^##)^^#>#100
* Dutetrated-tethriterated-tethracross, E100((#^^##)^^#>#)^((#^^##)^^#>#)100
* Tethriditerated-tethracross, E100(#^^##)^^#>(#+#)100
* Tethritriterated-tethracross, E100(#^^##)^^#>(#+#+#)100
* Tethriquaditerated-tethracross, E100(#^^##)^^#>(#+#+#+#)100
* Tethriquiditerated-tethracross, E100(#^^##)^^#>##5
* Tethrisiditerated-tethracross, E100(#^^##)^^#>##6
* Tethrisepiterated-tethracross, E100(#^^##)^^#>##7
* Tethri-ogditerated-tethracross, E100(#^^##)^^#>##8
* Tethri-noniterated-tethracross, E100(#^^##)^^#>##9
* Tethri-deciterated-tethracross, E100(#^^##)^^#>##10
* Tethrigriditerated-tethracross, E100(#^^##)^^#>##100
* Tethricubiculated-tethracross, E100(#^^##)^^#>###100
* Tethriquarticulated-tethracross, E100(#^^##)^^#>####100
* Tethriquinticulated-tethracross, E100(#^^##)^^#>#^#5
* Tethrisexticulated-tethracross, E100(#^^##)^^#>#^#6
* Tethrisepticulated-tethracross, E100(#^^##)^^#>#^#7
* Tethri-octiculated-tethracross, E100(#^^##)^^#>#^#8
* Tethrinoniculated-tethracross, E100(#^^##)^^#>#^#9
* Tethrideciculated-tethracross, E100(#^^##)^^#>#^#10
* Tethrispatialated-tethracross, E100(#^^##)^^#>#^#100
* Tethrispatial-squarediterated-tethracross, E100(#^^##)^^#>(#^#*#^#)100
* Tethrideuterspatialated-tethracross, E100(#^^##)^^#>#^##100
* Tethritritospatialated-tethracross, E100(#^^##)^^#>#^###100
* Tethritetertospatialated-tethracross, E100(#^^##)^^#>#^####100
* Tethripeptospatialated-tethracross, E100(#^^##)^^#>#^#^#5
* Tethriextospatialated-tethracross, E100(#^^##)^^#>#^#^#6
* Tethrieptospatialated-tethracross, E100(#^^##)^^#>#^#^#7
* Tethriogdospatialated-tethracross, E100(#^^##)^^#>#^#^#8
* Tethrientospatialated-tethracross, E100(#^^##)^^#>#^#^#9
* Tethridekatospatialated-tethracross, E100(#^^##)^^#>#^#^#10
* Tethrisuperspatialated-tethracross, E100(#^^##)^^#>#^#^#100
* Gralgathor-turreted-tethritertethracross, E100(#^^##)^^#>#^#^##100
* Tethriquadratetratediterated-tethracross, E100(#^^##)^^#>#^#^#^#100
* Tethriquintatetratediterated-tethracross, E100(#^^##)^^#>#^^#5
* Tethrisextatetratediterated-tethracross, E100(#^^##)^^#>#^^#6
* Tethriseptatetratediterated-tethracross, E100(#^^##)^^#>#^^#7
* Tethrioctatetratediterated-tethracross, E100(#^^##)^^#>#^^#8
* Tethrinonatetratediterated-tethracross, E100(#^^##)^^#>#^^#9
* Tethridecatetratediterated-tethracross, E100(#^^##)^^#>#^^#10
* Tethrastaculated-tethritertethracross / tethricentatetratediterated-tethracross, E100(#^^##)^^#>#^^#100
* Territethrastaculated-tethritertethracross, E100(#^^##)^^#>(#^^#)^^#100
* Tethriterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>#100
* Tethriditerstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>(#+#)100
* Tethritriterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>(#+#+#)100
* Tethriquaditerstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>(#+#+#+#)100
* Tethrigriditerstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>##100
* Tethricubiterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>###100
* Tethriquartiterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>####100
* Tethrispatialiterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>#^#100
* Tethrisuperspatialiterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>#^#^#100
* Tethriquadratetratediterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>#^^#4
* Tethriquintatetratediterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>#^^#5
* Tethrisextatetratediterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>#^^#6
* Tethriseptatetratediterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>#^^#7
* Tethrioctatetratediterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>#^^#8
* Tethrinonatetratediterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>#^^#9
* Tethridecatetratediterstaculated-tethritertethracross, E100(#^^##)^^#>#^^#>#^^#10
* Dustaculated-tethraturreted-tethritertethracross, E100(#^^##)^^#>#^^#>#^^#100
* Tristaculated-tethraturreted-tethritertethracross, E100(#^^##)^^#>#^^#>#^^#>#^^#100
* Tetrastaculated-tethraturreted-tethritertethracross, E100(#^^##)^^#>#^^##4
* Pentastaculated-tethraturreted-tethritertethracross, E100(#^^##)^^#>#^^##5
* Sexastaculated-tethraturreted-tethritertethracross, E100(#^^##)^^#>#^^##6
* Septastaculated-tethraturreted-tethritertethracross, E100(#^^##)^^#>#^^##7
* Octastaculated-tethraturreted-tethritertethracross, E100(#^^##)^^#>#^^##8
* Ennastaculated-tethraturreted-tethritertethracross, E100(#^^##)^^#>#^^##9
* Dekastaculated-tethraturreted-tethritertethracross, E100(#^^##)^^#>#^^##10
* Tethracrossturreted-tethritertethracross, E100(#^^##)^^#>#^^##100
* Deutero tethracross-turreted-tethritertethracross, E100(#^^##)^^#>#^^##*(#^^##)^^#>#^^##100
* Trito tethracross-turreted-tethritertethracross, E100((#^^##)^^#>#^^##)^#3
* Teterto tethracross-turreted-tethritertethracross, E100((#^^##)^^#>#^^##)^#4
* Dutetrated tethracross-turreted-tethritertethracross, E100((#^^##)^^#>#^^##)^((#^^##)^^#>#^^##)100
* Tritetrated tethracross-turreted-tethritertethracross, E100((#^^##)^^#>#^^##)^^#3
* Tethracruxifact-turreted-tethritertethracross, E100(#^^##)^^#>(#^^##)^#100
* Tethracruxitethrathoth-turreted-tethritertethracross, E100(#^^##)^^#>(#^^##)^(#^^#)100
* Dutetrated-tethracross-turreted-tethritertethracross, E100(#^^##)^^#>(#^^##)^(#^^##)100
* Dustaculated-tethritertethracross / territethracrossturreted-tethritertethracross / tethritertethracrossturreted-tethritertethracross, E100(#^^##)^^#>(#^^##)^^#100
* Tethriterated-tethracross-turreted-tethritertethracross, E100(#^^##)^^#>(#^^##)^^#>#100
* Tethracross-turreted-dustaculated-tethritertethracross, E100(#^^##)^^#>(#^^##)^^#>#^^##100
* Tristaculated-tethritertethracross, E100(#^^##)^^#>(#^^##)^^#>(#^^##)^^#100
* Tetrastaculated-tethritertethracross, E100(#^^##)^^##4
* Pentastaculated-tethritertethracross, E100(#^^##)^^##5
* Hexastaculated-tethritertethracross, E100(#^^##)^^##6
* Heptastaculated-tethritertethracross, E100(#^^##)^^##7
* Ogdastaculated-tethritertethracross, E100(#^^##)^^##8
* Ennastaculated-tethritertethracross, E100(#^^##)^^##9
* Dekastaculated-tethritertethracross, E100(#^^##)^^##10
* Secundotethrated-tethrinoocross, {100,100[1\1\3]2}
* Secundotethrated-tethracross, E100(#^^##)^^##100

=== Part 6.3: <math>f_{\zeta_1}^2(10)</math> ~ <math>f_{\eta_0}^2(10)</math> ===

* Deutero-secundotethrated-tethracross, E100(#^^##)^^##*(#^^##)^^##100
* Dutetrated-secundotethrated-tethracross, E100((#^^##)^^##)^((#^^##)^^##)100
* Terrible secundotethrated-tethracross, E100((#^^##)^^##)^^#100
* Tethriterated-secundotethrated-tethracross, E100((#^^##)^^##)^^#>#100
* Tethrispatialated-secundotethrated-tethracross, E100((#^^##)^^##)^^#>#^#100
* Tethracross-turreted-secundotethrated-tethracross, E100((#^^##)^^##)^^#>#^^##100
* Tethraducross-turreted-secundotethrated-tethracross, E100((#^^##)^^##)^^#>(#^^##)^^##100
* Dustaculated-secundotethrated-tethracross, E100((#^^##)^^##)^^#>((#^^##)^^##)^^#100
* Tristaculated-secundotethrated-tethracross, E100((#^^##)^^##)^^##3
* Quadrastaculated-secundotethrated-tethracross, E100((#^^##)^^##)^^##4
* Quinquastaculated-secundotethrated-tethracross, E100((#^^##)^^##)^^##5
* Sexastaculated-secundotethrated-tethracross, E100((#^^##)^^##)^^##6
* Septastaculated-secundotethrated-tethracross, E100((#^^##)^^##)^^##7
* Ogdastaculated-secundotethrated-tethracross, E100((#^^##)^^##)^^##8
* Ennastaculated-secundotethrated-tethracross, E100((#^^##)^^##)^^##9
* Dekastaculated-secundotethrated-tethracross, E100((#^^##)^^##)^^##10
* Thrice-tethrinoosecunda, {100,100[1\1\4]2}
* Thrice-tethrasecunda, E100((#^^##)^^##)^^##100
* Terrible thrice-tethrasecunda, E100(((#^^##)^^##)^^##)^^#100
* Tethriterated-thrice-tethrasecunda, E100(((#^^##)^^##)^^##)^^#>#100
* Dustaculated-thrice-territethrasecunda, E100(((#^^##)^^##)^^##)^^#>(((#^^##)^^##)^^##)^^#100
* Quatrice-tethrasecunda, E100(((#^^##)^^##)^^##)^^##100
* Quincice-tethrinoosecunda, {100,100[1\1\6]2}
* Quincice-tethrasecunda, E100#^^##>#5
* Sextice-tethrasecunda, E100#^^##>#6
* Septice-tethrasecunda, E100#^^##>#7
* Octice-tethrasecunda, E100#^^##>#8
* Nonice-tethrasecunda, E100#^^##>#9
* Decice-tethrasecunda, E100#^^##>#10
* Tethrinootercross, {100,100[1\1\1,2]2}
* Tethritercross / tethrasquared-iterator, E100#^^##>#100
* Tethrinooditercross, {100,100[1\1\1,3]2}
* Terrible tethritercross, E100(#^^##>#)^^#100
* Tethriterated-tethritercross, E100(#^^##>#)^^#>#100
* Terrisquared tethritercross, E100(#^^##>#)^^##100
* Tethriditercross, E100#^^##>(#+#)100
* Tethritritercross, E100#^^##>(#+#+#)100
* Tethriquaditercross, E100#^^##>(#+#+#+#)100
* Tethriquiditercross, E100#^^##>##5
* Tethrisiditercross, E100#^^##>##6
* Tethrisepitercross, E100#^^##>##7
* Tethri-ogditercross, E100#^^##>##8
* Tethrinonitercross, E100#^^##>##9
* Tethridecitercross, E100#^^##>##10
* Tethrigriditercross / tethrasquared-griditerator, E100#^^##>##100
* Tethricubiculcross / tethrasquared-cubiculator, E100#^^##>###100
* Tethriquarticulcross, E100#^^##>####100
* Tethriquinticulcross, E100#^^##>#^#5
* Tethrisexticulcross, E100#^^##>#^#6
* Tethrisepticulcross, E100#^^##>#^#7
* Tethri-octiculcross, E100#^^##>#^#8
* Tethrinoniculcross, E100#^^##>#^#9
* Tethrideciculcross, E100#^^##>#^#10
* Tethrispatialcross / tethrasquared-spatialator, E100#^^##>#^#100
* Tethrisuperspatialcross, E100#^^##>#^#^#100
* Tethritrimensionalcross, E100#^^##>#^#^#^#100
* Tethriquadramensionalcross, E100#^^##>#^^#5
* Tethriquintamensionalcross, E100#^^##>#^^#6
* Tethrisexamensionalcross, E100#^^##>#^^#7
* Tethrseptamensionalcross, E100#^^##>#^^#8
* Tethri-octamensionalcross, E100#^^##>#^^#9
* Tethrinonamensionalcross, E100#^^##>#^^#10
* Tethraidecamensionalcross, E100#^^##>#^^#11
* Tethraturreted-tethracross, E100#^^##>#^^#100
* Dustacutethraturreted-tethracross, E100#^^##>#^^#>#^^#100
* Tristacutethraturreted-tethracross, E100#^^##>#^^#>#^^#>#^^#100
* Tetrastacutethraturreted-tethracross, E100#^^##>#^^##4
* Pentastacutethraturreted-tethracross, E100#^^##>#^^##5
* Hexastacutethraturreted-tethracross, E100#^^##>#^^##6
* Heptastacutethraturreted-tethracross, E100#^^##>#^^##7
* Ogdastacutethraturreted-tethracross, E100#^^##>#^^##8
* Ennastacutethraturreted-tethracross, E100#^^##>#^^##9
* Uninzet, <math>f_{\zeta_{\zeta_0}}(10)</math>
* Dekastacutethraturreted-tethracross, E100#^^##>#^^##10
* Dustaculated-tethracross, E100#^^##>#^^##100
* Terrible dustaculated-tethracross, E100(#^^##>#^^##)^^#100
* Tethriterated dustaculated-tethracross, E100(#^^##>#^^##)^^#>#100
* Terrisecunded dustaculated-tethracross / Terrisquared dustaculated-tethracross, E100(#^^##>#^^##)^^##100
* Double terrisecunded dustaculated-tethracross / Terrisquared terrisquared dustaculated-tethracross, E100((#^^##>#^^##)^^##)^^##100
* Hundred-ex-terrisecunded dustaculated-tethracross / Terrisquarediter-dustaculated-tethracross, E100#^^##>(#^^##+#)100
* Tethracross-by-deuteron-turreted-tethracross, E100#^^##>(#^^##+#^^##)100
* Tethracross-by-gugold-turreted-tethracross, E100#^^##>(#^^##*#)100
* Deutertethracross-turreted-tethracross, E100#^^##>(#^^##*#^^##)100
* Tethracruxifact-turreted-tethracross, E100#^^##>(#^^##)^#100
* Grideutertethracross-turreted-tethracross, E100#^^##>(#^^##)^##100
* Tethracruxigodgathor-turreted-tethracross, E100#^^##>(#^^##)^#^#100
* Terrible-tethracross-turreted-tethracross, E100#^^##>(#^^##)^^#100
* Secundotethrated-tethracross-turreted-tethracross, E100#^^##>(#^^##)^^##100
* Thrice-tethrasecunda-turreted-tethracross, E100#^^##>((#^^##)^^##)^^##100
* Quatrice-tethrasecunda-turreted-tethracross, E100#^^##>(((#^^##)^^##)^^##)^^##100
* Tethritercross-turreted-tethracross, E100#^^##>#^^##>#100
* Tethriditercross-turreted-tethracross, E100#^^##>#^^##>(#+#)100
* Tethrigriditercross-turreted-tethracross, E100#^^##>#^^##>##100
* Tethrispatialcross-turreted-tethracross, E100#^^##>#^^##>#^#100
* Tethrathoth-turreted-dustaculated-tethracross, E100#^^##>#^^##>#^^#100
* Territethrathoth-turreted-dustaculated-tethracross, E100#^^##>#^^##>(#^^#)^^#100
* Tethriterturreted-dustaculated-tethracross, E100#^^##>#^^##>#^^#>#100
* Dustaculated-tethrathoth-turreted-dustaculated-tethracross, E100#^^##>#^^##>#^^#>#^^#100
* Binzet, <math>f_{\zeta_{\zeta_{\zeta_0}}}(10)</math>
* Tristaculated-tethracross, E100#^^##>#^^##>#^^##100
* Terrisquared tristaculated-tethracross, E100(#^^##>#^^##>#^^##)^^##100
* Terrisquared-dustaculated-tethracross-turreted-tethracross, E100#^^##>(#^^##>#^^##)^^##100
* Tethracruxifact-turreted-dustaculated-tethracross, E100#^^##>#^^##>(#^^##)^#100
* Territethracross-turreted-dustaculated-tethracross, E100#^^##>#^^##>(#^^##)^^#100
* Secundotethrated-tethracross-turreted-dustaculated-tethracross, E100#^^##>#^^##>(#^^##)^^##100
* Thrice-tethrasecunda-turreted-dustaculated-tethracross, E100#^^##>#^^##>((#^^##)^^##)^^##100
* Tethritercross-turreted-dustaculated-tethracross, E100#^^##>#^^##>#^^##>#100
* Trinzet, <math>f_{\zeta_{\zeta_{\zeta_{\zeta_0}}}}(10)</math>
* Tetrastaculated-tethracross, E100#^^##>#^^##>#^^##>#^^##100
* Tethritercross-turreted-tristaculated-tethracross, E100#^^##>#^^##>#^^##>#^^##>#100
* Quadrinzet, <math>f_{\eta_0[5]}(10)</math>
* Pentastaculated-tethracross, E100#^^###5
* Quintinzet, <math>f_{\eta_0[6]}(10)</math>
* Sexastaculated-tethracross, E100#^^###6
* Sextinzet, <math>f_{\eta_0[7]}(10)</math>
* Septastaculated-tethracross, E100#^^###7
* Septinzet, <math>f_{\eta_0[8]}(10)</math>
* Ogdastaculated-tethracross, E100#^^###8
* Octinzet, <math>f_{\eta_0[9]}(10)</math>
* Ennastaculated-tethracross, E100#^^###9
* Noninzet / triphi, <math>f_{\eta_0}(10)</math>
* Dekastaculated-tethracross, E100#^^###10
* Dekinzet, <math>f_{\eta_0[11]}(10)</math>
* Icosastaculated-tethracross, E100#^^###20
* Triantastaculated-tethracross, E100#^^###30
* Sarantastaculated-tethracross, E100#^^###40
* Penintastaculated-tethracross, E100#^^###50
* Exintastaculated-tethracross, E100#^^###60
* Ebdomintastaculated-tethracross, E100#^^###70
* Ogdontastaculated-tethracross, E100#^^###80
* Enenintastaculated-tethracross, E100#^^###90
* Tethrinoocubor, {100,100[1\1\1\2]2}
* Tethracubor / tethratertia, E100#^^###100
* Hektinzet, <math>f_{\eta_0[101]}(10)</math>
* Kilinzet, <math>f_{\eta_0[1001]}(10)</math>
* Meginzet, <math>f_{\eta_0[10^6+1]}(10)</math>
* Giginzet, <math>f_{\eta_0[10^9+1]}(10)</math>
* Terinzet, <math>f_{\eta_0[10^{12}+1]}(10)</math>
* Petinzet, <math>f_{\eta_0[10^{15}+1]}(10)</math>
* Exinzet, <math>f_{\eta_0[10^{18}+1]}(10)</math>
* Zettinzet, <math>f_{\eta_0[10^{21}+1]}(10)</math>
* Yottinzet, <math>f_{\eta_0[10^{24}+1]}(10)</math>

=== Part 6.4: <math>f_{\eta_0}^2(10)</math> ~ <math>f_{\varepsilon_{\eta_0+1}}^2(10)</math> ===

* Grand tethracubor, E100#^^###100#2
* Grangol-carta-tethracubor, E100#^^###100#100
* Grand grangol-carta-tethracubor, E100#^^###100#100#2
* Godgahlah-carta-tethracubor, E100#^^###100#^#100
* Tethrathoth-carta-tethracubor, E100#^^###100#^^#100
* Tethriterator-carta-tethracubor, E100#^^###100#^^#>#100
* Tethracross-carta-tethracubor, E100#^^###100#^^##100
* Tethrinoocubor-by-deuteron, {100,100[1\1\1\2]3}
* Tethracubor-by-deuteron, E100#^^###100#^^###100
* Tethracubor-by-triton, E100#^^###100#^^###100#^^###100
* Tethracubor-by-teterton, E100#^^###*#5
* Tethracubor-by-pepton, E100#^^###*#6
* Tethracubor-by-exton, E100#^^###*#7
* Tethracubor-by-epton, E100#^^###*#8
* Tethracubor-by-ogdon, E100#^^###*#9
* Tethracubor-by-enton, E100#^^###*#10
* Tethracubor-by-dekaton, E100#^^###*#11
* Tethrinoocuborgugold, {100,100[1\1\1\2]100}
* Tethracubor-by-hyperion, E100#^^###*#100
* Tethracubor-by-hecaton, E100#^^###*#101
* Tethracubor-by-deutero-hyperion, E100#^^###*##100
* Tethracubor-by-trito-hyperion, E100#^^###*###100
* Tethracubor-by-teterto-hyperion, E100#^^###*####100
* Tethracubor-by-godgahlah, E100#^^###*#^#100
* Tethracubor-by-gridgahlah, E100#^^###*#^##100
* Tethracubor-by-godgathor, E100#^^###*#^#^#100
* Tethracubor-by-godtothol, E100#^^###*#^#^#^#100
* Tethracubor-by-tethrathoth, E100#^^###*#^^#100
* Tethracubor-by-Monster-Giant, E100#^^###*(#^^#)^(#^^#)^#100
* Tethracubor-by-terrible-tethrathoth, E100#^^###*(#^^#)^^#100
* Tethracubor-by-Behemoth-Giant, E100#^^###*(#^^#>2)^(#^^#>2)^#100
* Tethracubor-by-terrible-terrible-tethrathoth, E100#^^###*#^^#>#3
* Tethracubor-by-Trihemoth-Giant, E100#^^###*(#^^#>3)^(#^^#>3)^#100
* Tethracubor-by-tethriterator, E100#^^###*#^^#>#100
* Tethracubor-by-dustaculated-tethrathoth, E100#^^###*#^^#>#^^#100
* Tethracubor-by-tethracross, E100#^^###*#^^##100
* Tethracubor-by-tethritercross, E100#^^###*#^^##>#100
* Tethracubor-by-dustaculated-tethracross, E100#^^###*#^^##>#^^##100
* Deutero-tethracubor, E100#^^###*#^^###100
* Trito-tethracubor, E100#^^###*#^^###*#^^###100
* Teterto-tethracubor, E100#^^###*#^^###*#^^###*#^^###100
* Pepto-tethracubor, E100(#^^###)^#5
* Exto-tethracubor, E100(#^^###)^#6
* Epto-tethracubor, E100(#^^###)^#7
* Ogdo-tethracubor, E100(#^^###)^#8
* Ento-tethracubor, E100(#^^###)^#9
* Dekato-tethracubor, E100(#^^###)^#10
* Isosto-tethracubor, E100(#^^###)^#20
* Trianto-tethracubor, E100(#^^###)^#30
* Saranto-tethracubor, E100(#^^###)^#40
* Peninto-tethracubor, E100(#^^###)^#50
* Exinto-tethracubor, E100(#^^###)^#60
* Ebdominto-tethracubor, E100(#^^###)^#70
* Ogdonto-tethracubor, E100(#^^###)^#80
* Eneninto-tethracubor, E100(#^^###)^#90
* Tethracuborfact / hecato-tethracubor, E100(#^^###)^#100
* Grideutertethracubor, E100(#^^###)^##100
* Kubicutethracubor, E100(#^^###)^###100
* Quarticutethracubor, E100(#^^###)^####100
* Quinticutethracubor, E100(#^^###)^#^#5
* Sexticutethracubor, E100(#^^###)^#^#6
* Septicutethracubor, E100(#^^###)^#^#7
* Octicutethracubor, E100(#^^###)^#^#8
* Nonicutethracubor, E100(#^^###)^#^#9
* Decicutethracubor, E100(#^^###)^#^#10
* Tethracuborgodgathored, E100(#^^###)^#^#100
* Tethracuborgralgathored, E100(#^^###)^#^##100
* Tethracuborgodtotholed, E100(#^^###)^#^#^#100
* Tethracubor-isptethrathoth, E100(#^^###)^#^^#100
* Tethracubor-isptethriterator, E100(#^^###)^#^^#>#100
* Tethracubor-isptethracross, E100(#^^###)^#^^##100
* Tethracubor-isptethritercross, E100(#^^###)^#^^##>#100
* Dutetrated-tethracubor / tethracubor-isptethracubor, E100(#^^###)^(#^^###)100
* Monster-Tethracubor, E100(#^^###)^(#^^###)^#100
* Tritetrated-tethracubor, E100(#^^###)^(#^^###)^(#^^###)100
* Quadratetrated-tethracubor, E100(#^^###)^^#4
* Quinquatetrated-tethracubor, E100(#^^###)^^#5
* Sexatetrated-tethracubor, E100(#^^###)^^#6
* Septatetrated-tethracubor, E100(#^^###)^^#7
* Octatetrated-tethracubor, E100(#^^###)^^#8
* Nonatetrated-tethracubor, E100(#^^###)^^#9
* Decatetrated-tethracubor, E100(#^^###)^^#10
* Vigintatetrated-tethracubor, E100(#^^###)^^#20
* Trigintatetrated-tethracubor, E100(#^^###)^^#30
* Quadragintatetrated-tethracubor, E100(#^^###)^^#40
* Quinquagintatetrated-tethracubor, E100(#^^###)^^#50
* Sexagintatetrated-tethracubor, E100(#^^###)^^#60
* Septuagintatetrated-tethracubor, E100(#^^###)^^#70
* Octogintatetrated-tethracubor, E100(#^^###)^^#80
* Nonagintatetrated-tethracubor, E100(#^^###)^^#90
* Terrible tethracubor, E100(#^^###)^^#100

=== Part 6.5: <math>f_{\varepsilon_{\eta_0+1}}^2(10)</math> ~ <math>f_{\eta_1}^2(10)</math> ===

* Terrible terrible tethracubor, E100((#^^###)^^#)^^#100
* Tethriterated-tethracubor / hundred-ex-terrible tethracubor, E100(#^^###)^^#>#100
* Dustaculated-territethracubor, E100(#^^###)^^#>(#^^###)^^#100
* Tristaculated-territethracubor, E100(#^^###)^^#>(#^^###)^^#>(#^^###)^^#100
* Tetrastaculated-territethracubor, E100(#^^###)^^##4
* Pentastaculated-territethracubor, E100(#^^###)^^##5
* Hexastaculated-territethracubor, E100(#^^###)^^##6
* Heptastaculated-territethracubor, E100(#^^###)^^##7
* Ogdastaculated-territethracubor, E100(#^^###)^^##8
* Ennastaculated-territethracubor, E100(#^^###)^^##9
* Dekastaculated-territethracubor, E100(#^^###)^^##10
* Icosastaculated-territethracubor, E100(#^^###)^^##20
* Triantastaculated-territethracubor, E100(#^^###)^^##30
* Sarantastaculated-territethracubor, E100(#^^###)^^##40
* Penintastaculated-territethracubor, E100(#^^###)^^##50
* Exintastaculated-territethracubor, E100(#^^###)^^##60
* Ebdomintastaculated-territethracubor, E100(#^^###)^^##70
* Ogdontastaculated-territethracubor, E100(#^^###)^^##80
* Enenintastaculated-territethracubor, E100(#^^###)^^##90
* Terrisquared-tethracubor / hectastaculated-territethracubor, E100(#^^###)^^##100
* Terrible terrisquared-tethracubor, E100((#^^###)^^##)^^#100
* Territerated terrisquared-tethracubor, E100((#^^###)^^##)^^#>#100
* Double-terrisquared-tethracubor, E100((#^^###)^^##)^^##100
* Triple-terrisquared-tethracubor, E100(((#^^###)^^##)^^##)^^##100
* Quadruple-terrisquared-tethracubor, E100(#^^###)^^##>#4
* Quintuple-terrisquared-tethracubor, E100(#^^###)^^##>#5
* Sextuple-terrisquared-tethracubor, E100(#^^###)^^##>#6
* Septuple-terrisquared-tethracubor, E100(#^^###)^^##>#7
* Octuple-terrisquared-tethracubor, E100(#^^###)^^##>#8
* Nonuple-terrisquared-tethracubor, E100(#^^###)^^##>#9
* Decuple-terrisquared-tethracubor, E100(#^^###)^^##>#10
* Vigintuple-terrisquared-tethracubor, E100(#^^###)^^##>#20
* Trigintuple-terrisquared-tethracubor, E100(#^^###)^^##>#30
* Quadragintuple-terrisquared-tethracubor, E100(#^^###)^^##>#40
* Quinquagintuple-terrisquared-tethracubor, E100(#^^###)^^##>#50
* Sexagintuple-terrisquared-tethracubor, E100(#^^###)^^##>#60
* Septuagintuple-terrisquared-tethracubor, E100(#^^###)^^##>#70
* Octogintuple-terrisquared-tethracubor, E100(#^^###)^^##>#80
* Nonagintuple-terrisquared-tethracubor, E100(#^^###)^^##>#90
* Terrisquarediter-tethracubor / centuple-terrisquared-tethracubor, E100(#^^###)^^##>#100
* Dustaculated-terrisquared-tethracubor, E100(#^^###)^^##>(#^^###)^^##100
* Tristaculated-terrisquared-tethracubor, E100(#^^###)^^###3
* Tetrastaculated-terrisquared-tethracubor, E100(#^^###)^^###4
* Pentastaculated-terrisquared-tethracubor, E100(#^^###)^^###5
* Hexastaculated-terrisquared-tethracubor, E100(#^^###)^^###6
* Heptastaculated-terrisquared-tethracubor, E100(#^^###)^^###7
* Ogdastaculated-terrisquared-tethracubor, E100(#^^###)^^###8
* Ennastaculated-terrisquared-tethracubor, E100(#^^###)^^###9
* Dekastaculated-terrisquared-tethracubor, E100(#^^###)^^###10
* Icosastaculated-terrisquared-tethracubor, E100(#^^###)^^###20
* Triantastaculated-terrisquared-tethracubor, E100(#^^###)^^###30
* Sarantastaculated-terrisquared-tethracubor, E100(#^^###)^^###40
* Penintastaculated-terrisquared-tethracubor, E100(#^^###)^^###50
* Exintastaculated-terrisquared-tethracubor, E100(#^^###)^^###60
* Ebdomintastaculated-terrisquared-tethracubor, E100(#^^###)^^###70
* Ogdontastaculated-terrisquared-tethracubor, E100(#^^###)^^###80
* Enenintastaculated-terrisquared-tethracubor, E100(#^^###)^^###90
* Tethraducubor / hectastaculated-terrisquared-tethracubor, E100(#^^###)^^###100

=== Part 6.6: <math>f_{\eta_1}^2(10)</math> ~ <math>f_{\vartheta_{0}}^2(10)</math> ===

* Terrible tethraducubor, E100((#^^###)^^###)^^#100
* Terrisquared-tethraducubor, E100((#^^###)^^###)^^##100
* Tethratricubor, E100((#^^###)^^###)^^###100
* Tethratetracubor, E100(((#^^###)^^###)^^###)^^###100
* Tethrapentacubor, E100#^^###>#5
* Tethrahexacubor, E100#^^###>#6
* Tethraheptacubor, E100#^^###>#7
* Tethra-octacubor, E100#^^###>#8
* Tethra-ennacubor, E100#^^###>#9
* Tethradekacubor, E100#^^###>#10
* Tethra-endekacubor, E100#^^###>#11
* Tethra-dodekacubor, E100#^^###>#12
* Tethra-triadekacubor, E100#^^###>#13
* Tethra-tetradekacubor, E100#^^###>#14
* Tethra-pentadekacubor, E100#^^###>#15
* Tethra-hexadekacubor, E100#^^###>#16
* Tethra-heptadekacubor, E100#^^###>#17
* Tethra-octadekacubor, E100#^^###>#18
* Tethra-ennadekacubor, E100#^^###>#19
* Tethra-icosacubor, E100#^^###>#20
* Tethra-triantacubor, E100#^^###>#30
* Tethra-sarantacubor, E100#^^###>#40
* Tethra-penintacubor, E100#^^###>#50
* Tethra-exintacubor, E100#^^###>#60
* Tethra-ebdomintacubor, E100#^^###>#70
* Tethra-ogdontacubor, E100#^^###>#80
* Tethra-enenintacubor, E100#^^###>#90
* Tethritercubor / tethrahectacubor / tethracubiter, E100#^^###>#100
* Tethriditercubor, E100#^^###>(#+#)100
* Tethritritercubor, E100#^^###>(#+#+#)100
* Tethriquaditercubor, E100#^^###>(#+#+#+#)100
* Tethriquiditercubor, E100#^^###>##5
* Tethrisiditercubor, E100#^^###>##6
* Tethrisepitercubor, E100#^^###>##7
* Tethri-ogditercubor, E100#^^###>##8
* Tethrinonitercubor, E100#^^###>##9
* Tethridecitercubor, E100#^^###>##10
* Tethrivigintitercubor, E100#^^###>##20
* Tethritrigintitercubor, E100#^^###>##30
* Tethriquadragintitercubor, E100#^^###>##40
* Tethriquinquagintitercubor, E100#^^###>##50
* Tethrisexagintitercubor, E100#^^###>##60
* Tethriseptuagintitercubor, E100#^^###>##70
* Tethri-octogintitercubor, E100#^^###>##80
* Tethrinonagintitercubor, E100#^^###>##90
* Tethrigriditercubor / tethricentitercubor, E100#^^###>##100
* Tethricubiculcubor, E100#^^###>###100
* Tethriquarticulcubor, E100#^^###>####100
* Tethriquinticulcubor, E100#^^###>#^#5
* Tethrisexticulcubor, E100#^^###>#^#6
* Tethrisepticulcubor, E100#^^###>#^#7
* Tethri-octiculcubor, E100#^^###>#^#8
* Tethrinoniculcubor, E100#^^###>#^#9
* Tethrideciculcubor, E100#^^###>#^#10
* Tethriviginticulcubor, E100#^^###>#^#20
* Tethritriginticulcubor, E100#^^###>#^#30
* Tethriquadraginticulcubor, E100#^^###>#^#40
* Tethriquinquaginticulcubor, E100#^^###>#^#50
* Tethrisexaginticulcubor, E100#^^###>#^#60
* Tethriseptuaginticulcubor, E100#^^###>#^#70
* Tethri-octoginticulcubor, E100#^^###>#^#80
* Tethri-nonaginticulcubor, E100#^^###>#^#90
* Tethricenticulcubor / Tethrispatialcubor, E100#^^###>#^#100
* Gridgahlah-turreted-tethracubor / Tethrideuterspatialcubor, E100#^^###>#^##100
* Godgathor-turreted-tethracubor / Tethrisuperspatialcubor, E100#^^###>#^#^#100
* Godtothol-turreted-tethracubor, E100#^^###>#^#^#^#100
* Tethrathoth-turreted-tethracubor, E100#^^###>#^^#100
* Monster-Giant-turreted-tethracubor, E100#^^###>(#^^#)^(#^^#)^#100
* Territethrathoth-turreted-tethracubor, E100#^^###>(#^^#)^^#100
* Behemoth-Giant-turreted-tethracubor, E100#^^###>(#^^#>2)^(#^^#>2)^#100
* Territerritethrathoth-turreted-tethracubor, E100#^^###>((#^^#)^^#)^^#100
* Trihemoth-Giant-turreted-tethracubor, E100#^^###>(#^^#>3)^(#^^#>3)^#100
* Tethriterator-turreted-tethracubor, E100#^^###>#^^#>#100
* Dustacultethrathoth-turreted-tethracubor, E100#^^###>#^^#>#^^#100
* Tethracross-turreted-tethracubor, E100#^^###>#^^##100
* Tethritercross-turreted-tethracubor, E100#^^###>#^^##>#100
* Godgahlah-turreted-tethracross-turreted-tethracubor / Tethrispatialcross-turreted-tethracubor, E100#^^###>#^^##>#^#100
* Tethrathoth-turreted-tethracross-turreted-tethracubor, E100#^^###>#^^##>#^^#100
* Dustacultethracross-turreted-tethracubor, E100#^^###>#^^##>#^^##100
* Uninet, <math>f_{\eta_{\eta_0}}(10)</math>
* Dustaculated-tethracubor, E100#^^###>#^^###100
* Terricubed dustaculated-tethracubor, E100(#^^###>#^^###)^^###100
* Tethraducubor-turreted-tethracubor, E100#^^###>(#^^###)^^###100
* Tethritercubor-turreted-tethracubor, E100#^^###>#^^###>#100
* Binet, <math>f_{\eta_{\eta_{\eta_0}}}(10)</math>
* Tristaculated-tethracubor, E100#^^###>#^^###>#^^###100
* Trinet, <math>f_{\eta_{\eta_{\eta_{\eta_0}}}}(10)</math>
* Tetrastaculated-tethracubor, E100#^^###>#^^###>#^^###>#^^###100
* Quadrinet, <math>f_{\varphi(4,0)[5]}(10)</math>
* Pentastaculated-tethracubor, E100#^^####5
* Quintinet, <math>f_{\varphi(4,0)[6]}(10)</math>
* Hexastaculated-tethracubor, E100#^^####6
* Sextinet, <math>f_{\varphi(4,0)[7]}(10)</math>
* Heptastaculated-tethracubor, E100#^^####7
* Septinet, <math>f_{\varphi(4,0)[8]}(10)</math>
* Ogdastaculated-tethracubor, E100#^^####8
* Octinet, <math>f_{\varphi(4,0)[9]}(10)</math>
* Ennastaculated-tethracubor, E100#^^####9
* Noninet / quadriphi, <math>f_{\varphi(4,0)}(10)</math>
* Dekastaculated-tethracubor, E100#^^####10
* Dekinet, <math>f_{\varphi(4,0)[11]}(10)</math>
* Icosastaculated-tethracubor, E100#^^####20
* Triantastaculated-tethracubor, E100#^^####30
* Sarantastaculated-tethracubor, E100#^^####40
* Penintastaculated-tethracubor, E100#^^####50
* Exintastaculated-tethracubor, E100#^^####60
* Ebdomintastaculated-tethracubor, E100#^^####70
* Ogdontastaculated-tethracubor, E100#^^####80
* Enenintastaculated-tethracubor, E100#^^####90
* Tethrinooteron, {100,100[1\1\1\1\2]2}
* Tethrateron / tethratesseract / tethraterror, E100#^^####100
* Hektinet, <math>f_{\varphi(4,0)[101]}(10)</math>
* Kilinet, <math>f_{\varphi(4,0)[1001]}(10)</math>
* Meginet, <math>f_{\varphi(4,0)[10^6+1]}(10)</math>
* Giginet, <math>f_{\varphi(4,0)[10^9+1]}(10)</math>
* Terinet, <math>f_{\varphi(4,0)[10^{12}+1]}(10)</math>
* Petinet, <math>f_{\varphi(4,0)[10^{15}+1]}(10)</math>
* Exinet, <math>f_{\varphi(4,0)[10^{18}+1]}(10)</math>
* Zettinet, <math>f_{\varphi(4,0)[10^{21}+1]}(10)</math>
* Yottinet, <math>f_{\varphi(4,0)[10^{24}+1]}(10)</math>

=== Part 6.7: <math>f_{\vartheta_{0}}^2(10)</math> ~ <math>f_{\varepsilon_{\vartheta_{0}+1}}^2(10)</math> ===

* Grand tethrateron, E100#^^####100#2
* Grangol-carta-tethrateron, E100#^^####100#100
* Grand grangol-carta-tethrateron, E100#^^####100#100#2
* Godgahlah-carta-tethrateron, E100#^^####100#^#100
* Godgathor-carta-tethrateron, E100#^^####100#^#^#100
* Godtothol-carta-tethrateron, E100#^^####100#^#^#^#100
* Tethrathoth-carta-tethrateron, E100#^^####100#^^#100
* Monster-Giant-carta-tethrateron, E100#^^####100(#^^#)^(#^^#)^#100
* Terrible-tethrathoth-carta-tethrateron, E100#^^####100(#^^#)^^#100
* Behemoth-Giant-carta-tethrateron, E100#^^####100(#^^#>2)^(#^^#>2)^#100
* Terrible-terrible-tethrathoth-carta-tethrateron, E100#^^####100#^^#>#3
* Trihemoth-Giant-carta-tethrateron, E100#^^####100(#^^#>3)^(#^^#>3)^#100
* Tethriterator-carta-tethrateron, E100#^^####100#^^#>#100
* Dustaculated-tethrathoth-carta-tethrateron, E100#^^####100#^^#>#^^#100
* Tethracross-carta-tethrateron, E100#^^####100#^^##100
* Tethracubor-carta-tethrateron, E100#^^####100#^^###100
* Tethrateron-by-deuteron, E100#^^####100#^^####100
* Tethrateron-by-triton, E100#^^####100#^^####100#^^####100
* Tethrateron-by-teterton, E100#^^####*#5
* Tethrateron-by-pepton, E100#^^####*#6
* Tethrateron-by-exton, E100#^^####*#7
* Tethrateron-by-epton, E100#^^####*#8
* Tethrateron-by-ogdon, E100#^^####*#9
* Tethrateron-by-enton, E100#^^####*#10
* Tethrateron-by-dekaton, E100#^^####*#11
* Tethrateron-by-hyperion, E100#^^####*#100
* Tethrateron-by-godgahlah, E100#^^####*#^#100
* Tethrateron-by-godgathor, E100#^^####*#^#^#100
* Tethrateron-by-godtothol, E100#^^####*#^#^#^#100
* Tethrateron-by-tethrathoth, E100#^^####*#^^#100
* Tethrateron-by-Monster-Giant, E100#^^####*(#^^#)^(#^^#)^#100
* Tethrateron-by-terrible-tethrathoth, E100#^^####*(#^^#)^^#100
* Tethrateron-by-Behemoth-Giant, E100#^^####*(#^^#>2)^(#^^#>2)^#100
* Tethrateron-by-terrible-terrible-tethrathoth, E100#^^####*#^^#>#3
* Tethrateron-by-Trihemoth-Giant, E100#^^####*(#^^#>3)^(#^^#>3)^#100
* Tethrateron-by-tethriterator, E100#^^####*#^^#>#100
* Tethrateron-by-dustaculated-tethrathoth, E100#^^####*#^^#>#^^#100
* Tethrateron-by-tethracross, E100#^^####*#^^##100
* Tethrateron-by-tethracubor, E100#^^####*#^^###100
* Deutero-tethrateron, E100#^^####*#^^####100
* Trito-tethrateron, E100#^^####*#^^####*#^^####100
* Teterto-tethrateron, E100(#^^####)^#4
* Pepto-tethrateron, E100(#^^####)^#5
* Exto-tethrateron, E100(#^^####)^#6
* Epto-tethrateron, E100(#^^####)^#7
* Ogdo-tethrateron, E100(#^^####)^#8
* Ento-tethrateron, E100(#^^####)^#9
* Dekato-tethrateron, E100(#^^####)^#10
* Isosto-tethrateron, E100(#^^####)^#20
* Trianto-tethrateron, E100(#^^####)^#30
* Saranto-tethrateron, E100(#^^####)^#40
* Peninto-tethrateron, E100(#^^####)^#50
* Exinto-tethrateron, E100(#^^####)^#60
* Ebdominto-tethrateron, E100(#^^####)^#70
* Ogdonto-tethrateron, E100(#^^####)^#80
* Eneninto-tethrateron, E100(#^^####)^#90
* Tethrateronifact, E100(#^^####)^#100
* Grideutertethrateron, E100(#^^####)^##100
* Kubicutethrateron, E100(#^^####)^###100
* Quarticutethrateron, E100(#^^####)^####100
* Quinticutethrateron, E100(#^^####)^#^#5
* Sexticutethrateron, E100(#^^####)^#^#6
* Septicutethrateron, E100(#^^####)^#^#7
* Octicutethrateron, E100(#^^####)^#^#8
* Nonicutethrateron, E100(#^^####)^#^#9
* Decicutethrateron, E100(#^^####)^#^#10
* Tethrateron-ad-godgahlah, E100(#^^####)^#^#100
* Tethrateron-ad-godgathor, E100(#^^####)^#^#^#100
* Tethrateron-ad-godtothol, E100(#^^####)^#^#^#^#100
* Tethrateron-ad-tethrathoth, E100(#^^####)^#^^#100
* Tethrateron-ad-Monster-Giant, E100(#^^####)^(#^^#)^(#^^#)^#100
* Tethrateron-ad-terrible-tethrathoth, E100(#^^####)^(#^^#)^^#100
* Tethrateron-ad-Behemoth-Giant, E100(#^^####)^(#^^#>2)^(#^^#>2)^#100
* Tethrateron-ad-terrible-terrible-tethrathoth, E100(#^^####)^#^^#>#3
* Tethrateron-ad-Trihemoth-Giant, E100(#^^####)^(#^^#>3)^(#^^#>3)^#100
* Tethrateron-ad-tethriterator, E100(#^^####)^#^^#>#100
* Tethrateron-ad-dustaculated-tethrathoth, E100(#^^####)^#^^#>#^^#100
* Tethrateron-ad-tethracross, E100(#^^####)^#^^##100
* Tethrateron-ad-tethracubor, E100(#^^####)^#^^###100
* Dutetrated-tethrateron, E100(#^^####)^(#^^####)100
* Tritetrated-tethrateron, E100(#^^####)^(#^^####)^(#^^####)100
* Quadratetrated-tethrateron, E100(#^^####)^^#4
* Quinquatetrated-tethrateron, E100(#^^####)^^#5
* Sexatetrated-tethrateron, E100(#^^####)^^#6
* Septatetrated-tethrateron, E100(#^^####)^^#7
* Octatetrated-tethrateron, E100(#^^####)^^#8
* Nonatetrated-tethrateron, E100(#^^####)^^#9
* Decatetrated-tethrateron, E100(#^^####)^^#10
* Terrible tethrateron, E100(#^^####)^^#100

=== Part 6.8: <math>f_{\varepsilon_{\vartheta_{0}+1}}^2(10)</math> ~ <math>f_{\Pi_{0}}^2(10)</math> ===

* Terrible terrible tethrateron, E100((#^^####)^^#)^^#100
* Three-ex-terrible tethrateron, E100(#^^####)^^#>#3
* Four-ex-terrible tethrateron, E100(#^^####)^^#>#4
* Five-ex-terrible tethrateron, E100(#^^####)^^#>#5
* Six-ex-terrible tethrateron, E100(#^^####)^^#>#6
* Seven-ex-terrible tethrateron, E100(#^^####)^^#>#7
* Eight-ex-terrible tethrateron, E100(#^^####)^^#>#8
* Nine-ex-terrible tethrateron, E100(#^^####)^^#>#9
* Ten-ex-terrible tethrateron, E100(#^^####)^^#>#10
* Territerated-tethrateron, E100(#^^####)^^#>#100
* Terriditerated-tethrateron, E100(#^^####)^^#>(#+#)100
* Territriterated-tethrateron, E100(#^^####)^^#>(#+#+#)100
* Terrigriditerated-tethrateron, E100(#^^####)^^#>##100
* Terricubiculated-tethrateron, E100(#^^####)^^#>###100
* Terriquarticulated-tethrateron, E100(#^^####)^^#>####100
* Godgahlah-turreted-territethrateron, E100(#^^####)^^#>#^#100
* Godgathor-turreted-territethrateron, E100(#^^####)^^#>#^#^#100
* Godtothol-turreted-territethrateron, E100(#^^####)^^#>#^#^#^#100
* Tethrathoth-turreted-territethrateron, E100(#^^####)^^#>#^^#100
* Monster-Giant-turreted-territethrateron, E100(#^^####)^^#>(#^^#)^(#^^#)^#100
* Territethrathoth-turreted-territethrateron, E100(#^^####)^^#>(#^^#)^^#100
* Behemoth-Giant-turreted-territethrateron, E100(#^^####)^^#>(#^^#>2)^(#^^#>2)^#100
* Territerritethrathoth-turreted-territethrateron, E100(#^^####)^^#>#^^#>#3
* Trihemoth-Giant-turreted-territethrateron, E100(#^^####)^^#>(#^^#>3)^(#^^#>3)^#100
* Tethriterator-turreted-territethrateron, E100(#^^####)^^#>#^^#>#100
* Dustacultethrathoth-turreted-territethrateron, E100(#^^####)^^#>#^^#>#^^#100
* Tethracross-turreted-territethrateron, E100(#^^####)^^#>#^^##100
* Tethracubor-turreted-territethrateron, E100(#^^####)^^#>#^^###100
* Tethrateron-turreted-territethrateron, E100(#^^####)^^#>#^^####100
* Dustaculated-territethrateron, E100(#^^####)^^#>(#^^####)^^#100
* Tristaculated-territethrateron, E100(#^^####)^^##3
* Tetrastaculated-territethrateron, E100(#^^####)^^##4
* Pentastaculated-territethrateron, E100(#^^####)^^##5
* Hexastaculated-territethrateron, E100(#^^####)^^##6
* Heptastaculated-territethrateron, E100(#^^####)^^##7
* Octastaculated-territethrateron, E100(#^^####)^^##8
* Ennastaculated-territethrateron, E100(#^^####)^^##9
* Dekastaculated-territethrateron, E100(#^^####)^^##10
* Terrisquared-tethrateron, E100(#^^####)^^##100
* Terrible terrisquared-tethrateron, E100((#^^####)^^##)^^#100
* Dustaculated-terrible-terrisquared-tethrateron, E100((#^^####)^^##)^^#>((#^^####)^^##)^^#100
* Double terrisquared-tethrateron, E100((#^^####)^^##)^^##100
* Terrible double terrisquared-tethrateron, E100(((#^^####)^^##)^^##)^^#100
* Dustaculated-terrible-double-terrisquared-tethrateron, E100(((#^^####)^^##)^^##)^^##2
* Triple terrisquared-tethrateron, E100(((#^^####)^^##)^^##)^^##100
* Quadruple terrisquared-tethrateron, E100(#^^####)^^##>#4
* Quintuple terrisquared-tethrateron, E100(#^^####)^^##>#5
* Sextuple terrisquared-tethrateron, E100(#^^####)^^##>#6
* Septuple terrisquared-tethrateron, E100(#^^####)^^##>#7
* Octuple terrisquared-tethrateron, E100(#^^####)^^##>#8
* Nonuple terrisquared-tethrateron, E100(#^^####)^^##>#9
* Decuple terrisquared-tethrateron, E100(#^^####)^^##>#10
* Centuple terrisquared-tethrateron, E100(#^^####)^^##>#100
* Godgahlah-turreted-terrisquared-tethrateron, E100(#^^####)^^##>#^#100
* Godgathor-turreted-terrisquared-tethrateron, E100(#^^####)^^##>#^#^#100
* Godtothol-turreted-terrisquared-tethrateron, E100(#^^####)^^##>#^#^#^#100
* Tethrathoth-turreted-terrisquared-tethrateron, E100(#^^####)^^##>#^^#100
* Monster-Giant-turreted-terrisquared-tethrateron, E100(#^^####)^^##>(#^^#)^(#^^#)^#100
* Territethrathoth-turreted-terrisquared-tethrateron, E100(#^^####)^^##>(#^^#)^^#100
* Tethriterator-turreted-terrisquared-tethrateron, E100(#^^####)^^##>#^^#>#100
* Dustacultethrathoth-turreted-terrisquared-tethrateron, E100(#^^####)^^##>#^^#>#^^#100
* Tethracross-turreted-terrisquared-tethrateron, E100(#^^####)^^##>#^^##100
* Tethracubor-turreted-terrisquared-tethrateron, E100(#^^####)^^##>#^^###100
* Tethrateron-turreted-terrisquared-tethrateron, E100(#^^####)^^##>#^^####100
* Dustaculated-terrisquared-tethrateron, E100(#^^####)^^##>(#^^####)^^##100
* Tristaculated-terrisquared-tethrateron, E100(#^^####)^^###3
* Tetrastaculated-terrisquared-tethrateron, E100(#^^####)^^###4
* Pentastaculated-terrisquared-tethrateron, E100(#^^####)^^###5
* Hexastaculated-terrisquared-tethrateron, E100(#^^####)^^###6
* Heptastaculated-terrisquared-tethrateron, E100(#^^####)^^###7
* Octastaculated-terrisquared-tethrateron, E100(#^^####)^^###8
* Ennastaculated-terrisquared-tethrateron, E100(#^^####)^^###9
* Dekastaculated-terrisquared-tethrateron, E100(#^^####)^^###10
* Terricubed-tethrateron, E100(#^^####)^^###100
* Double terricubed-tethrateron, E100((#^^####)^^###)^^###100
* Triple terricubed-tethrateron, E100(#^^####)^^###>#3
* Quadruple terricubed-tethrateron, E100(#^^####)^^###>#4
* Quintuple terricubed-tethrateron, E100(#^^####)^^###>#5
* Sextuple terricubed-tethrateron, E100(#^^####)^^###>#6
* Septuple terricubed-tethrateron, E100(#^^####)^^###>#7
* Octuple terricubed-tethrateron, E100(#^^####)^^###>#8
* Nonuple terricubed-tethrateron, E100(#^^####)^^###>#9
* Decuple terricubed-tethrateron, E100(#^^####)^^###>#10
* Centuple terricubed-tethrateron, E100(#^^####)^^###>#100
* Godgahlah-turreted-terricubed-tethrateron, E100(#^^####)^^###>#^#100
* Godgathor-turreted-terricubed-tethrateron, E100(#^^####)^^###>#^#^#100
* Godtothol-turreted-terricubed-tethrateron, E100(#^^####)^^###>#^#^#^#100
* Tethrathoth-turreted-terricubed-tethrateron, E100(#^^####)^^###>#^^#100
* Monster-Giant-turreted-terricubed-tethrateron, E100(#^^####)^^###>(#^^#)^(#^^#)^#100
* Territethrathoth-turreted-terricubed-tethrateron, E100(#^^####)^^###>(#^^#)^^#100
* Behemoth-Giant-turreted-terricubed-tethrateron, E100(#^^####)^^###>(#^^#>2)^(#^^#>2)^#100
* Territerritethrathoth-turreted-terricubed-tethrateron, E100(#^^####)^^###>#^^#>#3
* Trihemoth-Giant-turreted-terricubed-tethrateron, E100(#^^####)^^###>(#^^#>3)^(#^^#>3)^#100
* Tethriterator-turreted-terricubed-tethrateron, E100(#^^####)^^###>#^^#>#100
* Dustacultethrathoth-turreted-terricubed-tethrateron, E100(#^^####)^^###>#^^#>#^^#100
* Tethracross-turreted-terricubed-tethrateron, E100(#^^####)^^###>#^^##100
* Tethracubor-turreted-terricubed-tethrateron, E100(#^^####)^^###>#^^###100
* Tethrateron-turreted-terricubed-tethrateron, E100(#^^####)^^###>#^^####100
* Dustaculated-terricubed-tethrateron, E100(#^^####)^^###>(#^^####)^^###100
* Tristaculated-terricubed-tethrateron, E100(#^^####)^^####3
* Tetrastaculated-terricubed-tethrateron, E100(#^^####)^^####4
* Pentastaculated-terricubed-tethrateron, E100(#^^####)^^####5
* Hexastaculated-terricubed-tethrateron, E100(#^^####)^^####6
* Heptastaculated-terricubed-tethrateron, E100(#^^####)^^####7
* Octastaculated-terricubed-tethrateron, E100(#^^####)^^####8
* Ennastaculated-terricubed-tethrateron, E100(#^^####)^^####9
* Dekastaculated-terricubed-tethrateron, E100(#^^####)^^####10
* Tethraduteron, E100(#^^####)^^####100
* Tethratriteron, E100((#^^####)^^####)^^####100
* Tethratetrateron, E100#^^####>#4
* Tethrapentateron, E100#^^####>#5
* Tethrahexateron, E100#^^####>#6
* Tethraheptateron, E100#^^####>#7
* Tethra-octateron, E100#^^####>#8
* Tethra-ennateron, E100#^^####>#9
* Tethradekateron, E100#^^####>#10
* Tethra-endekateron, E100#^^####>#11
* Tethradodekateron, E100#^^####>#12
* Tethra-icosateron, E100#^^####>#20
* Tethra-hectateron / tethriterteron, E100#^^####>#100
* Godgahlah-turreted-tethrateron, E100#^^####>#^#100
* Godgathor-turreted-tethrateron, E100#^^####>#^#^#100
* Godtothol-turreted-tethrateron, E100#^^####>#^#^#^#100
* Tethrathoth-turreted-tethrateron, E100#^^####>#^^#100
* Monster-Giant-turreted-tethrateron, E100#^^####>(#^^#)^(#^^#)^#100
* Territethrathoth-turreted-tethrateron, E100#^^####>(#^^#)^^#100
* Behemoth-Giant-turreted-tethrateron, E100#^^####>(#^^#>2)^(#^^#>2)^#100
* Territerritethrathoth-turreted-tethrateron, E100#^^####>#^^#>#3
* Trihemoth-Giant-turreted-tethrateron, E100#^^####>(#^^#>3)^(#^^#>3)^#100
* Tethriterator-turreted-tethrateron, E100#^^####>#^^#>#100
* Dustacultethrathoth-turreted-tethrateron, E100#^^####>#^^#>#^^#100
* Tethracross-turreted-tethrateron, E100#^^####>#^^##100
* Tethracubor-turreted-tethrateron, E100#^^####>#^^###100
* Dustaculated-tethrateron, E100#^^####>#^^####100
* Tristaculated-tethrateron, E100#^^####>#^^####>#^^####100
* Tetrastaculated-tethrateron, E100#^^#####4
* Pentastaculated-tethrateron, E100#^^#####5
* Hexastaculated-tethrateron, E100#^^#####6
* Heptastaculated-tethrateron, E100#^^#####7
* Octastaculated-tethrateron, E100#^^#####8
* Ennastaculated-tethrateron, E100#^^#####9
* Quintiphi, <math>f_{\varphi(5,0)}(10)</math>
* Dekastaculated-tethrateron, E100#^^#####10
* Icosastaculated-tethrateron, E100#^^#####20
* Triantastaculated-tethrateron, E100#^^#####30
* Sarantastaculated-tethrateron, E100#^^#####40
* Penintastaculated-tethrateron, E100#^^#####50
* Exintastaculated-tethrateron, E100#^^#####60
* Ebdomintastaculated-tethrateron, E100#^^#####70
* Ogdontastaculated-tethrateron, E100#^^#####80
* Enenintastaculated-tethrateron, E100#^^#####90
* Tethrinoopeton, {100,100[1\1\1\1\1\2]2}
* Tethrapeton / tethrapenteract, E100#^^#^#5

=== Part 6.9: <math>f_{\Pi_{0}}^2(10)</math> ~ <math>f_{\varepsilon_{\Pi_{0}+1}}^2(10)</math> ===

* Grand tethrapeton, E100#^^#^(5)100#2
* Grangol-carta-tethrapeton, E100#^^#^(5)100#100
* Grand grangol-carta-tethrapeton, E100#^^#^(5)100#100#2
* Godgahlah-carta-tethrapeton, E100#^^#^(5)100#^#100
* Tethrathoth-carta-tethrapeton, E100#^^#^(5)100#^^#100
* Monster-Giant-carta-tethrapeton, E100#^^#^(5)100(#^^#)^(#^^#)^#100
* Territethrathoth-carta-tethrapeton, E100#^^#^(5)100(#^^#)^^#100
* Behemoth-Giant-carta-tethrapeton, E100#^^#^(5)100(#^^#>2)^(#^^#>2)^#100
* Territerritethrathoth-carta-tethrapeton, E100#^^#^(5)100#^^#>#3
* Trihemoth-Giant-carta-tethrapeton, E100#^^#^(5)100(#^^#>3)^(#^^#>3)^#100
* Tethriterator-carta-tethrapeton, E100#^^#^(5)100#^^#>#100
* Dustacultethrathoth-carta-tethrapeton, E100#^^#^(5)100#^^#>#^^#100
* Tethracross-carta-tethrapeton, E100#^^#^(5)100#^^##100
* Tethracubor-carta-tethrapeton, E100#^^#^(5)100#^^###100
* Tethrateron-carta-tethrapeton, E100#^^#^(5)100#^^####100
* Tethrapeton-by-deuteron, E100#^^#^(5)100#^^#^(5)100
* Tethrapeton-by-triton, E100#^^#^(5)100#^^#^(5)100#^^#^(5)100
* Tethrapeton-by-teterton, E100#^^#^(5)*#5
* Tethrapeton-by-pepton, E100#^^#^(5)*#6
* Tethrapeton-by-exton, E100#^^#^(5)*#7
* Tethrapeton-by-epton, E100#^^#^(5)*#8
* Tethrapeton-by-ogdon, E100#^^#^(5)*#9
* Tethrapeton-by-enton, E100#^^#^(5)*#10
* Tethrapeton-by-dekaton, E100#^^#^(5)*#11
* Tethrapeton-by-hyperion, E100#^^#^(5)*#100
* Tethrapeton-by-godgahlah, E100#^^#^(5)*#^#100
* Tethrapeton-by-tethrathoth, E100#^^#^(5)*#^^#100
* Tethrapeton-by-Monster-Giant, E100#^^#^(5)*(#^^#)^(#^^#)^#100
* Tethrapeton-by-terrible-tethrathoth, E100#^^#^(5)*(#^^#)^^#100
* Tethrapeton-by-Behemoth-Giant, E100#^^#^(5)*(#^^#>2)^(#^^#>2)^#100
* Tethrapeton-by-terrible-terrible-tethrathoth, E100#^^#^(5)*#^^#>#3
* Tethrapeton-by-Trihemoth-Giant, E100#^^#^(5)*(#^^#>3)^(#^^#>3)^#100
* Tethrapeton-by-tethriterator, E100#^^#^(5)*#^^#>#100
* Tethrapeton-by-dustaculated-tethrathoth, E100#^^#^(5)*#^^#>#^^#100
* Tethrapeton-by-tethracross, E100#^^#^(5)*#^^##100
* Tethrapeton-by-tethracubor, E100#^^#^(5)*#^^###100
* Tethrapeton-by-tethrateron, E100#^^#^(5)*#^^####100
* Deutero-tethrapeton, E100#^^#^(5)*#^^#^(5)100
* Trito-tethrapeton, E100#^^#^(5)*#^^#^(5)*#^^#^(5)100
* Teterto-tethrapeton, E100(#^^#^5)^#4
* Pepto-tethrapeton, E100(#^^#^5)^#5
* Exto-tethrapeton, E100(#^^#^5)^#6
* Epto-tethrapeton, E100(#^^#^5)^#7
* Ogdo-tethrapeton, E100(#^^#^5)^#8
* Ento-tethrapeton, E100(#^^#^5)^#9
* Dekato-tethrapeton, E100(#^^#^5)^#10
* Isosto-tethrapeton, E100(#^^#^5)^#20
* Trianto-tethrapeton, E100(#^^#^5)^#30
* Saranto-tethrapeton, E100(#^^#^5)^#40
* Peninto-tethrapeton, E100(#^^#^5)^#50
* Exinto-tethrapeton, E100(#^^#^5)^#60
* Ebdominto-tethrapeton, E100(#^^#^5)^#70
* Ogdonto-tethrapeton, E100(#^^#^5)^#80
* Eneninto-tethrapeton, E100(#^^#^5)^#90
* Tethrapetonifact, E100(#^^#^5)^#100
* Quadratatethrapeton, E100(#^^#^5)^##100
* Kubikutethrapeton, E100(#^^#^5)^###100
* Quarticutethrapeton, E100(#^^#^5)^####100
* Quinticutethrapeton, E100(#^^#^5)^#^#5
* Sexticutethrapeton, E100(#^^#^5)^#^#6
* Septicutethrapeton, E100(#^^#^5)^#^#7
* Octicutethrapeton, E100(#^^#^5)^#^#8
* Nonicutethrapeton, E100(#^^#^5)^#^#9
* Decicutethrapeton, E100(#^^#^5)^#^#10
* Tethrapeton-ipso-godgahlah, E100(#^^#^5)^#^#100
* Tethrapeton-ipso-tethrathoth, E100(#^^#^5)^#^^#100
* Tethrapeton-ipso-Monster-Giant, E100(#^^#^5)^(#^^#)^(#^^#)^#100
* Tethrapeton-ipso-terrible-tethrathoth, E100(#^^#^5)^(#^^#)^^#100
* Tethrapeton-ipso-Behemoth-Giant, E100(#^^#^5)^(#^^#>2)^(#^^#>2)^#100
* Tethrapeton-ipso-terrible-terrible-tethrathoth, E100(#^^#^5)^#^^#>#3
* Tethrapeton-ipso-Trihemoth-Giant, E100(#^^#^5)^(#^^#>3)^(#^^#>3)^#100
* Tethrapeton-ipso-tethriterator, E100(#^^#^5)^#^^#>#100
* Tethrapeton-ipso-dustaculated-tethrathoth, E100(#^^#^5)^#^^#>#^^#100
* Tethrapeton-ipso-tethracross, E100(#^^#^5)^#^^##100
* Tethrapeton-ipso-tethracubor, E100(#^^#^5)^#^^###100
* Tethrapeton-ipso-tethrateron, E100(#^^#^5)^#^^####100
* Dutetrated-tethrapeton, E100(#^^#^5)^(#^^#^5)100
* Tritetrated-tethrapeton, E100(#^^#^5)^(#^^#^5)^(#^^#^5)100
* Quadratetrated-tethrapeton, E100(#^^#^5)^^#4
* Quintatetrated-tethrapeton, E100(#^^#^5)^^#5
* Sexatetrated-tethrapeton, E100(#^^#^5)^^#6
* Septatetrated-tethrapeton, E100(#^^#^5)^^#7
* Octatetrated-tethrapeton, E100(#^^#^5)^^#8
* Nonatetrated-tethrapeton, E100(#^^#^5)^^#9
* Decatetrated-tethrapeton, E100(#^^#^5)^^#10
* Terrible tethrapeton, E100(#^^#^5)^^#100

=== Part 6.10: <math>f_{\varepsilon_{\Pi_{0}+1}}^2(10)</math> ~ <math>f_{\varpi_{0}}^2(10)</math> ===

* Terrible terrible tethrapeton, E100((#^^#^5)^^#)^^#100
* Three-ex-terrible tethrapeton, E100(#^^#^5)^^#>#3
* Four-ex-terrible tethrapeton, E100(#^^#^5)^^#>#4
* Five-ex-terrible tethrapeton, E100(#^^#^5)^^#>#5
* Six-ex-terrible tethrapeton, E100(#^^#^5)^^#>#6
* Seven-ex-terrible tethrapeton, E100(#^^#^5)^^#>#7
* Eight-ex-terrible tethrapeton, E100(#^^#^5)^^#>#8
* Nine-ex-terrible tethrapeton, E100(#^^#^5)^^#>#9
* Ten-ex-terrible tethrapeton, E100(#^^#^5)^^#>#10
* Territerated tethrapeton, E100(#^^#^5)^^#>#100
* Dustaculated-territethrapeton, E100(#^^#^5)^^#>(#^^#^5)^^#100
* Terrisquared-tethrapeton, E100(#^^#^5)^^##100
* Two-ex-terrisquared-tethrapeton, E100((#^^#^5)^^##)^^##100
* Three-ex-terrisquared-tethrapeton, E100(#^^#^5)^^##>#3
* Four-ex-terrisquared-tethrapeton, E100(#^^#^5)^^##>#4
* Five-ex-terrisquared-tethrapeton, E100(#^^#^5)^^##>#5
* Six-ex-terrisquared-tethrapeton, E100(#^^#^5)^^##>#6
* Seven-ex-terrisquared-tethrapeton, E100(#^^#^5)^^##>#7
* Eight-ex-terrisquared-tethrapeton, E100(#^^#^5)^^##>#8
* Nine-ex-terrisquared-tethrapeton, E100(#^^#^5)^^##>#9
* Ten-ex-terrisquared-tethrapeton, E100(#^^#^5)^^##>#10
* Tethritercrossed-tethrapeton, E100(#^^#^5)^^##>#100
* Dustaculated-terrisquared-tethrapeton, E100(#^^#^5)^^##>(#^^#^5)^^##100
* Terricubed-tethrapeton, E100(#^^#^5)^^###100
* Two-ex-terricubed-tethrapeton, E100((#^^#^5)^^###)^^###100
* Three-ex-terricubed-tethrapeton, E100(#^^#^5)^^###>#3
* Four-ex-terricubed-tethrapeton, E100(#^^#^5)^^###>#4
* Five-ex-terricubed-tethrapeton, E100(#^^#^5)^^###>#5
* Six-ex-terricubed-tethrapeton, E100(#^^#^5)^^###>#6
* Seven-ex-terricubed-tethrapeton, E100(#^^#^5)^^###>#7
* Eight-ex-terricubed-tethrapeton, E100(#^^#^5)^^###>#8
* Nine-ex-terricubed-tethrapeton, E100(#^^#^5)^^###>#9
* Ten-ex-terricubed-tethrapeton, E100(#^^#^5)^^###>#10
* Tethritercubed-tethrapeton, E100(#^^#^5)^^###>#100
* Dustaculated-terricubed-tethrapeton, E100(#^^#^5)^^###>(#^^#^5)^^###100
* Territesserated-tethrapeton, E100(#^^#^5)^^####100
* Two-ex-territesserated-tethrapeton, E100((#^^#^5)^^####)^^####100
* Three-ex-territesserated-tethrapeton, E100(#^^#^5)^^####>#3
* Four-ex-territesserated-tethrapeton, E100(#^^#^5)^^####>#4
* Five-ex-territesserated-tethrapeton, E100(#^^#^5)^^####>#5
* Six-ex-territesserated-tethrapeton, E100(#^^#^5)^^####>#6
* Seven-ex-territesserated-tethrapeton, E100(#^^#^5)^^####>#7
* Eight-ex-territesserated-tethrapeton, E100(#^^#^5)^^####>#8
* Nine-ex-territesserated-tethrapeton, E100(#^^#^5)^^####>#9
* Ten-ex-territesserated-tethrapeton, E100(#^^#^5)^^####>#10
* Tethritertesserated-tethrapeton, E100(#^^#^5)^^####>#100
* Dustaculated-territesserated-tethrapeton, E100(#^^#^5)^^####>(#^^#^5)^^####100
* Tethradupeton, E100(#^^#^5)^^#^(5)100
* Tethratripeton, E100((#^^#^5)^^#^5)^^#^(5)100
* Tethratetrapeton, E100(((#^^#^5)^^#^5)^^#^5)^^#^(5)100
* Tethrapentapeton, E100#^^(#^5)>#5
* Tethrahexapeton, E100#^^(#^5)>#6
* Tethraheptapeton, E100#^^(#^5)>#7
* Tethra-octapeton, E100#^^(#^5)>#8
* Tethra-ennapeton, E100#^^(#^5)>#9
* Tethradekapeton, E100#^^(#^5)>#10
* Tethra-endekapeton, E100#^^(#^5)>#11
* Tethradodekapeton, E100#^^(#^5)>#12
* Tethra-icosapeton, E100#^^(#^5)>#20
* Tethriterpeton, E100#^^(#^5)>#100
* Godgahlah-turreted-tethrapeton, E100#^^(#^5)>#^#100
* Tethrathoth-turreted-tethrapeton, E100#^^(#^5)>#^^#100
* Monster-Giant-turreted-tethrapeton, E100#^^(#^5)>(#^^#)^(#^^#)^#100
* Territethrathoth-turreted-tethrapeton, E100#^^(#^5)>(#^^#)^^#100
* Behemoth-Giant-turreted-tethrapeton, E100#^^(#^5)>(#^^#>2)^(#^^#>2)^#100
* Territerritethrathoth-turreted-tethrapeton, E100#^^(#^5)>#^^#>#3
* Trihemoth-Giant-turreted-tethrapeton, E100#^^(#^5)>(#^^#>3)^(#^^#>3)^#100
* Tethriterator-turreted-tethrapeton, E100#^^(#^5)>#^^#>#100
* Dustacultethrathoth-turreted-tethrapeton, E100#^^(#^5)>#^^#>#^^#100
* Tethracross-turreted-tethrapeton, E100#^^(#^5)>#^^##100
* Tethracubor-turreted-tethrapeton, E100#^^(#^5)>#^^###100
* Tethrateron-turreted-tethrapeton, E100#^^(#^5)>#^^####100
* Dustaculated-tethrapeton, E100#^^(#^5)>#^^#^(5)100
* Tristaculated-tethrapeton, E100#^^(#^5)>#^^(#^5)>#^^#^(5)100
* Tetrastaculated-tethrapeton, E100#^^(#^5)>#^^(#^5)>#^^(#^5)>#^^#^(5)100
* Pentastaculated-tethrapeton, E100#^^#^(6)5
* Hexastaculated-tethrapeton, E100#^^#^(6)6
* Heptastaculated-tethrapeton, E100#^^#^(6)7
* Octastaculated-tethrapeton, E100#^^#^(6)8
* Ennastaculated-tethrapeton, E100#^^#^(6)9
* Sextiphi, <math>f_{\varphi(6,0)}(10)</math>
* Dekastaculated-tethrapeton, E100#^^#^(6)10
* Icosastaculated-tethrapeton, E100#^^#^(6)20
* Triantastaculated-tethrapeton, E100#^^#^(6)30
* Sarantastaculated-tethrapeton, E100#^^#^(6)40
* Penintastaculated-tethrapeton, E100#^^#^(6)50
* Exintastaculated-tethrapeton, E100#^^#^(6)60
* Ebdomintastaculated-tethrapeton, E100#^^#^(6)70
* Ogdontastaculated-tethrapeton, E100#^^#^(6)80
* Enenintastaculated-tethrapeton, E100#^^#^(6)90
* Tethrinoohexon, {100,100[1\1\1\1\1\1\2]2}
* Tethrahexon / tethrahexeract, E100#^^#^#6

=== Part 6.11: <math>f_{\varpi_{0}}^2(10)</math> ~ <math>f_{\varphi(\omega,0)}^2(10)</math> ===

* Grand tethrahexon, E100#^^#^(6)100#2
* Grangol-carta-tethrahexon, E100#^^#^(6)100#100
* Grand grangol-carta-tethrahexon, E100#^^#^(6)100#100#2
* Godgahlah-carta-tethrahexon, E100#^^#^(6)100#^#100
* Tethrathoth-carta-tethrahexon, E100#^^#^(6)100#^^#100
* Tethracross-carta-tethrahexon, E100#^^#^(6)100#^^##100
* Tethracubor-carta-tethrahexon, E100#^^#^(6)100#^^###100
* Tethrateron-carta-tethrahexon, E100#^^#^(6)100#^^####100
* Tethrapeton-carta-tethrahexon, E100#^^#^(6)100#^^#^(5)100
* Tethrahexon-by-deuteron, E100#^^#^(6)100#^^#^(6)100
* Tethrahexon-by-triton, E100#^^#^(6)100#^^#^(6)100#^^#^(6)100
* Tethrahexon-by-teterton, E100(#^^#^6)*#5
* Tethrahexon-by-pepton, E100(#^^#^6)*#6
* Tethrahexon-by-exton, E100(#^^#^6)*#7
* Tethrahexon-by-epton, E100(#^^#^6)*#8
* Tethrahexon-by-ogdon, E100(#^^#^6)*#9
* Tethrahexon-by-enton, E100(#^^#^6)*#10
* Tethrahexon-by-dekaton, E100(#^^#^6)*#11
* Tethrahexon-by-hyperion, E100(#^^#^6)*#100
* Tethrahexon-by-godgahlah, E100(#^^#^6)*#^#100
* Tethrahexon-by-tethrathoth, E100(#^^#^6)*#^^#100
* Tethrahexon-by-tethracross, E100(#^^#^6)*#^^##100
* Tethrahexon-by-tethracubor, E100(#^^#^6)*#^^###100
* Tethrahexon-by-tethrateron, E100(#^^#^6)*#^^####100
* Tethrahexon-by-tethrapeton, E100(#^^#^6)*(#^^#^5)100
* Deutero-tethrahexon, E100#^^#^(6)*#^^#^(6)100
* Trito-tethrahexon, E100#^^#^(6)*#^^#^(6)*#^^#^(6)100
* Teterto-tethrahexon, E100#^^#^(6)*#^^#^(6)*#^^#^(6)*#^^#^(6)100
* Pepto-tethrahexon, E100(#^^#^6)^#5
* Exto-tethrahexon, E100(#^^#^6)^#6
* Epto-tethrahexon, E100(#^^#^6)^#7
* Ogdo-tethrahexon, E100(#^^#^6)^#8
* Ento-tethrahexon, E100(#^^#^6)^#9
* Dekato-tethrahexon, E100(#^^#^6)^#10
* Tethrahexonifact, E100(#^^#^6)^#100
* Quadratatethrahexon, E100(#^^#^6)^##100
* Kubikutethrahexon, E100(#^^#^6)^###100
* Quarticutethrahexon, E100(#^^#^6)^####100
* Quinticutethrahexon, E100(#^^#^6)^#^#5
* Sexticutethrahexon, E100(#^^#^6)^#^#6
* Septicutethrahexon, E100(#^^#^6)^#^#7
* Octicutethrahexon, E100(#^^#^6)^#^#8
* Nonicutethrahexon, E100(#^^#^6)^#^#9
* Decicutethrahexon, E100(#^^#^6)^#^#10
* Tethrahexon-ipso-godgahlah, E100(#^^#^6)^#^#100
* Tethrahexon-ipso-godgathor, E100(#^^#^6)^#^#^#100
* Tethrahexon-ipso-godtothol, E100(#^^#^6)^#^#^#^#100
* Tethrahexon-ipso-tethrathoth, E100(#^^#^6)^#^^#100
* Tethrahexon-ipso-tethracross, E100(#^^#^6)^#^^##100
* Tethrahexon-ipso-tethracubor, E100(#^^#^6)^#^^###100
* Tethrahexon-ipso-tethrateron, E100(#^^#^6)^#^^####100
* Tethrahexon-ipso-tethrapeton, E100(#^^#^6)^(#^^#^5)100
* Dutetrated-tethrahexon, E100(#^^#^6)^(#^^#^6)100
* Tritetrated-tethrahexon, E100(#^^#^6)^(#^^#^6)^(#^^#^6)100
* Quadratetrated-tethrahexon, E100(#^^#^6)^^#4
* Quinquatetrated-tethrahexon, E100(#^^#^6)^^#5
* Sexatetrated-tethrahexon, E100(#^^#^6)^^#6
* Septatetrated-tethrahexon, E100(#^^#^6)^^#7
* Octatetrated-tethrahexon, E100(#^^#^6)^^#8
* Nonatetrated-tethrahexon, E100(#^^#^6)^^#9
* Decatetrated-tethrahexon, E100(#^^#^6)^^#10
* Terrible tethrahexon, E100(#^^#^6)^^#100
* Terrible terrible tethrahexon, E100((#^^#^6)^^#)^^#100
* Three-ex-terrible tethrahexon, E100(#^^#^6)^^#>#3
* Four-ex-terrible tethrahexon, E100(#^^#^6)^^#>#4
* Territerated tethrahexon, E100(#^^#^6)^^#>#100
* Dustaculated-territethrahexon, E100(#^^#^6)^^#>(#^^#^6)^^#100
* Terrisquared-tethrahexon, E100(#^^#^6)^^##100
* Dustaculated-terrisquared-tethrahexon, E100(#^^#^6)^^##>(#^^#^6)^^##100
* Ennastaculated-terrisquared-tethrahexon, E100(#^^#^6)^^###9
* Ennastaculated-terricubed-tethrahexon, E100(#^^#^6)^^####9
* Ennastaculated-territesserated-tethrahexon, E100((#^^#^6)^^#^5)9
* Dustaculated-tethrahexon / tethrahexon-turreted-tethrahexon, E100#^^(#^6)>#^^(#^6)100
* Septiphi, <math>f_{\varphi(7,0)}(10)</math>
* Dekastaculated-tethrahexon, E100#^^(#^7)10
* Tethrinoohepton, {100,100[1\1\1\1\1\1\1\2]2}
* Tethrahepton, E100#^^#^#7
* Grand tethrahepton, E100#^^#^(7)100#2
* Grangol-carta-tethrahepton, E100#^^#^(7)100#100
* Tethrahepton-by-deuteron, E100#^^#^(7)100#^^#^(7)100
* Tethrahepton-by-hyperion, E100(#^^#^7)*#100
* Deutero-tethrahepton, E100#^^#^(7)*#^^#^(7)100
* Trito-tethrahepton, E100#^^#^(7)*#^^#^(7)*#^^#^(7)100
* Teterto-tethrahepton, E100(#^^#^7)^#4
* Pepto-tethrahepton, E100(#^^#^7)^#5
* Ogdo-tethrahepton, E100(#^^#^7)^#8
* Ento-tethrahepton, E100(#^^#^7)^#9
* Tethraheptonifact, E100(#^^#^7)^#100
* Terrible tethrahepton, E100(#^^#^7)^^#100
* Octiphi, <math>f_{\varphi(8,0)}(10)</math>
* Dekastaculated-tethrahepton, E100#^^(#^8)10
* Tethrinoo-ogdon, {100,100[1\1\1\1\1\1\1\1\2]2}
* Tethra-ogdon, E100#^^#^#8
* Deutero-tethra-ogdon, E100#^^#^(8)*#^^#^(8)100
* Trito-tethra-ogdon, E100#^^#^(8)*#^^#^(8)*#^^#^(8)100
* Teterto-tethra-ogdon, E100#^^#^(8)*#^^#^(8)*#^^#^(8)*#^^#^(8)100
* Ogdo-tethra-ogdon, E100(#^^#^8)^#8
* Noniphi, <math>f_{\varphi(9,0)}(10)</math>
* Tethrinoo-ennon, {100,100[1\1\1\1\1\1\1\1\1\2]2}
* Tethrennon, E100#^^#^#9
* Grand tethrennon, E100#^^#^(9)100#2
* Grangol-carta-tethrennon, E100#^^#^(9)100#100
* Tethrennon-by-deuteron, E100#^^#^(9)100#^^#^(9)100
* Deutero-tethrennon, E100#^^#^(9)*#^^#^(9)100
* Teterto-tethrennon, E100#^^#^(9)*#^^#^(9)*#^^#^(9)*#^^#^(9)100
* Tethrennonifact, E100(#^^#^9)^#100
* Dutetrated-tethrennon, E100(#^^#^9)^(#^^#^9)100
* Terrible tethrennon, E100(#^^#^9)^^#100
* Territerated tethrennon, E100(#^^#^9)^^#>#100
* Dustaculated-territethrennon, E100(#^^#^9)^^#>(#^^#^9)^^#100
* Terrisquared-tethrennon, E100(#^^#^9)^^##100
* Terricubed-tethrennon, E100(#^^#^9)^^###100
* Territesserated-tethrennon, E100(#^^#^9)^^####100
* Terripenterated-tethrennon, E100(#^^#^9)^^#####100
* Terrihexerated-tethrennon, E100(#^^#^9)^^######100
* Terrihepterated-tethrennon, E100(#^^#^9)^^#######100
* Terriocterated-tethrennon, E100(#^^#^9)^^########100
* Two-ex-terriocterated-tethrennon, E100((#^^#^9)^^#^8)^^#^(8)100
* Tethradu-ennon, E100(#^^#^9)^^#^(9)100
* Dekophi / omphi, <math>f_{\varphi(10,0)}(10)=f_{\varphi(\omega,0)}(10)</math>
* Tethrinoodekon, {100,100[1\1\1\1\1\1\1\1\1\1\2]2}
* Tethradekon, E100#^^#^#10
* Grand tethradekon, E100#^^#^(10)100#2
* Deutero-tethradekon, E100#^^#^(10)*#^^#^(10)100
* Teterto-tethradekon, E100#^^#^(10)*#^^#^(10)*#^^#^(10)*#^^#^(10)100
* Tethrinoo-icoson, {100,20[1[2¬2]2]2}
* Tethrinootope, {100,100[1[2¬2]2]2}
* Hektophi, <math>f_{\varphi(100,0)}(10)</math>
* ''Goppatope'', 100^^100100&10
* Tethratope / tethrahecton / tethratopos, E100#^^#^#100
* Deutero-tethrahecton, E100#^^#^(100)*#^^#^(100)100
* Humonurgium, <math>f_{\varphi(\omega,0)}(420)</math>
* Kilophi, <math>f_{\varphi(1000,0)}(10)</math>
* Tethrachillion, E100#^^#^#1000
* Tethramyrion, E100#^^#^#10000
* Megophi, <math>f_{\varphi(10^6,0)}(10)</math>
* Gigophi, <math>f_{\varphi(10^9,0)}(10)</math>
* Terophi, <math>f_{\varphi(10^{12},0)}(10)</math>
* Petophi, <math>f_{\varphi(10^{15},0)}(10)</math>
* Exophi, <math>f_{\varphi(10^{18},0)}(10)</math>
* Zettophi, <math>f_{\varphi(10^{21},0)}(10)</math>
* Yottophi, <math>f_{\varphi(10^{24},0)}(10)</math>

=== Part 6.12: <math>f_{\varphi(\omega,0)}^2(10)</math> ~ <math>f_{\Gamma_0}^2(10)</math> ===

* Grand tethratope, E100#^^#^#100#2
* Grangol-carta-tethratope, E100#^^#^#100#100
* Greagol-carta-tethratope, E100#^^#^#100#100#100
* Gugold-carta-tethratope, E100#^^#^#100##100
* Throogol-carta-tethratope, E100#^^#^#100###100
* Tetroogol-carta-tethratope, E100#^^#^#100####100
* Godgahlah-carta-tethratope, E100#^^#^#100#^#100
* Godgathor-carta-tethratope, E100#^^#^#100#^#^#100
* Godtothol-carta-tethratope, E100#^^#^#100#^#^#^#100
* Tethrathoth-carta-tethratope, E100#^^#^#100#^^#100
* Monster-Giant-carta-tethratope, E100#^^#^#100(#^^#)^(#^^#)^#100
* Tethracross-carta-tethratope, E100#^^#^#100#^^##100
* Tethracubor-carta-tethratope, E100#^^#^#100#^^###100
* Tethrateron-carta-tethratope, E100#^^#^#100#^^####100
* Tethratope-by-deuteron / tethratope-carta-tethratope, E100#^^#^#100#^^#^#100
* Tethratope-by-triton, E100#^^#^#100#^^#^#100#^^#^#100
* Tethratope-by-hyperion, E100#^^#^#*#100
* Deutero-tethratope, E100#^^#^#*#^^#^#100
* Hecato-tethratope / tethratopofact, E100(#^^#^#)^#100
* Terrible tethratope, E100(#^^#^#)^^#100
* Territertethratope / tethriterated-tethratope, E100(#^^#^#)^^#>#100
* Dustaculated-territethratope, E100(#^^#^#)^^#>(#^^#^#)^^#100
* Terrisquared tethratope, E100(#^^#^#)^^##100
* Terricubed tethratope, E100(#^^#^#)^^###100
* Territesserated tethratope, E100(#^^#^#)^^####100
* Tethradeutertope, E100(#^^#^#)^^#^#100
* Tethratritotope, E100((#^^#^#)^^#^#)^^#^#100
* Tethritertope, E100#^^(#^#)>#100
* Dustaculated-tethratope, E100#^^(#^#)>#^^(#^#)100
* Tethratopothoth, E100#^^(#^#*#)100
* Dustaculated-tethratopothoth, E100#^^(#^#*#)>#^^(#^#*#)100
* Tethratopocross, E100#^^(#^#*##)100
* Tethratopocubor, E100#^^(#^#*###)100
* Tethratopoteron, E100#^^(#^#*####)100
* Tethratopopeton, E100#^^(#^#*#####)100
* Tethratopodeus, E100#^^(#^#*#^#)100
* Tethratopodeusithoth, E100#^^(#^#*#^#*#)100
* Tethratopodeusicross, E100#^^(#^#*#^#*##)100
* Tethratopotruce, E100#^^(#^#*#^#*#^#)100
* Tethratopoquad, E100#^^(#^#*#^#*#^#*#^#)100
* Tethratopoquid, E100#^^(#^#*#^#*#^#*#^#*#^#)100
* Tethratoposid, E100#^^#^##6
* Tethrinoolattitope, {100,100[1[3¬2]2]2}
* Tethralattitope, E100#^^#^##100
* Even More Godder Tritri, 3 [3 {3 /// 3} 3] 3
* Tethralattitopothoth, E100#^^(#^##*#)100
* Tethralattitopotope, E100#^^(#^##*#^#)100
* Tethralattitopodeus, E100#^^(#^##*#^##)100
* ''Triakulus'', 3^^^3 & 3
* Tethralattitopotruce, E100#^^(#^##*#^##*#^##)100
* Tethralattitopoquad, E100#^^(#^##*#^##*#^##*#^##)100
* Tethracubitope, E100#^^#^###100
* Tethrinooquartitope, {100,100[1[5¬2]2]2}
* Tethraquarticutope, E100#^^#^####100
* Tethraquinticutope, E100#^^#^#####100
* Tethrasexticutope, E100#^^#^######100
* Tethrasepticutope, E100#^^#^#^(7)100
* Tethra-octicutope, E100#^^#^#^(8)100
* Tethrinooquartitope, {100,100[1[5¬2]2]2}
* Tethrinoononitope, {100,100[1[10¬2]2]2}
* Tethranonicutope, E100#^^#^#^(9)100
* Tethradecicutope, E100#^^#^#^(10)100
* Tethradecicutopononicutopo-octicutoposepticutoposexticutopoquinticutopoquarticutopocubitopolattitopotope, E100#^^(#^##########*#^#########*#^########*#^#######*#^######*#^#####*#^####*#^###*#^##*#^#)100
* Juice infused DLMAN, 17[1 {186 (/44) 416} 2]592 = 17[1 {196 `44` 416} 2]592
* Tethrato-godgathor / tethraspatialtope, E100#^^#^#^#100
* Tethrato-gotrigathor / dustaculated-tethraspatialtope, E100#^^(#^#^#)>#^^#^#^#100
* Tethrato-godgoldgathor, E100#^^(#^#^#*#)100
* Tethrato-godthroogathor, E100#^^(#^#^#*##)100
* Tethrato-godgathor-by-godgahlah-propinquus, E100#^^(#^#^#*#^#)100
* Tethrato-godgathor-by-gridgahlah-propinquus, E100#^^(#^#^#*#^##)100
* Tethrato-deutero-godgathor / tethraspatialtopodeus, E100#^^(#^#^#*#^#^#)100
* Tethrato-trito-godgathor / tethraspatialtopotruce, E100#^^(#^#^#*#^#^#*#^#^#)100
* Tethrato-godgathorfact / tethraspatialtopocentice, E100#^^#^(#^#*#)100
* Tethrato-deutero-godgathorfact, E100#^^(#^(#^#*#)*#^(#^#*#))100
* Tethrato-godgridgathor, E100#^^#^(#^#*##)100
* Tethrato-godkubikgathor, E100#^^#^(#^#*###)100
* Tethrato-godquarticgathor, E100#^^#^(#^#*####)100
* Tethrato-godgathordeus, E100#^^#^(#^#*#^#)100
* Tethrato-godgathordeucifact, E100#^^#^(#^#*#^#*#)100
* Tethrato-godgathortruce, E100#^^#^(#^#*#^#*#^#)100
* Tethrato-godgathorquad, E100#^^#^(#^#*#^#*#^#*#^#)100
* Tethrato-gralgathor, E100#^^#^#^##100
* Tethrato-godtothol, E100#^^#^#^#^#100
* Tethrato-godtertol, E100#^^#^^#5
* Tethrato-godtopol, E100#^^#^^#6
* Tethrato-godhathor, E100#^^#^^#7
* Tethrato-godheptol, E100#^^#^^#8
* Binphi, <math>f_{\varphi(\varphi(1,0),0)}(10)</math>
* Tethrinoogarxitri, {100,100[1[1[1\2]2¬2]2]2}
* '''Tethrato-tethrathoth''' / tethrarxitri, E100#^^#^^#100
* Hectastaculated-tethrato-tethrathoth / tethrato-tethrathoth-by-hyperion-propinquus, E100#^^(#^^#*#)100
* Tethrato-tethrathoth-by-godgahlah-propinquus, E100#^^(#^^#*#^#)100
* Tethrato-deutero-tethrathoth, E100#^^(#^^#*#^^#)100
* Tethrato-tethrafact, E100#^^(#^^#)^#100
* Tethrato-tethraduliath, E100#^^(#^^#)^(#^^#)100
* Tethrato-Monster-Giant, E100#^^(#^^#)^(#^^#)^#100
* Tethrato-tethrathoth-trebletetrate, E100#^^(#^^#)^(#^^#)^(#^^#)100
* Tethrato-Super-Monster-Giant, E100#^^(#^^#)^(#^^#)^(#^^#)^#100
* Tethrato-terrible-tethrathoth, E100#^^(#^^#)^^#100
* Tethrato-tethriterator, E100#^^(#^^#>#)100
* Tethrato-dustaculated-tethrathoth, E100#^^(#^^#>#^^#)100
* Tethrato-tethracross, E100#^^#^^##100
* Tethrato-tethracubor, E100#^^#^^###100
* Tethrato-tethratope, E100#^^#^^#^#100
* Brother-Giant / Cintaur, E100#^^#^#^^#^#100
* Tethrato-tethralattitope, E100#^^#^^#^##100
* Tethrato-tethraspatialtope / dutethrato-godgathor, E100#^^#^^#^#^#100
* Dutethrato-godtothol, E100#^^#^^#^#^#^#100
* Trinphi, <math>f_{\varphi(\varphi(\varphi(1,0),0),0)}(10)</math>
* Tethrinoogarxitet, {100,100[1[1[1[1[1\2]2¬2]2]2¬2]2]2}
* Tethrarxitet / tethrato-tethrato-tethrathoth, E100#^^#^^#^^#100
* Tethrato-tethrarxitri-by-gugold-propinquus, E100#^^(#^^#^^#*#)100
* Tethrato-deutero-tethrarxitri, E100#^^(#^^#^^#*#^^#^^#)100
* Tethrato-dustaculated-tethrarxitri, E100#^^(#^^(#^^#)>#^^#^^#)100
* Dutethrato-tethrathoth-by-gugold-propinquus, E100#^^#^^(#^^#*#)100
* Dutethrato-tethriterator, E100#^^#^^#^^#>#100
* Dutethrato-tethracross, E100#^^#^^#^^##100
* Dutethrato-tethratope, E100#^^#^^#^^#^#100
* Quadrinphi, <math>f_{\varphi(\varphi(\varphi(\varphi(1,0),0),0),0)}(10)</math>
* Tethrinoogarxipent, {100,100[1[1[1[1[1[1[1\2]2¬2]2]2¬2]2]2¬2]2]2}
* Tethrarxipent, E100#^^#^^#^^#^^#100
* Quintinphi, <math>f_{\Gamma_0[6]}(10)</math>
* Tethrinoogarxihex, {100,100[1[1[1[1[1[1[1[1[1\2]2¬2]2]2¬2]2]2¬2]2]2¬2]2]2}
* Tethrarxihex, E100#^^^#6
* Sextinphi, <math>f_{\Gamma_0[7]}(10)</math>
* Tethrinoogarxihept, {100,100[1[1[1[1[1[1[1[1[1[1[1\2]2¬2]2]2¬2]2]2¬2]2]2¬2]2]2¬2]2]2}
* Tethrarxihept, E100#^^^#7
* Septinphi, <math>f_{\Gamma_0[8]}(10)</math>
* Tethrinoogarxiogd, {100,100[1[1[1[1[1[1[1[1[1[1[1[1[1\2]2¬2]2]2¬2]2]2¬2]2]2¬2]2]2¬2]2]2¬2]2]2}
* Tethrarxi-ogd, E100#^^^#8
* Octinphi, <math>f_{\Gamma_0[9]}(10)</math>
* Tethrinoogarxienn, {100,100[1[1[1[1[1[1[1[1[1[1[1[1[1[1[1\2]2¬2]2]2¬2]2]2¬2]2]2¬2]2]2¬2]2]2¬2]2]2¬2]2]2}
* Tethrarxi-enn, E100#^^^#9
* Noninphi / Unexommthet, <math>f_{\Gamma_0}(10)</math>
* Pentabackthulhum, {10,10[1[1\2¬2]2]2}
* Tethrinoogarxideck, {100,10[1[1\2¬2]2]2}
* Tethrarxideck, E100#^^^#10
* Dekinphi, <math>f_{\Gamma_0[11]}(10)</math>
* Tethrinoogarxicose, {100,20[1[1\2¬2]2]2}
* Tethrarxicose, E100#^^^#20
* Tethrinoogarxitriane, {100,30[1[1\2¬2]2]2}
* Tethrarxitriane, E100#^^^#30
* Tethrinoogarxisarane, {100,40[1[1\2¬2]2]2}
* Tethrarxisarane, E100#^^^#40
* Tethrinoogarxipenine, {100,50[1[1\2¬2]2]2}
* Tethrarxipenine / tethrarxigole, E100#^^^#50
* Tethrinoogarxiexine, {100,60[1[1\2¬2]2]2}
* Tethrarxi-exine, E100#^^^#60
* Tethrinoogarxiebdomine, {100,70[1[1\2¬2]2]2}
* Tethrarxi-ebdomine, E100#^^^#70
* Tethrinoogarxiogdone, {100,80[1[1\2¬2]2]2}
* Tethrarxi-ogdone, E100#^^^#80
* Tethrinoogarxienenine, {100,90[1[1\2¬2]2]2}
* Tethrarxi-enenine, E100#^^^#90
* Pentacthuloogol / tethrinoogarxihect, {100,100[1[1\2¬2]2]2}
* Pentacthulhum / tethrarxihect, E100#^^^#100
* ''Kungulus'', <math>X \uparrow \uparrow \uparrow 100 \& 10</math>
* ''Second Kungulus'', {100,100,3} & 10
* Onii-chan-Giant, E100#^^#^#^^#^#^^#^ ... #^^#^#100 (100 #^^#'s)
* Hektinphi, <math>f_{\Gamma_0[101]}(10)</math>
* Tethrinoogarxigigas, {100,500[1[1\2¬2]2]2}
* Tethrarxigigas, E100#^^^#500
* Mariupol, <math>f_{\Gamma_0}(576)</math>
* Tethrinoogarxichill, {100,1000[1[1\2¬2]2]2}
* Tethrarxichill, E100#^^^#1,000
* Kilinphi, <math>f_{\Gamma_0[1001]}(10)</math>
* Tethrinoogarximyr, {100,10000[1[1\2¬2]2]2}
* Tethrarximyr, E100#^^^#10,000
* Tethrarxigong, E100#^^^#100,000
* Pentacthulhugong, E100,000#^^^#100,000
* Meginphi, <math>f_{\Gamma_0[10^6+1]}(10)</math>
* Tethrinoogarxi-octad, {100,{10,8}[1[1\2¬2]2]2}
* Tethrarxi-octad, E100#^^^#100,000,000
* Giginphi, <math>f_{\Gamma_0[10^9+1]}(10)</math>
* Great Wall, E100#^^#^^#>#^^#^^#>#^^#^^#>...#^^#^^#>#^^#^^#100 (with 10,000,000,000 #^^#^^#'s)
* Terinphi, <math>f_{\Gamma_0[10^{12}+1]}(10)</math>
* Petinphi, <math>f_{\Gamma_0[10^{15}+1]}(10)</math>
* Tethrinoogarxi-sedeniad], {100,{10,16}[1[1\2¬2]2]2}
* Tethrarxi-sedeniad, E100#^^^#10,000,000,000,000,000
* Exinphi, <math>f_{\Gamma_0[10^{18}+1]}(10)</math>
* Zettinphi, <math>f_{\Gamma_0[10^{21}+1]}(10)</math>
* Yottinphi, <math>f_{\Gamma_0[10^{24}+1]}(10)</math>
* Tethrarxigoogliad, E100#^^^#(10100)
* Tethrarxigrangliad, E100#^^^#(E100#100)

== Bachmann's collapsing level ==

=== Part 6.13: <math>f_{\Gamma_0}^2(10)</math> ~ <math>f_{\Gamma_1}^2(10)</math> ===

* Grand pentacthulhum / grand tethrarxihect / tethrarxitethrarxihect, E100#^^^#100#2
* Grand grand pentacthulhum, E100#^^^#100#3
* Triple grand pentacthulhum, E100#^^^#100#4
* Quadruple grand pentacthulhum, E100#^^^#100#5
* Quintuple grand pentacthulhum, E100#^^^#100#6
* Sextuple grand pentacthulhum, E100#^^^#100#7
* Septuple grand pentacthulhum, E100#^^^#100#8
* Octuple grand pentacthulhum, E100#^^^#100#9
* Nonuple grand pentacthulhum, E100#^^^#100#10
* Decuple grand pentacthulhum, E100#^^^#100#11
* Grangol-carta-pentacthulhum, E100#^^^#100#100
* Greagol-carta-pentacthulhum, E100#^^^#100#100#100
* Gigangol-carta-pentacthulhum, E100#^^^#100#100#100#100
* Gugold-carta-pentacthulhum, E100#^^^#100##100
* Gammaxul, <math>200![200(1)2]</math>
* Throogol-carta-pentacthulhum, E100#^^^#100###100
* Tethratope-carta-pentacthulhum, E100#^^^#100#^^#^#100
* Tethrarxitri-carta-pentacthulhum, E100#^^^#100#^^#^^#100
* Pentacthulhutri, E100#^^^#100#^^^#100
* Pentacthulhutet, E100#^^^#100#^^^#100#^^^#100
* Pentacthulhupent, E100#^^^#*#5
* Pentacthulhuhex, E100#^^^#*#6
* Pentacthulhuhept, E100#^^^#*#7
* Gammabixul, <math>200![200,200(1)2]</math>
* Deutero-pentacthulhum, E100#^^^#*#^^^#100
* Trito-pentacthulhum, E100#^^^#*#^^^#*#^^^#100
* Pentacthulhufact, E100(#^^^#)^#100
* Gammatrixul, <math>200![200,200,200(1)2]</math>
* Quarticupentacthulhum, E100(#^^^#)^####100
* Dutetrated-pentacthulhum, E100(#^^^#)^#^^^#100
* Tritetrated-pentacthulhum, E100(#^^^#)^(#^^^#)^(#^^^#)100
* Quadratetrated-pentacthulhum, E100(#^^^#)^^#4
* Quinquatetrated-pentacthulhum, E100(#^^^#)^^#5
* Sexatetrated-pentacthulhum, E100(#^^^#)^^#6
* Septatetrated-pentacthulhum, E100(#^^^#)^^#7
* Octatetrated-pentacthulhum, E100(#^^^#)^^#8
* Terrible pentacthulhum, E100(#^^^#)^^#100
* Dustaculated-terripentacthulhum, E100(#^^^#)^^#>#(#^^^#)^^#100
* Terrisquared pentacthulhum, E100(#^^^#)^^##100
* Terricubed pentacthulhum, E100(#^^^#)^^###100
* Territesserated pentacthulhum, E100(#^^^#)^^####100
* Terripenterated pentacthulhum, E100(#^^^#)^^#####100
* Territoped-pentacthuloogol, {100,100[1[2¬2]2[1\2¬2]2]2}
* Territoped pentacthulhum, E100(#^^^#)^^#^#100
* Dupentated-pentacthuloogol, {100,100[1[1[1[1[2¬2]2]2¬2]2]2¬2]2[1\2¬2]2]2}
* Dupentated-pentacthulhum / pentacthulhutetripso-pentacthulhum, E100(#^^^#)^^(#^^^#)100
* Terrible dupentated-pentacthulhum, E100((#^^^#)^^(#^^^#))^^#100
* Terrisquared dupentated-pentacthulhum, E100((#^^^#)^^(#^^^#))^^##100
* Tripentacthulated-pentacthulhum, E100(((#^^^#)^^(#^^^#))^^(#^^^#))^^(#^^^#)100
* Dustaculated-dupentated-pentacthulhum, E100(#^^^#)^^(#^^^#)>(#^^^#)^^(#^^^#)100
* Pentacthulhu-by-hyperia-tetrated-pentacthulhum, E100(#^^^#)^^(#^^^#*#)100
* Pentacthulhu-by-deutero-hyperia-tetrated-pentacthulhum, E100(#^^^#)^^(#^^^#*##)100
* Pentacthulhu-deutero-pentacthulhutetrate, E100(#^^^#)^^(#^^^#*#^^^#)100
* Pentacthulhu-trito-pentacthulhutetrate, E100(#^^^#)^^(#^^^#*#^^^#*#^^^#)100
* Pentacthulhu-terripentacthulhutetrate, E100(#^^^#)^^(#^^^#)^^#100
* Pentacthulhu-terrisquared-pentacthulhutetrate, E100(#^^^#)^^(#^^^#)^^##100
* Pentacthulhu-terricubed-pentacthulhutetrate, E100(#^^^#)^^(#^^^#)^^###100
* Pentacthulhu-territoped-pentacthulhutetrate, E100(#^^^#)^^(#^^^#)^^#^#100
* Tripentated-pentacthulhum, E100(#^^^#)^^(#^^^#)^^(#^^^#)100
* Quadrapentated-pentacthulhum, E100(#^^^#)^^^#4
* Quinquapentated-pentacthulhum, E100(#^^^#)^^^#5
* Sexapentated-pentacthulhum, E100(#^^^#)^^^#6
* Septapentated-pentacthulhum, E100(#^^^#)^^^#7
* Octapentated-pentacthulhum, E100(#^^^#)^^^#8
* Nonapentated-pentacthulhum, E100(#^^^#)^^^#9
* Decapentated-pentacthulhum, E100(#^^^#)^^^#10
* Pentacthuloodugon, {100,100[1[1\2¬2]3]2}
* Pentacthuldugon / horrible pentacthulhum, E100(#^^^#)^^^#100

=== Part 6.14: <math>f_{\Gamma_1}^2(10)</math> ~ <math>f_{\varphi(2,0,0)}^2(10)</math> ===

* Grand pentacthuldugon, E100(#^^^#)^^^#100#2
* Gamthraxul, <math>200![200(1)3]</math>
* Dutetrated-pentacthuldugon, E100((#^^^#)^^^#)^((#^^^#)^^^#)100
* Terrible pentacthuldugon, E100((#^^^#)^^^#)^^#100
* Terrisquared pentacthuldugon, E100((#^^^#)^^^#)^^##100
* Terrixitried pentacthuldugon / pentacthuldugon-tethrathothitetrate, E100((#^^^#)^^^#)^^#^^#100
* Pentacthuldugon-pentacthulhutetrate, E100((#^^^#)^^^#)^^(#^^^#)100
* Pentacthuldugon-dupentated-pentacthulhutetrate, E100((#^^^#)^^^#)^^(#^^^#)^^(#^^^#)100
* Dupentated-pentacthuldugon, E100((#^^^#)^^^#)^^((#^^^#)^^^#)100
* Pentacthuldugon-by-hyperia-tetrated-pentacthuldugon, E100((#^^^#)^^^#)^^((#^^^#)^^^#*#)100
* Deutero-pentacthuldugon-tetrated-pentacthuldugon, E100((#^^^#)^^^#)^^((#^^^#)^^^#*(#^^^#)^^^#)100
* Terripentacthuldugon-tetrated-pentacthuldugon, E100((#^^^#)^^^#)^^((#^^^#)^^^#)^^#100
* Tripentated-pentacthuldugon, E100((#^^^#)^^^#)^^((#^^^#)^^^#)^^((#^^^#)^^^#)100
* Quadrapentated-pentacthuldugon, E100((#^^^#)^^^#)^^((#^^^#)^^^#)^^((#^^^#)^^^#)^^((#^^^#)^^^#)100
* Pentacthultrigon, E100((#^^^#)^^^#)^^^#100
* Dupentated-pentacthultrigon, E100(((#^^^#)^^^#)^^^#)^^(((#^^^#)^^^#)^^^#)100
* Gappingly / Griddigol, E100((#^^^#)#^^^#)#^^^#)^^((#^^^#^^^#)^^^(#^^^#)100
* Pentacthulootetragon, {100,100[1[1\2¬2]5]2}
* Pentacthultetragon, E100(((#^^^#)^^^#)^^^#)^^^#100
* Pentacthulpentagon, E100((((#^^^#)^^^#)^^^#)^^^#)^^^#100
* Pentacthulhexagon, E100#^^^#>#6
* Pentacthulheptagon, E100#^^^#>#7
* Pentacthuloctagon, E100#^^^#>#8
* Pentacthulennagon, E100#^^^#>#9
* Pentacthuldekagon, E100#^^^#>#10
* Pentacthulooterator, {100,100[1[1\2¬2]1,2]2}
* Pentacthuliterator / pentacthulhum ba'al, E100#^^^#>#100
* Hugexul, 200![200(1)200]
* Kilohugexul, (200![200(1)200])![200(1)200]
* Megahugexul, ((200![200(1)200])![200(1)200])![200(1)200]
* Gigahugexul, (((200![200(1)200])![200(1)200])![200(1)200])![200(1)200]
* Terahugexul, 200(![200(1)200])5
* Petahugexul, 200(![200(1)200])6
* Exahugexul, 200(![200(1)200])7
* Grand Hugexul, 200(![200(1)200])200![200(1)200]+1
* Grand Kilohugexul, 200(![200(1)200])(200![200(1)200])![200(1)200]+1
* Grand Megahugexul, 200(![200(1)200])((200![200(1)200])![200(1)200])![200(1)200]+1
* Grand Gigahugexul, 200(![200(1)200])200(![200(1)200])4+1
* Grand Terahugexul, 200(![200(1)200])200(![200(1)200])5+1
* Grand Petahugexul, 200(![200(1)200])200(![200(1)200])6+1
* Grand Exahugexul, 200(![200(1)200])200(![200(1)200])7+1
* Bigrand Hugexul, 200(![200(1)200])200(![200(1)200])200![200(1)200]+1+1
* Trigrand Hugexul, 200(![200(1)200])200(![200(1)200])200(![200(1)200])200![200(1)200]+1+1+1
* Quadgrand Hugexul, 200(![200(1)200])200(![200(1)200])200(![200(1)200])200(![200(1)200])200![200(1)200]+1+1+1+1
* Quintgrand Hugexul
* Grand pentacthuliterator / great and horrible pentacthulhum, E100#^^^#>#100#2
* Pentacthuliterfact, E100(#^^^#>#)^#100
* Terrible pentacthuliterator, E100(#^^^#>#)^^#100
* Pentacthuliterator-pentacthulhutetrate / pentacthulhum-tetrated-pentacthuliterator, E100(#^^^#>#)^^(#^^^#)100
* Pentacthuldugon-tetrated-pentacthuliterator, E100(#^^^#>#)^^((#^^^#)^^^#)100
* Dupentated-pentacthuliterator, E100(#^^^#>#)^^(#^^^#>#)100
* Horrible pentacthuliterator, E100(#^^^#>#)^^^#100
* Double-horrible pentacthuliterator, E100((#^^^#>#)^^^#)^^^#100
* Pentacthulditerator, E100#^^^#>(#+#)100
* Pentacthultriterator, E100#^^^#>(#+#+#)100
* Pentacthulooquadiator, {100,100[1[1\2¬2]1,5]2}
* Pentacthulquaditerator, E100#^^^#>(#+#+#+#)100
* Pentacthuloogridiator, {100,100[1[1\2¬2]1,1,2]2}
* Pentacthulgriditerator, E100#^^^#>##100
* Superior Hugexul, 200![200(1)200,200]
* Superior Kilohugexul, (200![200(1)200,200])![200(1)200,200]
* Superior Grand Hugexul, 200(![200(1)200,200])200![200(1)200,200]+1
* Superior Bigrand Hugexul, 200(![200(1)200,200])200(![200(1)200,200])200![200(1)200,200]+1+1
* Horrible pentacthulgriditerator, E100(#^^^#>##)^^^#100
* Pentacthuloocubiator, {100,100[1[1\2¬2]1,1,1,2]2}
* Pentacthulcubiculator, E100#^^^#>###100
* Pentacthulquarticulator, E100#^^^#>####100
* Pentacthulquinticulator, E100#^^^#>#####100
* Pentacthulsexticulator, E100#^^^#>#^#6
* Pentacthulsepticulator, E100#^^^#>#^#7
* Godgahlah-turreted-pentacthulhum / pentacthulspatialator, E100#^^^#>#^#100
* Tethrathoth-turreted-pentacthulhum, E100#^^^#>#^^#100
* Tethriterator-turreted-pentacthulhum, E100#^^^#>#^^#>#100
* Tethrigriditer-turreted-tethrathoth, E100#^^^#>#^^#>##100
* Tethrispatialaturreted-pentacthulhum, E100#^^^#>#^^#>#^#100
* Dustaculated-tethrathothiturreted-pentacthulhum, E100#^^^#>#^^#>#^^#100
* Tethracross-turreted-pentacthulhum, E100#^^^#>#^^##100
* Tethracubor-turreted-pentacthulhum, E100#^^^#>#^^###100
* Tethrateron-turreted-pentacthulhum, E100#^^^#>#^^####100
* Tethrapeton-turreted-pentacthulhum, E100#^^^#>#^^#####100
* Tethratope-turreted-pentacthulhum, E100#^^^#>#^^#^#100
* Tethrarxitri-turreted-pentacthulhum, E100#^^^#>#^^#^^#100
* Tethrarxitet-turreted-pentacthulhum, E100#^^^#>#^^#^^#^^#100
* Uningam, <math>f_{\Gamma_{\Gamma_0}}(10)</math>
* Dustaculated-pentacthulhum, E100#^^^#>#^^^#100
* Horrible dustaculated-pentacthulhum, E100(#^^^#>#^^^#)^^^#100
* Horriterated-dustaculated-pentacthulhum, E100#^^^#>(#^^^#+#)100
* Deuterpentacthulhum-turreted-pentacthulhum, E100#^^^#>(#^^^#*#^^^#)100
* Pentacthulhufact-turreted-pentacthulhum, E100#^^^#>(#^^^#)^#100
* Terripentacthulhuturreted-pentacthulhum, E100#^^^#>(#^^^#)^^#100
* Dupentated-pentacthulhuturreted-pentacthulhum, E100#^^^#>(#^^^#)^^(#^^^#)100
* Pentacthuldugon-turreted-pentacthulhum, E100#^^^#>(#^^^#)^^^#100
* Pentacthuliterator-turreted-pentacthulhum, E100#^^^#>#^^^#>#100
* Pentacthulgriditerator-turreted-pentacthulhum, E100#^^^#>#^^^#>##100
* Pentacthulspatialator-turreted-pentacthulhum, E100#^^^#>#^^^#>#^#100
* Bingam, <math>f_{\Gamma_{\Gamma_{\Gamma_0}}}(10)</math>
* Tristaculated-pentacthulhum, E100#^^^#>#^^^#>#^^^#100
* Tringam, <math>f_{\Gamma_{\Gamma_{\Gamma_{\Gamma_0}}}}(10)</math>
* Tetrastaculated-pentacthulhum, E100#^^^#>#^^^#>#^^^#>#^^^#100
* Quadringam, <math>f_{\varphi(1,1,0)[5]}(10)</math>
* Pentastaculated-pentacthulhum, E100#^^^#>#^^^#>#^^^#>#^^^#>#^^^#100
* Quintingam, <math>f_{\varphi(1,1,0)[6]}(10)</math>
* Sextingam, <math>f_{\varphi(1,1,0)[7]}(10)</math>
* Septingam, <math>f_{\varphi(1,1,0)[8]}(10)</math>
* Octingam, <math>f_{\varphi(1,1,0)[9]}(10)</math>
* Noningam / unaddommthet, <math>f_{\varphi(1,1,0)}(10)</math>
* Dekingam, <math>f_{\varphi(1,1,0)[11]}(10)</math>
* Pentacthuloocross, {100,100[1[1\2¬2]1\2]2}
* Pentacthulcross, E100#^^^##100
* ''Bungulus (RedBandServerYT)'' / bikungulus, {100,1002,3} & 10
* Hektingam, <math>f_{\varphi(1,1,0)[101]}(10)</math>
* Bisuperior Hugexul, 200![200(1)200,200,200]
* Bisuperior Kilohugexul, (200![200(1)200,200,200])![200(1)200,200,200
* Bisuperior Grand Hugexul, 200(![200(1)200,200,200])200![200(1)200,200,200]+1
* Bisuperior Bigrand Hugexul, 200(![200(1)200,200,200])200(![200(1)200,200,200])200![200(1)200,200,200]+1+1
* Kilingam, <math>f_{\varphi(1,1,0)[1001]}(10)</math>
* Megingam, <math>f_{\varphi(1,1,0)[10^6+1]}(10)</math>
* Gigingam, <math>f_{\varphi(1,1,0)[10^9+1]}(10)</math>
* Teringam, <math>f_{\varphi(1,1,0)[10^{12}+1]}(10)</math>
* Petingam, <math>f_{\varphi(1,1,0)[10^{15}+1]}(10)</math>
* Exingam, <math>f_{\varphi(1,1,0)[10^{18}+1]}(10)</math>
* Zettingam, <math>f_{\varphi(1,1,0)[10^{21}+1]}(10)</math>
* Yottingam, <math>f_{\varphi(1,1,0)[10^{24}+1]}(10)</math>
* Grand pentacthulcross, E100#^^^##100#2
* Deutero-pentacthulcross, E100#^^^##*#^^^##100
* Dutetrated-pentacthulcross, E100(#^^^##)^(#^^^##)100
* Terrible pentacthulcross, E100(#^^^##)^^#100
* Dupentated-pentacthulcross, E100(#^^^##)^^(#^^^##)100
* Horrible pentacthulcross, E100(#^^^##)^^^#100
* Horriterated pentacthulcross, E100(#^^^##)^^^#>#100
* Dustaculated-horripentacthulcross, E100(#^^^##)^^^#>(#^^^##)^^^#100
* Pentacthulooducross, {100,100[1[1\2¬2]1\3]2}
* Pentacthulducross, E100(#^^^##)^^^##100
* Pentacthultricross, E100((#^^^##)^^^##)^^^##100
* Pentacthulootetracross, {100,100[1[1\2¬2]1\5]2}
* Pentacthultetracross, E100#^^^##>#4
* Pentacthulpentacross, E100#^^^##>#5
* Pentacthulootercross, {100,100[1[1\2¬2]1\1,2]2}
* Pentacthulitercross, E100#^^^##>#100
* Dustaculated-pentacthulcross, E100#^^^##>#^^^##100
* Menger sponge, E[20]3###^^^###3
* Tristaculated-pentacthulcross, E100#^^^##>#^^^##>#^^^##100
* Baddommthet, <math>f_{\varphi(1,2,0)}(10)</math>
* Pentacthuloocubor, {100,100[1[1\2¬2]1\1\2]2}
* Pentacthulcubor, E100#^^^###100
* Pentacthulitercubor, E100#^^^###>#100
* Dustaculated-pentacthulcubor, E100#^^^###>#^^^###100
* Traddommthet, <math>f_{\varphi(1,3,0)}(10)</math>
* Pentacthulteron, E100#^^^####100
* Quadraddommthet, <math>f_{\varphi(1,4,0)}(10)</math>
* Pentacthulpeton, E100#^^^#^#5
* Quintaddommthet, <math>f_{\varphi(1,5,0)}(10)</math>
* Pentacthulhexon, E100#^^^#^#6
* Sextaddommthet, <math>f_{\varphi(1,6,0)}(10)</math>
* Pentacthulhepton, E100#^^^#^#7
* Septaddommthet, <math>f_{\varphi(1,7,0)}(10)</math>
* Pentacthul-ogdon, E100#^^^#^#8
* Octaddommthet, <math>f_{\varphi(1,8,0)}(10)</math>
* Pentacthulennon, E100#^^^#^#9
* Nonaddommthet, <math>f_{\varphi(1,9,0)}(10)</math>
* Pentacthuloodekon, {100,100[1[1\2¬2]1\1\1\1\1\1\1\1\1\2]2}
* Pentacthuldekon, E100#^^^#^#10
* Dekaddommthet, <math>f_{\varphi(1,\omega,0)}(10)</math>
* Pentacthulootope, {100,100[1[1\2¬2]1[2¬2]2]2}
* Pentacthultope / pentacthulhecton, E100#^^^#^#100
* Hektaddommthet, <math>f_{\varphi(1,100,0)}(10)</math>
* Kiladdommthet, <math>f_{\varphi(1,1000,0)}(10)</math>
* Megaddommthet, <math>f_{\varphi(1,10^6,0)}(10)</math>
* Gigaddommthet, <math>f_{\varphi(1,10^9,0)}(10)</math>
* Teraddommthet, <math>f_{\varphi(1,10^{12},0)}(10)</math>
* Petaddommthet, <math>f_{\varphi(1,10^{15},0)}(10)</math>
* Exaddommthet, <math>f_{\varphi(1,10^{18},0)}(10)</math>
* Zettaddommthet, <math>f_{\varphi(1,10^{21},0)}(10)</math>
* Yottaddommthet, <math>f_{\varphi(1,10^{24},0)}(10)</math>
* Pentacthultopothoth, E100#^^^(#^#*#)100
* Pentacthultopocross, E100#^^^(#^#*##)100
* Pentacthultopodeus, E100#^^^(#^#*#^#)100
* Pentacthultopotruce, E100#^^^(#^#*#^#*#^#)100
* Pentacthuloolattitope, {100,100[1[1\2¬2]1[3¬2]2]2}
* Pentacthulattitope, E100#^^^#^##100
* Pentacthuloocubitope, {100,100[1[1\2¬2]1[4¬2]2]2}
* Pentacthulcubitope, E100#^^^#^###100
* Pentacthuloogodgathor, {100,100[1[1\2¬2]1[1,2¬2]2]2}
* Pentacthulto-godgathor, E100#^^^#^#^#100
* Pentacthulto-tethrathoth, E100#^^^#^^#100
* Pentacthulootethrinoogol, {100,100[1[1\2¬2]1[1[1\2]2¬2]2]2}
* Pentacthularxitri / pentacthulto-pentacthulhum, E100#^^^#^^^#100
* Pentacthuloogarxitri, {100,100[1[1\2¬2]1[1[1[1\2¬2]2]2¬2]2]2}
* Pentacthularxitet, E100#^^^#^^^#^^^#100
* Pentacthuloogarxipent, {100,5[1[1\2¬2]1[1\2¬2]2]2}
* Pentacthuloogarxideck, {100,10[1[1\2¬2]1[1\2¬2]2]2}
* Pentacthuloogarxicose, {100,20[1[1\2¬2]1[1\2¬2]2]2}
* Pentacthuloogarxipenine, {100,50[1[1\2¬2]1[1\2¬2]2]2}
* Hexacthulhum / pentacthularxihect, E100#^^^^#100
* ''Quadrunculus'', <math>X \uparrow \uparrow \uparrow \uparrow 100 \& 10 </math>

=== Part 6.15: <math>f_{\varphi(2,0,0)}^2(10)</math> ~ <math>f_{\varphi(\omega,0,0)}^2(10)</math> ===

* Grand hexacthulhum, E100#^^^^#100#2
* Grangol-carta-hexacthulhum, E100#^^^^#100#100
* Hexacthulhum-by-deuteron, E100#^^^^#100#^^^^#100
* Hexacthulhufact, E100(#^^^^#)^#100
* Terrible hexacthulhum, E100(#^^^^#)^^#100
* Horrible hexacthulhum, E100(#^^^^#)^^^#100
* Duhexated-hexacthulhum, E100(#^^^^#)^^^(#^^^^#)100
* Hexadeucthulhum / horrendous hexacthulhum, E100(#^^^^#)^^^^#100
* Hexacthuliterator, E100#^^^^#>#100
* Hugebixul, 200![200(1)200(1)200]
* Kilohugebixul, (200![200(1)200(1)200])![200(1)200(1)200]
* Megahugebixul, ((200![200(1)200(1)200])![200(1)200(1)200])![200(1)200(1)200]
* Gigahugebixul, (((200![200(1)200(1)200])![200(1)200(1)200])![200(1)200(1)200])![200(1)200(1)200]
* Grand Hugebixul, 200(![200(1)200(1)200])200![200(1)200(1)200]+1
* Grand Kilohugebixul, 200(![200(1)200(1)200])(200![200(1)200(1)200])![200(1)200(1)200]+1
* Grand Megahugebixul, 200(![200(1)200(1)200])((200![200(1)200(1)200])![200(1)200(1)200])![200(1)200(1)200]+1
* Grand Gigahugebixul, 200(![200(1)200(1)200])200(![200(1)200(1)200])4+1
* Bigrand Hugebixul, 200(![200(1)200(1)200])200(![200(1)200(1)200])200![200(1)200(1)200]+1+1
* Trigrand Hugebixul
* Superior Hugebixul, 200![200(1)200(1)200,200]
* Superior Kilohugebixul, (200![200(1)200(1)200,200])![200(1)200(1)200,200]
* Superior Megahugebixul, ((200![200(1)200(1)200,200])![200(1)200(1)200,200])![200(1)200(1)200,200]
* Superior Grand Hugebixul, 200(![200(1)200(1)200,200])200![200(1)200(1)200,200]+1
* Superior Grand Kilohugebixul, 200(![200(1)200(1)200,200])(200![200(1)200(1)200,200])![200(1)200(1)200,200]+1
* Superior Grand Megahugebixul, 200(![200(1)200(1)200,200])200(![200(1)200(1)200,200])3+1
* Superior Bigrand Hugebixul, 200(![200(1)200(1)200,200])200(![200(1)200(1)200,200])200![200(1)200(1)200,200]+1+1
* Dustaculated hexacthulhum, E100#^^^^#>#^^^^#100
* Hexacthulcross, E100#^^^^##100
* Bisuperior Hugebixul, 200![200(1)200(1)200,200,200]
* Bisuperior Kilohugebixul, (200![200(1)200(1)200,200,200])![200(1)200(1)200,200,200]
* Bisuperior Megahugebixul, ((200![200(1)200(1)200,200,200])![200(1)200(1)200,200,200])![200(1)200(1)200,200,200]
* Bisuperior Grand Hugebixul, 200(![200(1)200(1)200,200,200])200![200(1)200(1)200,200,200]+1
* Bisuperior Grand Kilohugebixul, 200(![200(1)200(1)200,200,200])(200![200(1)200(1)200,200,200])![200(1)200(1)200,200,200]+1
* Bisuperior Grand Megahugebixul, 200(![200(1)200(1)200,200,200])200(![200(1)200(1)200,200,200])3+1
* Bisuperior Bigrand Hugebixul
* Hexacthulcubor, E100#^^^^###100
* Hexacthulhexon, E100(#^^^^#^6)100
* Hexacthuliterhexon, E100#^^^^(#^6)>#100
* Hexacthultope / hexacthulhecton, E100#^^^^#^#100
* Hexacthularxitri, E100#^^^^#^^^^#100
* Joe pellinger, 203^431,112,937#^^^^########^^^^######>#^#203,431,112,937
* Grand joe pellinger, 203^431,112,937#^^^^########^^^^######>#^#203,431,112,937#2
* Heptacthulhum / hexacthularxihect, E100#{5}#100
* Hepacthuloogol, {100,100[1[1\2¬2]1[1\2¬2]1[1\2¬2]2]2}
* ''Quintunculus'', <math>\{X,100,5\}\ \&\ 10</math>
* Heptacthuliterator / heptacthulhum ba'al, E100#{5}#>#100
* Hugetrixul, 200![200(1)200(1)200(1)200]
* Kilohugetrixul, (200![200(1)200(1)200(1)200])![200(1)200(1)200(1)200]
* Megahugetrixul, ((200![200(1)200(1)200(1)200])![200(1)200(1)200(1)200])![200(1)200(1)200(1)200]
* Gigahugetrixul, 200(![200(1)200(1)200(1)200])4
* Grand Hugetrixul, 200(![200(1)200(1)200(1)200])200![200(1)200(1)200(1)200]+1
* Grand Kilohugetrixul, 200(![200(1)200(1)200(1)200])(200![200(1)200(1)200(1)200])![200(1)200(1)200(1)200]+1
* Grand Megahugetrixul, 200(![200(1)200(1)200(1)200])200(![200(1)200(1)200(1)200])3+1
* Grand Gigahugetrixul, 200(![200(1)200(1)200(1)200])200(![200(1)200(1)200(1)200])4+1
* Bigrand Hugetrixul, 200(![200(1)200(1)200(1)200])200(![200(1)200(1)200(1)200])200![200(1)200(1)200(1)200]+1+1
* Trigrand Hugetrixul
* Superior Hugetrixul, 200![200(1)200(1)200(1)200,200]
* Superior Kilohugetrixul, (200![200(1)200(1)200(1)200,200])![200(1)200(1)200(1)200,200]
* Superior Megahugetrixul, ((200![200(1)200(1)200(1)200,200])![200(1)200(1)200(1)200,200])![200(1)200(1)200(1)200,200]
* Superior Grand Hugetrixul, 200(![200(1)200(1)200(1)200,200])200![200(1)200(1)200(1)200,200]+1
* Superior Grand Kilohugetrixul, 200(![200(1)200(1)200(1)200,200])200(![200(1)200(1)200(1)200,200])2+1
* Superior Grand Megahugetrixul, 200(![200(1)200(1)200(1)200,200])200(![200(1)200(1)200(1)200,200])3+1
* Superior Bigrand Hugetrixul
* Bisuperior Hugetrixul, 200![200(1)200(1)200(1)200,200,200]
* Bisuperior Kilohugetrixul, (200![200(1)200(1)200(1)200,200,200])![200(1)200(1)200(1)200,200,200]
* Bisuperior Megahugetrixul, ((200![200(1)200(1)200(1)200,200,200])![200(1)200(1)200(1)200,200,200])![200(1)200(1)200(1)200,200,200]
* Bisuperior Grand Hugetrixul, 200(![200(1)200(1)200(1)200,200,200])200![200(1)200(1)200(1)200,200,200]+1
* Bisuperior Grand Kilohugetrixul, 200(![200(1)200(1)200(1)200,200,200])200(![200(1)200(1)200(1)200,200,200])2+1
* Bisuperior Grand Megahugetrixul, 200(![200(1)200(1)200(1)200,200,200])200(![200(1)200(1)200(1)200,200,200])3+1
* Bisuperior Bigrand Hugetrixul
* Honiara, E[13]Mentalize#{5}###^^#>#^#^^#>(#^^^^#)^^^(#^^^^#)>(#^#*#+#) (Hyper pectrol number)
* Ogdacthulhum / heptacthularxihect, E100#{6}#100
* Ogdacthuloogol, {100,100[1[1\2¬2]1[1\2¬2]1[1\2¬2]1[1\2¬2]2]2}
* Ogdacthulhufact, E100(#{6}#)^#100
* Ogdacthulhum-ipso-godgahlah, E100(#{6}#)^#^#100
* Dutetrated ogdacthulhum, E100(#{6}#)^(#{6}#)100
* Ogdacthuliterator, E100#{6}#>#100
* Hugequaxul, 200![200(1)200(1)200(1)200(1)200]
* Kilohugequaxul, (200![200(1)200(1)200(1)200(1)200])![200(1)200(1)200(1)200(1)200]
* Megahugequaxul, ((200![200(1)200(1)200(1)200(1)200])![200(1)200(1)200(1)200(1)200])![200(1)200(1)200(1)200(1)200]
* Gigahugequaxul, 200(![200(1)200(1)200(1)200(1)200])4
* Grand Hugequaxul, 200(![200(1)200(1)200(1)200(1)200])200![200(1)200(1)200(1)200(1)200]+1
* Grand Kilohugequaxul, 200(![200(1)200(1)200(1)200(1)200])(200![200(1)200(1)200(1)200(1)200])![200(1)200(1)200(1)200(1)200]+1
* Grand Megahugequaxul, 200(![200(1)200(1)200(1)200(1)200])200(![200(1)200(1)200(1)200(1)200])3+1
* Grand Gigahugequaxul, 200(![200(1)200(1)200(1)200(1)200])200(![200(1)200(1)200(1)200(1)200])4+1
* Bigrand Hugequaxul
* Trigrand Hugequaxul
* Superior Hugequaxul, 200![200(1)200(1)200(1)200(1)200,200]
* Superior Kilohugequaxul, (200![200(1)200(1)200(1)200(1)200,200])![200(1)200(1)200(1)200(1)200,200]
* Superior Megahugequaxul, 200(![200(1)200(1)200(1)200(1)200,200])3
* Superior Grand Hugequaxul, 200(![200(1)200(1)200(1)200(1)200,200])200![200(1)200(1)200(1)200(1)200,200]+1
* Superior Grand Kilohugequaxul, 200(![200(1)200(1)200(1)200(1)200,200])200(![200(1)200(1)200(1)200(1)200,200])2+1
* Superior Grand Megahugequaxul, 200(![200(1)200(1)200(1)200(1)200,200])200(![200(1)200(1)200(1)200(1)200,200])3+1
* Superior Bigrand Hugequaxul
* Bisuperior Hugequaxul, 200![200(1)200(1)200(1)200(1)200,200,200]
* Bisuperior Kilohugequaxul, (200![200(1)200(1)200(1)200(1)200,200,200])![200(1)200(1)200(1)200(1)200,200,200]
* Bisuperior Megahugequaxul, 200(![200(1)200(1)200(1)200(1)200,200,200])3
* Bisuperior Grand Hugequaxul, 200(![200(1)200(1)200(1)200(1)200,200,200])200![200(1)200(1)200(1)200(1)200,200,200]+1
* Bisuperior Grand Kilohugequaxul
* Bisuperior Grand Megahugequaxul
* Bisuperior Bigrand Hugequaxul
* Ennacthulhum / ogdacthularxihect, E100#{7}#100
* Ennacthuloogol, {100,100[1[1\2¬2]1[1\2¬2]1[1\2¬2]1[1\2¬2]1[1\2¬2]2]2}
* Grand ennacthulhum, E100#{7}#100#2
* Grangol-carta-ennacthulhum, E100#{7}#100#100
* Godgahlah-carta-ennacthulhum, E100#{7}#100#^#100
* Tethrathoth-carta-ennactulhum, E100#{7}#100#^^#100
* Pentacthulhum-carta-ennacthulhum, E100#{7}#100#^^^#100
* hexacthulhum-carta-ennacthulhum, E100#{7}#100#^^^^#100
* Heptacthulhum-carta-ennacthulhum, E100#{7}#100#{5}#100
* Ogdacthulhum-carta-ennacthulhum, E100#{7}#100#{6}#100
* Ennacthulhum-carta-ennacthulhum / Ennacthulhum-by-deuteron, E100#{7}#100#{7}#100
* Deutero-ennacthulhum, E100#{7}#*#{7}#100
* Ennacthulhufact, E100(#{7}#)^#100
* Terrible ennacthulhum, E100(#{7}#)^^#100
* Horrible ennacthulhum, E100(#{7}#)^^^#100
* Horrendous ennacthulhum, E100(#{7}#)^^^^#100
* Ennacthuliterator / ennacthulhum ba'al, E100#{7}#>#100
* Grand ennacthuliterator / great and ennorredous ennacthulhum, E100#{7}#>#100#2
* Dustaculated ennacthulhum, E100#{7}#>#{7}#100
* Ennacthulcross, E100#{7}##100
* Ennacthulcubor, E100#{7}###100
* Ennacthultope, E100#{7}#^#100
* Ennacthularxitri, E100#{7}#{7}#100
* Dekacthulhum / ennacthularxihect, E100#{8}#100
* Dekacthuloogol, {100,100[1[1\2¬2]1[1\2¬2]1[1\2¬2]1[1\2¬2]1[1\2¬2]1[1\2¬2]2]2}
* Ennacthularxigigas, E100#{8}#500
* Ennacthularxichill, E100#{8}#1000
* Grand dekacthulhum, E100#{8}#100#2 = E100#{8}#dekacthulhum
* Deutero-dekacthulhum, E100#{8}#*#{8}#100
* Dekacthulcross, E100#{8}##100
* Dekacthularxitri / dekacthulto-dekacthulhum, E100#{8}#{8}#100
* Dekacthularxitet, E100#{8}#{8}#{8}#100 = E100#{9}#4
* Dekacthularxihect, E100#{9}#100
* ''Tridecatrix'', {10,10,10} & 10
* Goliath, E100#{10}#100 = E100#{#}#10
* Backongulus, {10,10[1[2\2¬2]2]2}
* Triadekacthuloogol, {100,10[1[2\2¬2]2]2}
* Icosacthuloogol, {100,17[1[2\2¬2]2]2}
* Golligog, E100#{50}#100 = E100#{#}#50
* Gollinoogol, {100,49[1[2\2¬2]2]2}
* Godsgodgulus, E100#{#}#100 = E100#{100}#100
* Godsgodgoogol, {100,99[1[2\2¬2]2]2}
* Godsgoduloogol, {100,100[1[2\2¬2]2]2}
* Joeligog, E100#{#}#203 = E100#{203}#100
* Gigantorgog, E100#{#}#500 = E100#{500}#100
* Godsgodgoogolchime, {100,999[1[2\2¬2]2]2}
* Godsgodgoogoltoll, {100,9999[1[2\2¬2]2]2}
* Godsgodgulusgong, E100,000#{#}#100,000
* Godsgodgoogolgong, {100,99999[1[2\2¬2]2]2}
* Pseuligog, E100#{#}#44435622 = E100#{44435622}#100
* Popacthulhum, E100#{#}#P = E100#{P}#100 where P is the world population right now (increases throughout time)
* Colossigog, E100#{#}#50,000,000,000,000,000 = E100#{50,000,000,000,000,000}#100
* Colossoogol, {100,5*10^16[1[2\2¬2]2]2}

=== Part 6.16: <math>f_{\varphi(\omega,0,0)}^2(10)</math> ~ <math>f_{\varphi(1,0,0,0)}^2(10)</math> ===

* Grand godsgodgulus, E100#{#}#100#2
* Grand grand godsgodgulus, E100#{#}#100#3
* Triple grand godsgodgulus, E100#{#}#100#4
* Quadruple grand godsgodgulus, E100#{#}#100#5
* Grangol-carta-godsgodgulus, E100#{#}#100#100
* Greagol-carta-godsgodgulus, E100#{#}#100#100#100
* Gigangol-carta-godsgodgulus, E100#{#}#100#100#100#100
* Godsgodgulus-by-deuteron, E100#{#}#100#{#}#100
* Godsgodgulus-by-triton, E100#{#}#100#{#}#100#{#}#100
* Godsgodgulus-by-teterton, E100#{#}#100#{#}#100#{#}#100#{#}#100
* Godsgodgulus-by-hyperion, E100#{#}#*#100
* Godsgodgulus-by-pentacthulhum, E100#{#}#*#^^^#100
* Deutero-godsgodgulus, E100#{#}#*#{#}#100
* Godsgodgulfact, E100(#{#}#)^#100
* Grideutergodsgodgulus / quadrata-godsgodgulus, E100(#{#}#)^##100
* Kubicugodsgodgulus / kubiku-godsgodgulus, E100(#{#}#)^###100
* Quarticugodsgodgulus / quarticu-godsgodgulus, E100(#{#}#)^####100
* Quinticu-godsgodgulus, E100(#{#}#)^#^#5
* Sexticu-godsgodgulus, E100(#{#}#)^#^#6
* Septicu-godsgodgulus, E100(#{#}#)^#^#7
* Octicu-godsgodgulus, E100(#{#}#)^#^#8
* Nonicu-godsgodgulus, E100(#{#}#)^#^#9
* Decicu-godsgodgulus, E100(#{#}#)^#^#10
* Godsgodgulipso-godgahlah, E100(#{#}#)^#^#100
* Godsgodgulipso-tethrathoth, E100(#{#}#)^#^^#100
* Godsgodgulipso-pentacthulhum, E100(#{#}#)^#^^^#100
* Godsgodgulipso-hexacthulhum, E100(#{#}#)^#^^^^#100
* Godsgodgulipso-heptacthulhum, E100(#{#}#)^#{5}#100
* Godsgodgulipso-odgacthulhum, E100(#{#}#)^#{6}#100
* Godsgodgulipso-ennacthulhum, E100(#{#}#)^#{7}#100
* Godsgodgulipso-deckacthulhum, E100(#{#}#)^#{8}#100
* Dutetrated-godsgodgulus, E100(#{#}#)^(#{#}#)100
* Tritetrated-godsgodgulus, E100(#{#}#)^(#{#}#)^(#{#}#)100
* Quadratetrated-godsgodgulus, E100(#{#}#)^(#{#}#)^(#{#}#)^(#{#}#)100
* Quinquatetrated-godsgodgulus, E100(#{#}#)^^#5
* Sexatetrated-godsgodgulus, E100(#{#}#)^^#6
* Septaquatetrated-godsgodgulus, E100(#{#}#)^^#7
* Octatetrated-godsgodgulus, E100(#{#}#)^^#8
* Nonatetrated-godsgodgulus, E100(#{#}#)^^#9
* Decatetrated-godsgodgulus, E100(#{#}#)^^#10
* Terrible godsgodgulus, E100(#{#}#)^^#100
* Terrisquared godsgodgulus, E100(#{#}#)^^##100
* Terricubed godsgodgulus, E100(#{#}#)^^###100
* Territesserated godsgodgulus, E100(#{#}#)^^####100
* Territoped godsgodgulus, E100(#{#}#)^^#^#100
* Tethrathoth-tetrated godsgodgulus, E100(#{#}#)^^#^^#100
* Pentacthulhum-tetrated godsgodgulus, E100(#{#}#)^^#^^^#100
* Hexacthulhum-tetrated godsgodgulus, E100(#{#}#)^^#^^^^#100
* Heptacthulhum-tetrated godsgodgulus, E100(#{#}#)^^#{5}#100
* Dupentated godsgodgulus, E100(#{#}#)^^(#{#}#)100
* Tripentated godsgodgulus, E100(#{#}#)^^(#{#}#)^^(#{#}#)100
* Quadrapentated godsgodgulus, E100(#{#}#)^^^#4
* Horrible godsgodgulus, E100(#{#}#)^^^#100
* Horrendous godsgodgulus, E100(#{#}#)^^^^#100
* Heptorrendous godsgodgulus, E100(#{#}#){5}#100
* Ogdorrendous godsgodgulus, E100(#{#}#){6}#100
* Ennorrendous godsgodgulus, E100(#{#}#){7}#100
* Dekorrendous godsgodgulus, E100(#{#}#){8}#100
* Godsgodeugulus, E100(#{#}#){#}#100
* Godsgodeugulusfact, E100((#{#}#){#}#)^#100
* Terrible godsgodeugulus, E100((#{#}#){#}#)^^#100
* Horrible godsgodeugulus, E100((#{#}#){#}#)^^^#100
* Horrendous godsgodeugulus, E100((#{#}#){#}#)^^^^#100
* Godsgotrigulus, E100((#{#}#){#}#){#}#100
* Godsgodguliterator / godsgodgulus ba'al, E100#{#}#>#100
* Grand godsgodguliterator / great and blasphemous godsgodgulus, E100#{#}#>#100#2
* Godsgodgulitertri, E100#{#}#>#100#{#}#>#100
* Godsgodgulitera-by-hyperion, E100#{#}#>#*#100
* Deutero-godsgodguliterator, E100#{#}#>#*#{#}#>#100
* Godsgodguliterfact, E100(#{#}#>#)^#100
* Terrible godsgodguliterator, E100(#{#}#>#)^^#100
* Horrible godsgodguliterator, E100(#{#}#>#)^^^#100
* Horrendous godsgodguliterator, E100(#{#}#>#)^^^^#100
* Godsgodgudous godsgodguliterator, E100(#{#}#>#){#}#100
* Godsgodgucubiterator, E100#{#}#>###100
* Tethrathoth-tetrated godsgodgulus, E100#{#}#>#^^#100
* Pentacthulhum-tetrated godsgodgulus, E100#{#}#>#^^^#100
* Hexacthulhum-tetrated godsgodgulus, E100#{#}#>#^^^^#100
* Dustaculated godsgodgulus, E100#{#}#>#{#}#100
* Tristaculated godsgodgulus, E100#{#}#>#{#}#>#{#}#100
* Tetrastaculated godsgodgulus, E100#{#}#>#{#}#>#{#}#>#{#}#100
* Pentastaculated godsgodgulus, E100#{#}##5
* Hexastaculated godsgodgulus, E100#{#}##6
* Heptastaculated godsgodgulus, E100#{#}##7
* Ogdastaculated godsgodgulus, E100#{#}##8
* Ennastaculated godsgodgulus, E100#{#}##9
* Dekastaculated godsgodgulus, E100#{#}##10
* Godsgodgulcross, E100#{#}##100
* Grand godsgodgulcross, E100#{#}##100#2
* Godsgodgulcross-by-deuteron, E100#{#}##100#{#}##100
* Godsgodgulcross-by-hyperion, E100#{#}##*#100
* Godsgodgulcrossafact, E100(#{#}##)^#100
* Terrible godsgodgulcross, E100(#{#}##)^^#100
* Horrible godsgodgulcross, E100(#{#}##)^^^#100
* Horrendous godsgodgulcross, E100(#{#}##)^^^^#100
* Godsgodgulcro-godsgodgulus, E100(#{#}##){#}#100
* Godsgodguldeucross, E100(#{#}##){#}##100
* Godsgodgultricross, E100#{#}##>#3
* Godsgodgultercross, E100#{#}##>#100
* Godsgodgugridtercross, E100#{#}##>##100
* Dustaculated godsgodgulcross, E100#{#}##>#{#}##100
* Tristaculated godsgodgulcross, E100#{#}###3
* Tetrastaculated godsgodgulcross, E100#{#}###4
* Godsgodgulcubor, E100#{#}###100
* Godsgodgulteron, E100#{#}####100
* Godsgodgultope, E100#{#}#^#100
* Godsgodarxitri, E100#{#}#{#}#100
* Godsgodarxitet, E100#{#}#{#}#{#}#100
* Godsgodgulhenus, E100#{#+1}#100
* Godsgodguliterhenus, E100#{#+1}#>#100
* Godsgodgulhencross, E100#{#+1}##100
* Godsgodgulhencubor, E100#{#+1}###100
* Godsgodgulhentope, E100#{#+1}#^#100
* Godsgodeus, E100#{#+#}#100
* Godsgotreus, E100#{#+#+#}#100
* Godsgoquadeus, E100#{#+#+#+#}#100
* Godsgridoogol, {100,100[1[3\2¬2]2]2}
* Godskubioogol, {100,100[1[4\2¬2]2]2}
* Godsquartioogol, {100,100[1[5\2¬2]2]2}
* Centuroogol, {100,100[1[1,2\2¬2]2]2}
* The centurion, E100#{#^#}#100
* Super centurion, E100#{#^^#}#100
* Pentacthulhu-centurion, E100#{#^^^#}#100
* Hexacthulhu-centurion, E100#{#^^^^#}#100
* Ohmygosh-ohmygosh-ohmygooosh / godsgodgul-centurion, E100#{#{#}#}#100
* Bexommthet, <math>f_{\theta(\Omega^2,0)}(10)</math>
* Blasphemorbackulus, {10,10[1[1\3¬2]2]2}
* Blasphemorgulus, E100{#,#,1,2}100
* ''Gonguldeus'', {10,100,1,2} & 10
* Blasphemorgoogol, {100,100[1[1\3¬2]2]2}

=== Part 6.17: <math>f_{\varphi(1,0,0,0)}^2(10)</math> ~ <math>f_{\varphi(1,0,0,0,0)}^2(10)</math> ===

* Grand blasphemorgulus, E100{#,#,1,2}100#2
* Grand grand blasphemorgulus, E100{#,#,1,2}100#3
* Grangol-carta-blasphemorgulus, E100{#,#,1,2}100#100
* Greagol-carta-blasphemorgulus, E100{#,#,1,2}100#100#100
* Blasphemorgulus-by-deuteron, E100{#,#,1,2}100{#,#,1,2}100
* Blasphemorgulus-by-hyperion, E100{#,#,1,2}*#100
* Deutero-blasphemorgulus, E100{#,#,1,2}*{#,#,1,2}100
* Blasphemorgulfact, E100({#,#,1,2})^#100
* Terrible blasphemorgulus, E100({#,#,1,2})^^#100
* Horrible blasphemorgulus, E100({#,#,1,2})^^^#100
* Horrendous blasphemorgulus, E100({#,#,1,2})^^^^#100
* Blasphemormygosh-blasphemormygosh, E100({#,#,1,2}){{#,#,1,2}}({#,#,1,2})100
* <nowiki>Tweilasphemorgue, E100{{#,#,1,2},100,1,2}100</nowiki>
* Frielasphemorgue, E100{#,#+1,1,2}3
* Fiorilasphemorgue, E100{#,#+1,1,2}4
* Finnasphemorgue, E100{#,#+1,1,2}5
* Sexasphemorgue, E100{#,#+1,1,2}6
* Sjournalasphemorgue, E100{#,#+1,1,2}7
* Attalasphemorgue, E100{#,#+1,1,2}8
* Neiulasphemorgue, E100{#,#+1,1,2}9
* Tenasphemorgue, E100{#,#+1,1,2}10
* <nowiki>Blasphemorguliterator, E100#{{1}}#>#100</nowiki>
* Hundrelasphemorgue, E100{#,#+1,1,2}100
* Enormaxul, 200![200(2)200]
* Thouselasphemorgue, E100{#,#+1,1,2}1,000
* Milliasphemorgue, E100{#,#+1,1,2}1,000,000
* Kiloenormaxul, (200![200(2)200])![200(2)200]
* Megaenormaxul, ((200![200(2)200])![200(2)200])![200(2)200]
* Gigaenormaxul, (((200![200(2)200])![200(2)200])![200(2)200])![200(2)200]
* Teraenormaxul, 200(![200(2)200])5
* Petaenormaxul, 200(![200(2)200])6
* Exaenormaxul, 200(![200(2)200])7
* Grand Enormaxul, 200(![200(2)200])200![200(2)200]+1
* Grand Kiloenormaxul, 200(![200(2)200])(200![200(2)200])![200(2)200]+1
* Grand Megaenormaxul, 200(![200(2)200])((200![200(2)200])![200(2)200])![200(2)200]+1
* Grand Gigaenormaxul, 200(![200(2)200])200(![200(2)200])4+1
* Grand Teraenormaxul, 200(![200(2)200])200(![200(2)200])5+1
* Grand Petaenormaxul, 200(![200(2)200])200(![200(2)200])6+1
* Grand Exaenormaxul, 200(![200(2)200])200(![200(2)200])7+1
* Bigrand Enormaxul, 200(![200(2)200])200(![200(2)200])200![200(2)200]+1+1
* Bigrand Kiloenormaxul, 200(![200(2)200])200(![200(2)200])(200![200(2)200])![200(2)200]+1+1
* Bigrand Megaenormaxul, 200(![200(2)200])200(![200(2)200])((200![200(2)200])![200(2)200])![200(2)200]+1+1
* Trigrand Enormaxul, 200(![200(2)200])200(![200(2)200])200(![200(2)200])200![200(2)200]+1+1+1
* Trigrand Kiloenormaxul, 200(![200(2)200])200(![200(2)200])200(![200(2)200])200(![200(2)200])2+1+1+1
* Trigrand Megaenormaxul, 200(![200(2)200])200(![200(2)200])200(![200(2)200])200(![200(2)200])3+1+1+1
* Quadgrand Enormaxul, 200(![200(2)200])200(![200(2)200])200(![200(2)200])200(![200(2)200])200![200(2)200]+1+1+1+1
* Quintgrand Enormaxul
* Superior Enormaxul, 200![200(2)200,200]
* Superior Kiloenormaxul, (200![200(2)200,200])![200(2)200,200]
* Superior Megaenormaxul, ((200![200(2)200,200])![200(2)200,200])![200(2)200,200]
* Superior Gigaenormaxul, (((200![200(2)200,200])![200(2)200,200])![200(2)200,200])![200(2)200,200]
* Superior Grand Enormaxul, 200(![200(2)200,200])200![200(2)200,200]+1
* Superior Grand Kiloenormaxul, 200(![200(2)200,200])(200![200(2)200,200])![200(2)200,200]+1
* Superior Grand Megaenormaxul, 200(![200(2)200,200])((200![200(2)200,200])![200(2)200,200])![200(2)200,200]+1
* Superior Grand Gigaenormaxul, 200(![200(2)200,200])(((200![200(2)200,200])![200(2)200,200])![200(2)200,200])![200(2)200,200]+1
* Superior Bigrand Enormaxul, 200(![200(2)200,200])200(![200(2)200,200])200![200(2)200,200]+1+1
* Superior Trigrand Enormaxul, 200(![200(2)200,200])200(![200(2)200,200])200(![200(2)200,200])200![200(2)200,200]+1+1+1
* Bisuperior Enormaxul, 200![200(2)200,200,200]
* Bisuperior Kiloenormaxul, (200![200(2)200,200,200])![200(2)200,200,200]
* Bisuperior Megaenormaxul, ((200![200(2)200,200,200])![200(2)200,200,200])![200(2)200,200,200]
* Bisuperior Gigaenormaxul, (((200![200(2)200,200,200])![200(2)200,200,200])![200(2)200,200,200])![200(2)200,200,200]
* Bisuperior Grand Enormaxul, 200(![200(2)200,200,200])200![200(2)200,200,200]+1
* Bisuperior Grand Kiloenormaxul, 200(![200(2)200,200,200])(200![200(2)200,200,200])![200(2)200,200,200]+1
* Bisuperior Grand Megaenormaxul, 200(![200(2)200,200,200])200(![200(2)200,200,200])3+1
* Bisuperior Grand Gigaenormaxul, 200(![200(2)200,200,200])200(![200(2)200,200,200])4+1
* Bisuperior Bigrand Enormaxul, 200(![200(2)200,200,200])200(![200(2)200,200,200])200![200(2)200,200,200]+1+1
* Bisuperior Trigrand Enormaxul
* ''Ludicriss'', E100&(1)100
* ''Grand ludicriss'', E100&(1)100#2
* ''Blasphemorgulcross'', <nowiki>E100#{{1}}##100</nowiki>
* ''Agoraphobia'', E100&(&(&(...(&(&({#,#,1,2})))...))) with 100 &'s ~ E100#*^#100
* ''Gongultreus'', {10,100,1,3} & 10
* ''Grand agoraphobia'', E100&(&(...&({#,#,1,2})... ))100 w/agoraphobia &'s
* ''Blasphemorgulcubor'', <nowiki>E100#{{1}}###100</nowiki>
* ''Astralthrathoth'', E100#*^^#100
* ''Blasphemorgultope'', <nowiki>E100#{{1}}#^#100</nowiki>
* ''Blasphemorgularxitri'', <nowiki>E100#{{1}}#{{1}}#100</nowiki>
* ''Blasphemordeugulus'', <nowiki>E100#{{2}}#100</nowiki>
* ''Mulporatrix'', {10,100,2,2} & 10
* ''Tethrathoth-carta-blasphemordeugulus, <nowiki>E100#{{2}}#100#^^#100</nowiki>''
* ''Pentacthulhum-carta-blasphemordeugulus, <nowiki>E100#{{2}}#100#^^^#100</nowiki>''
* ''Hexacthulhum-carta-blasphemordeugulus, <nowiki>E100#{{2}}#100#^^^^#100</nowiki>''
* ''Godsgodgulus-carta-blasphemordeugulus, <nowiki>E100#{{2}}#100#{#}#100</nowiki>''
* ''Blasphemorgulus-carta-blasphemordeugulus, <nowiki>E100#{{2}}#100#{{1}}#100</nowiki>''
* ''Blasphemordeugulus-by-deuteron, <nowiki>E100#{{2}}#100#{{2}}#100</nowiki>''
* ''Blasphemordeugulus-by-triton, <nowiki>E100#{{2}}#100#{{2}}#100#{{2}}#100</nowiki>''
* ''Blasphemordeugulus-by-teterton, <nowiki>E100#{{2}}#100#{{2}}#100#{{2}}#100#{{2}}#100</nowiki>''
* ''Blasphemordeugulus-by-hyperion, <nowiki>E100#{{2}}#*#100</nowiki>''
* ''Blasphemortrigulus'', <nowiki>E100#{{3}}#100</nowiki>
* ''Humingulus'', {10,10,100,2} & 10
* ''Deusus-godsgodgogle'', <nowiki>E100#{{#}}#100</nowiki>
* ''Gongultreus'', {10,100,1,3} & 10
* ''Trilasphemorgulus'' / Blasphemorguldeus, <nowiki>E100#{{{1}}}#100</nowiki>
* Enormabixul, 200![200(2)200(2)200]
* Kiloenormabixul, (200![200(2)200(2)200])![200(2)200(2)200]
* Megaenormabixul, ((200![200(2)200(2)200])![200(2)200(2)200])![200(2)200(2)200]
* Gigaenormabixul, (((200![200(2)200(2)200])![200(2)200(2)200])![200(2)200(2)200])![200(2)200(2)200]
* Grand Enormabixul, 200(![200(2)200(2)200])200![200(2)200(2)200]+1
* Grand Kiloenormabixul, 200(![200(2)200(2)200])(200![200(2)200(2)200])![200(2)200(2)200]+1
* Grand Megaenormabixul, 200(![200(2)200(2)200])((200![200(2)200(2)200])![200(2)200(2)200])![200(2)200(2)200]+1
* Grand Gigaenormabixul, 200(![200(2)200(2)200])200(![200(2)200(2)200])4+1
* Bigrand Enormabixul, 200(![200(2)200(2)200])200(![200(2)200(2)200])200![200(2)200(2)200]+1+1
* Trigrand Enormabixul
* Superior Enormabixul, 200![200(2)200(2)200,200]
* Superior Kiloenormabixul, (200![200(2)200(2)200,200])![200(2)200(2)200,200]
* Superior Megaenormabixul, ((200![200(2)200(2)200,200])![200(2)200(2)200,200])![200(2)200(2)200,200]
* Superior Grand Enormabixul, 200(![200(2)200(2)200,200])200![200(2)200(2)200,200]+1
* Superior Grand Kiloenormabixul, 200(![200(2)200(2)200,200])(200![200(2)200(2)200,200])![200(2)200(2)200,200]+1
* Superior Grand Megaenormabixul, 200(![200(2)200(2)200,200])200(![200(2)200(2)200,200])3+1
* Superior Bigrand Enormabixul, 200(![200(2)200(2)200,200])200(![200(2)200(2)200,200])200![200(2)200(2)200,200]+1+1
* Bisuperior Enormabixul, 200![200(2)200(2)200,200,200]
* Bisuperior Kiloenormabixul, (200![200(2)200(2)200,200,200])![200(2)200(2)200,200,200]
* Bisuperior Megaenormabixul, ((200![200(2)200(2)200,200,200])![200(2)200(2)200,200,200])![200(2)200(2)200,200,200]
* Bisuperior Grand Enormabixul, 200(![200(2)200(2)200,200,200])200![200(2)200(2)200,200,200]+1
* Bisuperior Grand Kiloenormabixul, 200(![200(2)200(2)200,200,200])(200![200(2)200(2)200,200,200])![200(2)200(2)200,200,200]+1
* Bisuperior Grand Megaenormabixul, 200(![200(2)200(2)200,200,200])200(![200(2)200(2)200,200,200])3+1
* Bisuperior Bigrand Enormabixul
* ''Blasphemordeuguldeus'', <nowiki>E100#{{{2}}}#100</nowiki>
* ''Treusus-godsgodgogle'', <nowiki>E100#{{{#}}}#100</nowiki>
* ''Humangulus'', {10,10,100,3} & 10
* ''Blasphemorgultruce'', <nowiki>E100#{{{{1}}}}#100</nowiki>
* ''Gongulquadeus'', {10,100,1,4} & 10
* Enormatrixul, 200![200(2)200(2)200(2)200]
* Kiloenormatrixul, (200![200(2)200(2)200(2)200])![200(2)200(2)200(2)200]
* Megaenormatrixul, ((200![200(2)200(2)200(2)200])![200(2)200(2)200(2)200])![200(2)200(2)200(2)200]
* Gigaenormatrixul, 200(![200(2)200(2)200(2)200])4
* Grand Enormatrixul, 200(![200(2)200(2)200(2)200])200![200(2)200(2)200(2)200]+1
* Grand Kiloenormatrixul, 200(![200(2)200(2)200(2)200])(200![200(2)200(2)200(2)200])![200(2)200(2)200(2)200]+1
* Grand Megaenormatrixul, 200(![200(2)200(2)200(2)200])200(![200(2)200(2)200(2)200])3+1
* Grand Gigaenormatrixul, 200(![200(2)200(2)200(2)200])200(![200(2)200(2)200(2)200])4+1
* Bigrand Enormatrixul, 200(![200(2)200(2)200(2)200])200(![200(2)200(2)200(2)200])200![200(2)200(2)200(2)200]+1+1
* Trigrand Enormatrixul
* Superior Enormatrixul, 200![200(2)200(2)200(2)200,200]
* Superior Kiloenormatrixul, (200![200(2)200(2)200(2)200,200])![200(2)200(2)200(2)200,200]
* Superior Megaenormatrixul, ((200![200(2)200(2)200(2)200,200])![200(2)200(2)200(2)200,200])![200(2)200(2)200(2)200,200]
* Superior Grand Enormatrixul, 200(![200(2)200(2)200(2)200,200])200![200(2)200(2)200(2)200,200]+1
* Superior Grand Kiloenormatrixul, 200(![200(2)200(2)200(2)200,200])200(![200(2)200(2)200(2)200,200])2+1
* Superior Grand Megaenormatrixul, 200(![200(2)200(2)200(2)200,200])200(![200(2)200(2)200(2)200,200])3+1
* Superior Bigrand Enormatrixul
* Bisuperior Enormatrixul, 200![200(2)200(2)200(2)200,200,200]
* Bisuperior Kiloenormatrixul, (200![200(2)200(2)200(2)200,200,200])![200(2)200(2)200(2)200,200,200]
* Bisuperior Megaenormatrixul, ((200![200(2)200(2)200(2)200,200,200])![200(2)200(2)200(2)200,200,200])![200(2)200(2)200(2)200,200,200]
* Bisuperior Grand Enormatrixul, 200(![200(2)200(2)200(2)200,200,200])200![200(2)200(2)200(2)200,200,200]+1
* Bisuperior Grand Kiloenormatrixul, 200(![200(2)200(2)200(2)200,200,200])200(![200(2)200(2)200(2)200,200,200])2+1
* Bisuperior Grand Megaenormatrixul, 200(![200(2)200(2)200(2)200,200,200])200(![200(2)200(2)200(2)200,200,200])3+1
* Bisuperior Bigrand Enormatrixul
* ''Quadeusus-godsgodgogle'', <nowiki>E100#{{{{#}}}}#100</nowiki>
* ''Humeengulus'', {10,10,100,4} & 10
* ''Blasphemorgulquad'', <nowiki>E100#{{{{{1}}}}}#100</nowiki>
* ''Gongulquideus'', {10,100,1,5} & 10
* Enormaquaxul, 200![200(2)200(2)200(2)200(2)200]
* Kiloenormaquaxul, (200![200(2)200(2)200(2)200(2)200])![200(2)200(2)200(2)200(2)200]
* Megaenormaquaxul, ((200![200(2)200(2)200(2)200(2)200])![200(2)200(2)200(2)200(2)200])![200(2)200(2)200(2)200(2)200]
* Gigaenormaquaxul, 200(![200(2)200(2)200(2)200(2)200])4
* Grand Enormaquaxul, 200(![200(2)200(2)200(2)200(2)200])200![200(2)200(2)200(2)200(2)200]+1
* Grand Kiloenormaquaxul, 200(![200(2)200(2)200(2)200(2)200])200(![200(2)200(2)200(2)200(2)200])2+1
* Grand Megaenormaquaxul, 200(![200(2)200(2)200(2)200(2)200])200(![200(2)200(2)200(2)200(2)200])3+1
* Grand Gigaenormaquaxul, 200(![200(2)200(2)200(2)200(2)200])200(![200(2)200(2)200(2)200(2)200])4+1
* Bigrand Enormaquaxul
* Trigrand Enormaquaxul
* Superior Enormaquaxul, 200![200(2)200(2)200(2)200(2)200,200]
* Superior Kiloenormaquaxul, (200![200(2)200(2)200(2)200(2)200,200])![200(2)200(2)200(2)200(2)200,200]
* Superior Megaenormaquaxul, 200(![200(2)200(2)200(2)200(2)200,200])3
* Superior Grand Enormaquaxul, 200(![200(2)200(2)200(2)200(2)200,200])200![200(2)200(2)200(2)200(2)200,200]+1
* Superior Grand Kiloenormaquaxul, 200(![200(2)200(2)200(2)200(2)200,200])200(![200(2)200(2)200(2)200(2)200,200])2+1
* Superior Grand Megaenormaquaxul, 200(![200(2)200(2)200(2)200(2)200,200])200(![200(2)200(2)200(2)200(2)200,200])3+1
* Superior Bigrand Enormaquaxul
* Bisuperior Enormaquaxul, 200![200(2)200(2)200(2)200(2)200,200,200]
* Bisuperior Kiloenormaquaxul, (200![200(2)200(2)200(2)200(2)200,200,200])![200(2)200(2)200(2)200(2)200,200,200]
* Bisuperior Megaenormaquaxul, 200(![200(2)200(2)200(2)200(2)200,200,200])3
* Bisuperior Grand Enormaquaxul, 200(![200(2)200(2)200(2)200(2)200,200,200])200![200(2)200(2)200(2)200(2)200,200,200]+1
* Bisuperior Grand Kiloenormaquaxul
* Bisuperior Grand Megaenormaquaxul
* Bisuperior Bigrand Enormaquaxul
* ''Humowngulus'', {10,10,100,5} & 10
* ''Gongulsideus'', {10,100,1,6} & 10
* ''Humungulus'', {10,10,100,6} & 10
* Super Even More Godder Tritri, 3 [3 {3 <3 / 3> 3} 3] 3
* ''Generatrix'', {10,10,10,10} & 10
* ''Gorgonghoulgog'', E100*(#)100
* ''General gogulus'', E100{#,#,#,#}100
* ''Grand gorgonghoulgog'', E100*(#)100#2
* ''The gathering''
* ''Blasphemorgulus regiment|Howling gorgonghoulgog'', E100*(*(#))100
* ''Blasphemorgulus regiment|Howling howling gorgonghoulgog'', E100*(*(*(#)))100
* Trexommthet, <math>f_{\theta(\Omega^3,0)}(10)</math>
* Blasphemormegabackulus / mega blasphemorbackulus, {10,10[1[1\4¬2]2]2}
* ''Transmorgrifihgh'', E100*(*(...*(*(#))...))100 w/100 *'s ~ E100#/^#100
* Mega blasphemorgoogol, {100,100[1[1\4¬2]2]2}

=== Part 6.18: <math>f_{\varphi(1,0,0,0,0)}^2(10)</math> ~ <math>f_{\psi_0(\Omega^{\Omega^\omega})}^2(10)</math> ===
* ''Incridulus'', {10,10,10,100,2} & 10
* ''Incradulus'', {10,10,10,100,3} & 10
* ''Increedulus'', {10,10,10,100,4} & 10
* ''Incrowdulus'', {10,10,10,100,5} & 10
* ''Incrundulus'', {10,10,10,100,6} & 10
* ''Pendecatrix'', {10,10,10,10,10} & 10 = 5 & 10 & 10
* ''Tercredulus'', {10,10,10,10,100} & 10
* Quadrexommthet, <math>f_{\theta(\Omega^4,0)}(10)</math>
* ''Tercridulus'', {10,10,10,10,100,2} & 10
* ''Tercradulus'', {10,10,10,10,100,3} & 10
* ''Tercreedulus'', {10,10,10,10,100,4} & 10
* ''Tercrowdulus'', {10,10,10,10,100,5} & 10
* ''Hexdecatrix'', {10,10,10,10,10,10} & 10 = 6 & 10 & 10
* ''Pencredulus'', {10,10,10,10,10,100} & 10
* Quintexommthet, <math>f_{\theta(\Omega^5,0)}(10)</math>
* ''Pencridulus'', {10,10,10,10,10,100,2} & 10
* ''Pencradulus'', {10,10,10,10,10,100,3} & 10
* ''Pencreedulus'', {10,10,10,10,10,100,4} & 10
* ''Excredulus'', {10,10,10,10,10,10,100} & 10
* Sextexommthet, <math>f_{\theta(\Omega^6,0)}(10)</math>
* ''Excridulus'', {10,10,10,10,10,10,100,2} & 10
* ''Excradulus'', {10,10,10,10,10,10,100,3} & 10
* ''Excreedulus'', {10,10,10,10,10,10,100,4} & 10
* ''Epcredulus'', {10,10,10,10,10,10,10,100} & 10
* Septexommthet, <math>f_{\theta(\Omega^7,0)}(10)</math>
* ''Ogcredulus'', {10,10,10,10,10,10,10,10,100} & 10
* ''Lineatrix'', 10 & 10 & 10
* Octexommthet, <math>f_{\theta(\Omega^8,0)}(10)</math>
* ''Encredulus'', {10,10,10,10,10,10,10,10,10,100} & 10
* Demagoogol, {100,100[1[1\9¬2]2]2}
* ''Demagogue'', E100{#,10(1)2}100
* Nonexommthet, <math>f_{\theta(\Omega^9,0)}(10)</math>
* ''Decredulus'', {10,10,10,10,10,10,10,10,10,10,100} & 10
* Dekexommthet, <math>f_{\theta(\Omega^{10},0)}(10)</math>
* Small veblasphemorbackulus, {10,10[1[1\1,2¬2]2]2}
* Ominongoogol, {100,100[1[1\1,2¬2]2]2}
* ''Goobawamba'', <math>\{10,100 (1) 2\}\ \&\ 10</math>
* Small veblasphemorgoogol, {100,100[1[1\1,2¬2]2]2}
* Hektexommthet, <math>f_{\theta(\Omega^{100},0)}(10)</math>
* ''Ominongulus'', E100{#,100(1)2}100
* Destruxul, 200![200(200)200]
* Kilodestruxul, (200![200(200)200])![200(200)200]
* Megadestruxul, ((200![200(200)200])![200(200)200])![200(200)200]
* Gigadestruxul, (((200![200(200)200])![200(200)200])![200(200)200])![200(200)200]
* Teradestruxul, 200(![200(200)200])5
* Petadestruxul, 200(![200(200)200])6
* Exadestruxul, 200(![200(200)200])7
* Grand Destruxul, 200(![200(200)200])200![200(200)200]+1
* Grand Kilodestruxul, 200(![200(200)200])(200![200(200)200])![200(200)200]+1
* Grand Megadestruxul, 200(![200(200)200])((200![200(200)200])![200(200)200])![200(200)200]+1
* Grand Gigadestruxul, 200(![200(200)200])200(![200(200)200])4+1
* Grand Teradestruxul, 200(![200(200)200])200(![200(200)200])5+1
* Grand Petadestruxul, 200(![200(200)200])200(![200(200)200])6+1
* Grand Exadestruxul, 200(![200(200)200])200(![200(200)200])7+1
* Bigrand Destruxul, 200(![200(200)200])200(![200(200)200])200![200(200)200]+1+1
* Bigrand Kilodestruxul, 200(![200(200)200])200(![200(200)200])(200![200(200)200])![200(200)200]+1+1
* Bigrand Megadestruxul, 200(![200(200)200])200(![200(200)200])((200![200(200)200])![200(200)200])![200(200)200]+1+1
* Trigrand Destruxul, 200(![200(200)200])200(![200(200)200])200(![200(200)200])200![200(200)200]+1+1+1
* Trigrand Kilodestruxul
* Quadgrand Destruxul
* Quintgrand Destruxul
* Great Destruxul, 200![200(200)200(200)200]
* Great Kilodestruxul, (200![200(200)200(200)200])![200(200)200(200)200]
* Great Megadestruxul, ((200![200(200)200(200)200])![200(200)200(200)200])![200(200)200(200)200]
* Great Gigadestruxul, (((200![200(200)200(200)200])![200(200)200(200)200])![200(200)200(200)200])![200(200)200(200)200]
* Great Grand Destruxul, 200(![200(200)200(200)200])200![200(200)200(200)200]+1
* Great Grand Kilodestruxul, 200(![200(200)200(200)200])(200![200(200)200(200)200])![200(200)200(200)200]+1
* Great Grand Megadestruxul, 200(![200(200)200(200)200])200(![200(200)200(200)200])3+1
* Great Grand Gigadestruxul, 200(![200(200)200(200)200])200(![200(200)200(200)200])4+1
* Great Bigrand Destruxul, 200(![200(200)200(200)200])200(![200(200)200(200)200])200![200(200)200(200)200]+1+1
* Great Trigrand Destruxul
* Bigreat Destruxul, 200![200(200)200(200)200(200)200]
* Bigreat Kilodestruxul, (200![200(200)200(200)200(200)200])![200(200)200(200)200(200)200]
* Bigreat Megadestruxul, ((200![200(200)200(200)200(200)200])![200(200)200(200)200(200)200])![200(200)200(200)200(200)200]
* Bigreat Gigadestruxul, (((200![200(200)200(200)200(200)200])![200(200)200(200)200(200)200])![200(200)200(200)200(200)200])![200(200)200(200)200(200)200]
* Bigreat Grand Destruxul, 200(![200(200)200(200)200(200)200])200![200(200)200(200)200(200)200]+1
* Bigreat Grand Kilodestruxul, 200(![200(200)200(200)200(200)200])200(![200(200)200(200)200(200)200])2+1
* Bigreat Grand Megadestruxul, 200(![200(200)200(200)200(200)200])200(![200(200)200(200)200(200)200])3+1
* Bigreat Grand Gigadestruxul, 200(![200(200)200(200)200(200)200])200(![200(200)200(200)200(200)200])4+1
* Bigreat Bigrand Destruxul
* Bigreat Trigrand Destruxul
* Võro, <math>f_{\psi_0(\Omega^{\Omega^\omega})}(420)</math> in the fast-growing hierarchy (using the extended Buchholz's function, ψ0(Ω^Ω^ω) denotes the small Veblen ordinal)
* Kilexommthet, <math>f_{\theta(\Omega^{1000},0)}(10)</math>
* Megexommthet, <math>f_{\theta(\Omega^{10^6},0)}(10)</math>
* ''Pseudomonarchia daemonum'', E100#{#,#(1)2}44,435,622
* Gigexommthet, <math>f_{\theta(\Omega^{10^9},0)}(10)</math>
* Terexommthet, <math>f_{\theta(\Omega^{10^{12}},0)}(10)</math>
* Petexommthet, <math>f_{\theta(\Omega^{10^{15}},0)}(10)</math>
* Exexommthet, <math>f_{\theta(\Omega^{10^{18}},0)}(10)</math>
* Zettexommthet, <math>f_{\theta(\Omega^{10^{21}},0)}(10)</math>
* Yottexommthet, <math>f_{\theta(\Omega^{10^{24}},0)}(10)</math>
* ''Dorsatrix'', <math>\{10,(10^{100}) (1) 2\}\ \&\ 10</math>
* ''Lineatrixplex'', {10,lineatrix(1)2} & 10

=== Part 6.19: <math>f_{\psi_0(\Omega^{\Omega^\omega})}^2(10)</math> ~ <math>f_{\psi_0(\Omega^{\Omega^\Omega})}^2(10)</math> ===
* ''Grand ominongulus'', E100{#,#(1)2}100#2
* ''Grangol-carta-ominongulus'', E100{#,#(1)2}100#100
* Bird's number, <math>\approx f_{\vartheta(\Omega^{\omega})+2}(f_{\vartheta(\Omega^{\omega})+1}(f_{\vartheta(\Omega^{\omega})}(f_{\vartheta(\Omega^{\omega})}(7))))</math>
* ''Godgahlah-carta-ominongulus'', E100{#,#(1)2}100#^#100
* ''Godsgodgulus-carta-ominongulus'', E100{#,#(1)2}100#{#}#100
* ''Ominongulus-by-deuteron'', E100{#,#(1)2}100{#,#(1)2}100
* ''Ominongulus-by-triton'', E100{#,#(1)2}100{#,#(1)2}100{#,#(1)2}100
* '''TREE sequence|TREE[3]''' (lower bound)
* Treegol (BlankEntity) (TREE[10100])
* Factoree, (TREE[200!] = TREE(7.88657867365 × 10374])
* Apple Tree (TREE[Apple])
* Fresh Xeno-Nobel-Multidimensional Stardust Onion from the future (TREE[gonion])
* Egg Salad (TREE[g{Egg,Egg(Egg,Egg)Egg,Egg}!1010100])
* Multiversoogol, {100,100[1[2\1,2¬2]2]2}
* Metaversoogol, {100,100[1[1\1,1,2¬2]1[1[3\2¬2]1[3\2¬2]1[3\2¬2]1[3\2¬2]2]2]2}
* ''Bixtendol'', s(3,3{1``2}2)
* Destrubixul, 200![200([200(200)200])200]
* Kilodestrubixul, (200![200([200(200)200])200])![200([200(200)200])200]
* Megadestrubixul, 200(![200([200(200)200])200])3
* Gigadestrubixul, 200(![200([200(200)200])200])4
* Grand Destrubixul, 200(![200([200(200)200])200])200![200([200(200)200])200]+1
* Grand Kilodestrubixul, 200(![200([200(200)200])200])(200![200([200(200)200])200])![200([200(200)200])200]+1
* Grand Megadestrubixul, 200(![200([200(200)200])200])200(![200([200(200)200])200])3+1
* Grand Gigadestrubixul, 200(![200([200(200)200])200])200(![200([200(200)200])200])4+1
* Bigrand Destrubixul, 200(![200([200(200)200])200])200(![200([200(200)200])200])200![200([200(200)200])200]+1+1
* Trigrand Destrubixul
* Great Destrubixul, 200![200([200(200)200(200)200])200(200)200]
* Great Kilodestrubixul, 200(![200([200(200)200(200)200])200(200)200])2
* Great Megadestrubixul, 200(![200([200(200)200(200)200])200(200)200])3
* Great Grand Destrubixul
* Great Grand Kilodestrubixul
* Great Grand Megadestrubixul
* Great Bigrand Destrubixul
* Bigreat Destrubixul, 200![200([200(200)200(200)200(200)200])200(200)200(200)200]
* Bigreat Kilodestrubixul, 200(![200([200(200)200(200)200(200)200])200(200)200(200)200])2
* Bigreat Megadestrubixul, 200(![200([200(200)200(200)200(200)200])200(200)200(200)200])3
* Bigreat Grand Destrubixul
* Bigreat Grand Kilodestrubixul
* Bigreat Grand Megadestrubixul
* Bigreat Bigrand Destrubixul
* Destrutrixul, 200![200([200([200(200)200])200])200]
* Kilodestrutrixul, 200(![200([200([200(200)200])200])200])2
* Megadestrutrixul, 200(![200([200([200(200)200])200])200])3
* Gigadestrutrixul, 200(![200([200([200(200)200])200])200])4
* Grand Destrutrixul, 200(![200([200([200(200)200])200])200])200![200([200([200(200)200])200])200]+1
* Grand Kilodestrutrixul, 200(![200([200([200(200)200])200])200])200(![200([200([200(200)200])200])200])2+1
* Grand Megadestrutrixul, 200(![200([200([200(200)200])200])200])200(![200([200([200(200)200])200])200])3+1
* Grand Gigadestrutrixul, 200(![200([200([200(200)200])200])200])200(![200([200([200(200)200])200])200])4+1
* Bigrand Destrutrixul
* Trigrand Destrutrixul
* Great Destrutrixul, 200![200([200([200(200)200(200)200])200(200)200])200(200)200]
* Great Kilodestrutrixul, 200(![200([200([200(200)200(200)200])200(200)200])200(200)200])2
* Great Megadestrutrixul, 200(![200([200([200(200)200(200)200])200(200)200])200(200)200])3
* Great Grand Destrutrixul
* Great Grand Kilodestrutrixul
* Great Grand Megadestrutrixul
* Great Bigrand Destrutrixul
* Bigreat Destrutrixul, 200![200([200([200(200)200(200)200(200)200])200(200)200(200)200])200(200)200(200)200]
* Bigreat Kilodestrutrixul, 200(![200([200([200(200)200(200)200(200)200])200(200)200(200)200])200(200)200(200)200])2
* Bigreat Megadestrutrixul, 200(![200([200([200(200)200(200)200(200)200])200(200)200(200)200])200(200)200(200)200])3
* Bigreat Grand Destrutrixul
* Bigreat Grand Kilodestrutrixul
* Bigreat Grand Megadestrutrixul
* Bigreat Bigrand Destrutrixul
* Destruquaxul, 200![200([200([200([200(200)200])200])200])200]
* Kilodestruquaxul, 200(![200([200([200([200(200)200])200])200])200])2
* Megadestruquaxul, 200(![200([200([200([200(200)200])200])200])200])3
* Gigadestruquaxul, 200(![200([200([200([200(200)200])200])200])200])4
* Grand Destruquaxul, 200(![200([200([200([200(200)200])200])200])200])200![200([200([200([200(200)200])200])200])200]+1
* Grand Kilodestruquaxul
* Grand Megadestruquaxul
* Grand Gigadestruquaxul
* Bigrand Destruquaxul
* Trigrand Destruquaxul
* Great Destruquaxul, 200![200([200([200([200(200)200(200)200])200(200)200])200(200)200])200(200)200]
* Great Kilodestruquaxul, 200(![200([200([200([200(200)200(200)200])200(200)200])200(200)200])200(200)200])2
* Great Megadestruquaxul, 200(![200([200([200([200(200)200(200)200])200(200)200])200(200)200])200(200)200])3
* Great Grand Destruquaxul
* Great Grand Kilodestruquaxul
* Great Grand Megadestruquaxul
* Great Bigrand Destruquaxul
* Bigreat Destruquaxul, 200![200([200([200([200(200)200(200)200(200)200])200(200)200(200)200])200(200)200(200)200])200(200)200(200)200]
* Bigreat Kilodestruquaxul, 200(![200([200([200([200(200)200(200)200(200)200])200(200)200(200)200])200(200)200(200)200])200(200)200(200)200])2
* Bigreat Megadestruquaxul, 200(![200([200([200([200(200)200(200)200(200)200])200(200)200(200)200])200(200)200(200)200])200(200)200(200)200])3
* Bigreat Grand Destruquaxul
* Bigreat Grand Kilodestruquaxul
* Bigreat Grand Megadestruquaxul
* Bigreat Bigrand Destruquaxul
* Bitetrommthet, <math>f_{\theta(\Omega^\Omega,0)}(10)</math>
* ''Gibbawamba'', <math>\{10,100,2 (1) 2\}\ \&\ 10</math>
* Little birdie, {100,100[1[1\1\2¬2]2]2}
* Białystok, <math>f_{\psi_0(\Omega^{\Omega^{\Omega}})}(576)</math>

=== Part 6.20: <math>f_{\psi_0(\Omega^{\Omega^\Omega})}^2(10)</math> ~ <math>f_{\psi_0(\varepsilon_{\Omega+1})}^2(10)</math> ===
* ''Gabbawamba'', <math>\{10,100,3 (1) 2\}\ \&\ 10</math>
* ''Geebawamba'', <math>\{10,100,4 (1) 2\}\ \&\ 10</math>
* ''Gibawamba'', <math>\{10,100,5 (1) 2\}\ \&\ 10</math>
* ''Gobbawamba'', <math>\{10,100,6 (1) 2\}\ \&\ 10</math>
* ''Gabawamba'', <math>\{10,100,7 (1) 2\}\ \&\ 10</math>
* ''Boobawamba'', <math>\{10,10,100 (1) 2\}\ \&\ 10</math>
* ''Corporawamba'', <math>\{10,100,1,2 (1) 2\}\ \&\ 10</math>
* ''Mulporawamba'', <math>\{10,100,2,2 (1) 2\}\ \&\ 10</math>
* ''Powporawamba'', <math>\{10,100,3,2 (1) 2\}\ \&\ 10</math>
* ''Terporawamba'', <math>\{10,100,4,2 (1) 2\}\ \&\ 10</math>
* ''Pepporawamba'', <math>\{10,100,5,2 (1) 2\}\ \&\ 10</math>
* ''Hexporawamba'', <math>\{10,100,6,2 (1) 2\}\ \&\ 10</math>
* ''Bibbawamba'', <math>\{10,10,100,2 (1) 2\}\ \&\ 10</math>
* ''Corplodawamba'', <math>\{10,100,1,3 (1) 2\}\ \&\ 10</math>
* ''Babbawamba'', <math>\{10,10,100,3 (1) 2\}\ \&\ 10</math>
* ''Cordetawamba'', <math>\{10,100,1,4 (1) 2\}\ \&\ 10</math>
* ''Beebawamba'', <math>\{10,10,100,4 (1) 2\}\ \&\ 10</math>
* ''Bibawamba'', <math>\{10,10,100,5 (1) 2\}\ \&\ 10</math>
* ''Bobbawamba'', <math>\{10,10,100,6 (1) 2\}\ \&\ 10</math>
* ''Babawamba'', <math>\{10,10,100,7 (1) 2\}\ \&\ 10</math>
* ''Troobawamba'', <math>\{10,10,10,100 (1) 2\}\ \&\ 10</math>
* ''Tribbawamba'', <math>\{10,10,10,100,2 (1) 2\}\ \&\ 10</math>
* ''Trabbawamba'', <math>\{10,10,10,100,3 (1) 2\}\ \&\ 10</math>
* ''Treebawamba'', <math>\{10,10,10,100,4 (1) 2\}\ \&\ 10</math>
* ''Quadroobawamba'', <math>\{10,10,10,10,100 (1) 2\}\ \&\ 10</math>
* ''Quintoobawamba'', <math>\{10,10,10,10,10,100 (1) 2\}\ \&\ 10</math>
* ''Sextoobawamba'', <math>\{10,10,10,10,10,10,100 (1) 2\}\ \&\ 10</math>
* ''Goobawantra'', <math>\{10,100 (1) 3\}\ \&\ 10</math>
* ''Gibbawantra'', <math>\{10,100,2 (1) 3\}\ \&\ 10</math>
* ''Gabbawantra'', <math>\{10,100,3 (1) 3\}\ \&\ 10</math>
* ''Geebawantra'', <math>\{10,100,4 (1) 3\}\ \&\ 10</math>
* ''Gibawantra'', <math>\{10,100,5 (1) 3\}\ \&\ 10</math>
* ''Gobbawantra'', <math>\{10,100,6 (1) 3\}\ \&\ 10</math>
* ''Gabawantra'', <math>\{10,100,7 (1) 3\}\ \&\ 10</math>
* ''Boobawantra'', <math>\{10,10,100 (1) 3\}\ \&\ 10</math>
* ''Troobawantra'', <math>\{10,10,10,100 (1) 3\}\ \&\ 10</math>
* ''Quadroobawantra'', <math>\{10,10,10,10,100 (1) 3\}\ \&\ 10</math>
* ''Goobawanquadra'', <math>\{10,100 (1) 4\}\ \&\ 10</math>
* ''Boobawanquadra'', <math>\{10,10,100 (1) 4\}\ \&\ 10</math>
* ''Troobawanquadra'', <math>\{10,10,10,100 (1) 4\}\ \&\ 10</math>
* ''Goobawanquinta'', <math>\{10,100 (1) 5\}\ \&\ 10</math>
* ''Emperatrix'', <math>\{10,10 (1) 10\}\ \&\ 10</math>
* ''Gossablossla'', <math>\{10,10 (1) 100\}\ \&\ 10</math>
* ''Hecatonchirechelon'', E100{#,#(1)#}100
* ''Gissablossla'', <math>\{10,10 (1) 100,2\}\ \&\ 10</math>
* ''Gassablossla'', <math>\{10,10 (1) 100,3\}\ \&\ 10</math>
* ''Geesablossla'', <math>\{10,10 (1) 100,4\}\ \&\ 10</math>
* ''Gussablossla'', <math>\{10,10 (1) 100,5\}\ \&\ 10</math>
* ''Hyperlatrix'', <math>\{10,10 (1) 10,10\}\ \&\ 10</math>
* ''Mossablossla'', <math>\{10,10 (1) 10,100\}\ \&\ 10</math>
* ''Missablossla'', <math>\{10,10 (1) 10,100,2\}\ \&\ 10</math>
* ''Massablossla'', <math>\{10,10 (1) 10,100,3\}\ \&\ 10</math>
* ''Meesablossla'', <math>\{10,10 (1) 10,100,4\}\ \&\ 10</math>
* ''Mussablossla'', <math>\{10,10 (1) 10,100,5\}\ \&\ 10</math>
* ''Bossablossla'', <math>\{10,10 (1) 10,10,100\}\ \&\ 10</math>
* ''Bissablossla'', <math>\{10,10 (1) 10,10,100,2\}\ \&\ 10</math>
* ''Bassablossla'', <math>\{10,10 (1) 10,10,100,3\}\ \&\ 10</math>
* ''Beesablossla'', <math>\{10,10 (1) 10,10,100,4\}\ \&\ 10</math>
* ''Trossablossla'', <math>\{10,10 (1) 10,10,10,100\}\ \&\ 10</math>
* ''Quadrossablossla'', <math>\{10,10 (1) 10,10,10,10,100\}\ \&\ 10</math>
* ''Quintossablossla'', <math>\{10,10 (1) 10,10,10,10,10,100\}\ \&\ 10</math>
* ''Sextossablossla'', <math>\{10,10 (1) 10,10,10,10,10,10,100\}\ \&\ 10</math>
* ''Diteratrix'', <math>\{10,10 (1)(1) 2\}\ \&\ 10</math>
* ''Goobaduamba'', <math>\{10,100 (1)(1) 2\}\ \&\ 10</math>
* ''Gibbaduamba'', <math>\{10,100,2 (1)(1) 2\}\ \&\ 10</math>
* ''Goobaduantra'', <math>\{10,100 (1)(1) 3\}\ \&\ 10</math>
* ''Goobaduanquadra'', <math>\{10,100 (1)(1) 4\}\ \&\ 10</math>
* ''Admiratrix'', <math>\{10,10 (1)(1) 10\}\ \&\ 10</math>
* ''Dutridecatrix'', <math>\{10,3 (2) 2\}\ \&\ 10</math>
* Mega Super Even More Godder Tritri, 3 [3 {3 <3 / 3 / 3> 3} 3] 3
* ''Triteratrix'', <math>\{10,10 (1)(1)(1) 2\}\ \&\ 10</math>
* ''Goobatriombia'', <math>\{10,100 (1)(1)(1) 2\}\ \&\ 10</math>
* ''Goobatriontria'', <math>\{10,100 (1)(1)(1) 2\}\ \&\ 10</math>
* ''Goobaquardimbia'', <math>\{10,100 (1)(1)(1)(1) 2\}\ \&\ 10</math>
* ''Goobaquindingia'', <math>\{10,100 (1)(1)(1)(1)(1) 2\}\ \&\ 10</math>
* ''Goobasesixtia'', <math>\{10,100 \underbrace{(1)(1)\dots(1)(1)}_{6\ (1)\text{'s}} 2\}\ \&\ 10</math>
* ''Goobasebiptia'', <math>\{10,100 \underbrace{(1)(1)\dots(1)(1)}_{7\ (1)\text{'s}} 2\}\ \&\ 10</math>
* ''Goobagogdiktia'', <math>\{10,100 \underbrace{(1)(1)\dots(1)(1)}_{8\ (1)\text{'s}} 2\}\ \&\ 10</math>
* ''Goobanogdiktia'', <math>\{10,100 \underbrace{(1)(1)\dots(1)(1)}_{9\ (1)\text{'s}} 2\}\ \&\ 10</math>
* ''Xaplorgulus'', <math>\{10,10 (2) 2\}\ \&\ 10</math>
* ''Goobadektimtia'', <math>\{10,100 \underbrace{(1)(1)\dots(1)(1)}_{10\ (1)\text{'s}} 2\}\ \&\ 10</math>
* ''Goxxogogulus'', E100{100x100&#}100
* ''Goxxablorg'', <math>\{10,100 (2) 2\}\ \&\ 10</math>
* ''Gixxablorg'', <math>\{10,100,2 (2) 2\}\ \&\ 10</math>
* ''Gaxxablorg'', <math>\{10,100,2 (2) 2\}\ \&\ 10</math>
* ''Boxxablorg'', <math>\{10,10,100 (2) 2\}\ \&\ 10</math>
* ''Troxxablorg'', <math>\{10,10,10,100 (2) 2\}\ \&\ 10</math>
* ''Grand xaplorgulus'', <math>\{10,10 (2) 3\}\ \&\ 10</math>
* ''Gooxadworg'', <math>\{10,100 (2)(2) 2\}\ \&\ 10</math>
* ''Goxxathrorg'', <math>\{10,100 (2)(2)(2) 2\}\ \&\ 10</math>
* ''Goxxaquorg'', <math>\{10,100 (2)(2)(2)(2) 2\}\ \&\ 10</math>
* ''Cosslorgulus'', <math>\{10,10 (3) 2\}\ \&\ 10</math>
* ''Cloxxogogulus'', E100{100x100x100&#}100
* ''Coxxablorg'', <math>\{10,100 (3) 2\}\ \&\ 10</math>
* ''Coxxadworg'', <math>\{10,100 (3)(3) 2\}\ \&\ 10</math>
* ''Coxxathrorg'', <math>\{10,100 (3)(3)(3) 2\}\ \&\ 10</math>
* ''Coxxaquorg'', <math>\{10,100 (3)(3)(3)(3) 2\}\ \&\ 10</math>
* ''Tesslorgulus'', <math>\{10,10 (4) 2\}\ \&\ 10</math>
* ''Teroxxogogulus'', E100{100^4&#}100
* ''Toxxablorg'', <math>\{10,100 (4) 2\}\ \&\ 10</math>
* ''Pesslorgulus'', <math>\{10,10 (5) 2\}\ \&\ 10</math>
* ''Poxxablorg'', <math>\{10,100 (5) 2\}\ \&\ 10</math>
* ''Hesslorgulus'', <math>\{10,10 (6) 2\}\ \&\ 10</math>
* ''Hexxablorg'', <math>\{10,100 (6) 2\}\ \&\ 10</math>
* ''Zesslorgulus'', <math>\{10,10 (7) 2\}\ \&\ 10</math>
* ''Zexxablorg'', <math>\{10,100 (7) 2\}\ \&\ 10</math>
* ''Yosslorgulus'', <math>\{10,10 (8) 2\}\ \&\ 10</math>
* ''Yoxxablorg'', <math>\{10,100 (8) 2\}\ \&\ 10</math>
* ''Brosslorgulus'', <math>\{10,10 (9) 2\}\ \&\ 10</math>
* ''Broxxablorg'', <math>\{10,100 (9) 2\}\ \&\ 10</math>
* ''Gosslorgulus'', <math>\{10,10 (10) 2\}\ \&\ 10</math>
* ''Gexxablorg'', <math>\{10,100 (10) 2\}\ \&\ 10</math>
* ''Cosmatrix'', <math>\{10,10 (10) 10\}\ \&\ 10</math>
* ''Mosslorgulus'', <math>\{10,10 (20) 2\}\ \&\ 10</math>
* ''Hasslorgulus'', <math>\{10,10 (30) 2\}\ \&\ 10</math>
* ''Kysslorgulus'', <math>\{10,10 (40) 2\}\ \&\ 10</math>
* ''Pisslorgulus'', <math>\{10,10 (50) 2\}\ \&\ 10</math>
* ''Sasslorgulus'', <math>\{10,10 (60) 2\}\ \&\ 10</math>
* ''Pexxlorgulus'', <math>\{10,10 (70) 2\}\ \&\ 10</math>
* ''Nisslorgulus'', <math>\{10,10 (80) 2\}\ \&\ 10</math>
* ''Zozzlorgulus'', <math>\{10,10 (90) 2\}\ \&\ 10</math>
* ''Golapulus'' / Alphlorgulus, <math>\{10,10 (100) 2\}\ \&\ 10</math>
* ''Brobdingnagongule'', E100{100^100&#}100
* ''Besslorgulus'', <math>\{10,10 (200) 2\}\ \&\ 10</math>
* ''Gasslorgulus'', <math>\{10,10 (300) 2\}\ \&\ 10</math>
* ''Desslorgulus'', <math>\{10,10 (400) 2\}\ \&\ 10</math>
* Zitrite, <math>f_{\psi_0(\Omega^{\Omega^{\Omega^\omega}})}(420)</math> in the fast-growing hierarchy (using the extended Buchholz's function)
* ''Thesslorgulus'', <math>\{10,10 (500) 2\}\ \&\ 10</math>
* ''Iottlorgulus'', <math>\{10,10 (600) 2\}\ \&\ 10</math>
* ''Kapplorgulus'', <math>\{10,10 (700) 2\}\ \&\ 10</math>
* ''Lasslorgulus'', <math>\{10,10 (800) 2\}\ \&\ 10</math>
* ''Sigglorgulus'', <math>\{10,10 (900) 2\}\ \&\ 10</math>
* Tritetrommthet, <math>f_{\theta(\Omega^{\Omega^\Omega},0)}(10)</math>
* ''Ginglapulus'', <math>\{10,100 (0,2) 2\}\ \&\ 10</math>
* Belgorod, <math>f_{\psi_0(\Omega^{\Omega^{\Omega^{\Omega}}})}(576) = f_{\psi_0(\psi_{1}^5(0))}(576)</math> in the fast-growing hierarchy (using the extended Buchholz's function)
* ''Ganglapulus'', <math>\{10,100 (0,3) 2\}\ \&\ 10</math>
* ''Geenglapulus'', <math>\{10,100 (0,4) 2\}\ \&\ 10</math>
* ''Gownglapulus'', <math>\{10,100 (0,5) 2\}\ \&\ 10</math>
* ''Gunglapulus'', <math>\{10,100 (0,6) 2\}\ \&\ 10</math>
* ''Bolapulus'', <math>\{10,100 (0,0,1) 2\}\ \&\ 10</math>
* ''Binglapulus'', <math>\{10,100 (0,0,2) 2\}\ \&\ 10</math>
* ''Banglapulus'', <math>\{10,100 (0,0,3) 2\}\ \&\ 10</math>
* ''Beenglapulus'', <math>\{10,100 (0,0,4) 2\}\ \&\ 10</math>
* ''Trolapulus'', <math>\{10,100 (0,0,0,1) 2\}\ \&\ 10</math>
* ''Tringlapulus'', <math>\{10,100 (0,0,0,2) 2\}\ \&\ 10</math>
* ''Tranglapulus'', <math>\{10,100 (0,0,0,3) 2\}\ \&\ 10</math>
* ''Quadrolapulus'', <math>\{10,100 (0,0,0,0,1) 2\}\ \&\ 10</math>
* ''Quadringlapulus'', <math>\{10,100 (0,0,0,0,2) 2\}\ \&\ 10</math>
* ''Quintolapulus'', <math>\{10,100 (0,0,0,0,0,1) 2\}\ \&\ 10</math>
* ''Sextolapulus'', <math>\{10,100 (0,0,0,0,0,0,1) 2\}\ \&\ 10</math>
* ''Goplapulus'' / ''Centolapulus'', <math>\{10,100 ((1)1) 2\}\ \&\ 10</math>
* Quadritetrommthet, <math>f_{\theta(\Omega^{\Omega^{\Omega^\Omega}},0)}(10)</math>
* ''Goplapulusfact'', <math>\{10,100 (1(1)1) 2\}\ \&\ 10</math>
* ''Gogridplapulus'', <math>\{10,100 (2(1)1) 2\}\ \&\ 10</math>
* ''Gokubikplapulus'', <math>\{10,100 (3(1)1) 2\}\ \&\ 10</math>
* ''Gogolapulplapulus'', <math>\{10,100 (0,1(1)1) 2\}\ \&\ 10</math>
* ''Gogolapulplapulusfact'', <math>\{10,100 (1,1(1)1) 2\}\ \&\ 10</math>
* ''Gogolagridpulplapulus'', <math>\{10,100 (2,1(1)1) 2\}\ \&\ 10</math>
* ''Gogolakubikpulplapulus'', <math>\{10,100 (3,1(1)1) 2\}\ \&\ 10</math>
* ''Gogolapulusdeusplapulus'', <math>\{10,100 (0,2(1)1) 2\}\ \&\ 10</math>
* ''Gogolapulustruceplapulus'', <math>\{10,100 (0,3(1)1) 2\}\ \&\ 10</math>
* ''Gobolapulplapulus'', <math>\{10,100 (0,0,1(1)1) 2\}\ \&\ 10</math>
* ''Gotrolapulplapulus'', <math>\{10,100 (0,0,0,1(1)1) 2\}\ \&\ 10</math>
* ''Goplapulusdeus'', <math>\{10,100 ((1)2) 2\}\ \&\ 10</math>
* ''Goplapulustruce'', <math>\{10,100 ((1)3) 2\}\ \&\ 10</math>
* ''Hyper-golapulusfact'', <math>\{10,100 ((1)0,1) 2\}\ \&\ 10</math>
* ''Hyper-ginglapulusfact'', <math>\{10,100 ((1)0,2) 2\}\ \&\ 10</math>
* ''Hyper-ganglapulusfact'', <math>\{10,100 ((1)0,3) 2\}\ \&\ 10</math>
* ''Hyper-bolapulusfact'', <math>\{10,100 ((1)0,0,1) 2\}\ \&\ 10</math>
* ''Hyper-trolapulusfact'', <math>\{10,100 ((1)0,0,0,1) 2\}\ \&\ 10</math>
* ''Giplapulus'', <math>\{10,100 ((1)(1)1) 2\}\ \&\ 10</math>
* ''Gaplapulus'', <math>\{10,100 ((1)(1)(1)1) 2\}\ \&\ 10</math>
* ''Geeplapulus'', <math>\{10,100 ((1)(1)(1)(1)1) 2\}\ \&\ 10</math>
* ''Boplapulus'', <math>\{10,100 ((2)1) 2\}\ \&\ 10</math>
* ''Biplapulus'', <math>\{10,100 ((2)(2)1) 2\}\ \&\ 10</math>
* ''Troplapulus'', <math>\{10,100 ((3)1) 2\}\ \&\ 10</math>
* ''Quadroplapulus'', <math>\{10,100 ((4)1) 2\}\ \&\ 10</math>
* ''Goduplapulus'', <math>\{10,100 ((0,1)1) 2\}\ \&\ 10</math>
* Quintitetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow5,0)}(10)</math>
* ''Giduplapulus'', <math>\{10,100 ((0,2)1) 2\}\ \&\ 10</math>
* ''Boduplapulus'', <math>\{10,100 ((0,0,1)1) 2\}\ \&\ 10</math>
* ''Gotriplapulus'', <math>\{10,100 (((1)1)1) 2\}\ \&\ 10</math>
* Sextitetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow6,0)}(10)</math>
* ''Goquadriplapulus'', <math>\{10,100 (((0,1)1)1) 2\}\ \&\ 10</math>
* Septitetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow7,0)}(10)</math>
* ''Goquintiplapulus'', <math>\{10,100 ((((1)1)1)1) 2\}\ \&\ 10</math>
* Octitetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow8,0)}(10)</math>
* Nonitetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow9,0)}(10)</math>
* Dekotetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow10,0)}(10)</math>
* ''Lugubrigoth'', E100{#^^#&#}100
* Lugubrigoogol, {100,100[1[1¬3]2]2}
* ''Quathragoth/goplatoth'', <math>10\uparrow\uparrow100 \& 10 \& 10</math>
* Hektotetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow100,0)}(10)</math>
* Extremexul, 200![1(1)[2200,200,200,200
* Extremedollaxul, 200$0]3]
* Kiloextremexul, (200![1(1)[2200,200,200,200)![1(1)[2200,200,200,200
* Megaextremexul, ((200![1(1)[2200,200,200,200)![1(1)[2200,200,200,200)![1(1)[2200,200,200,200
* Gigaextremexul, 200(![1(1)[2200,200,200,200)4
* Teraextremexul, 200(![1(1)[2200,200,200,200)5
* Petaextremexul, 200(![1(1)[2200,200,200,200)6
* Exaextremexul, 200(![1(1)[2200,200,200,200)7
* Grand Extremexul, 200(![1(1)[2200,200,200,200)200![1(1)[2200,200,200,200+1
* Grand Kiloextremexul, 200(![1(1)[2200,200,200,200)(200![1(1)[2200,200,200,200)![1(1)[2200,200,200,200+1
* Grand Megaextremexul, 200(![1(1)[2200,200,200,200)200(![1(1)[2200,200,200,200)3+1
* Grand Gigaextremexul, 200(![1(1)[2200,200,200,200)200(![1(1)[2200,200,200,200)4+1
* Grand Teraextremexul, 200(![1(1)[2200,200,200,200)200(![1(1)[2200,200,200,200)5+1
* Grand Petaextremexul, 200(![1(1)[2200,200,200,200)200(![1(1)[2200,200,200,200)6+1
* Grand Exaextremexul, 200(![1(1)[2200,200,200,200)200(![1(1)[2200,200,200,200)7+1
* Bigrand Extremexul, 200(![1(1)[2200,200,200,200)200(![1(1)[2200,200,200,200)200![1(1)[2200,200,200,200+1+1
* Bigrand Kiloextremexul
* Bigrand Megaextremexul
* Trigrand Extremexul
* Trigrand Kiloextremexul
* Trigrand Megaextremexul
* Quadgrand Extremexul
* Quintgrand Extremexul
* Kilotetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow1000,0)}(10)</math>
* Megotetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow10^6,0)}(10)</math>
* Gigotetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow10^9,0)}(10)</math>
* Terotetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow10^{12},0)}(10)</math>
* Petotetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow10^{15},0)}(10)</math>
* Exotetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow10^{18},0)}(10)</math>
* Zettotetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow10^{21},0)}(10)</math>
* Yottotetrommthet, <math>f_{\theta(\Omega\uparrow\uparrow10^{24},0)}(10)</math>

== Higher computable level ==

=== Part 6.21: <math>f_{\psi_0(\Omega_2)}^2(10)</math> ~ <math>f_{\psi_0(\Omega_\omega)}^2(10)</math> ===

* Trugubrigoogol, {100,100[1[1¬4]2]2}
* Omega Mega Super Even More Godder Tritri, 3 [3 {3 // 3} 3] 3
* Tetrugubrigoogol, {100,100[1[1¬5]2]2}
* Pentugubrigoogol, {100,100[1[1¬6]2]2}
* Hexugubrigoogol, {100,100[1[1¬7]2]2}
* Heptugubrigoogol, {100,100[1[1¬8]2]2}
* Ogdugubrigoogol, {100,100[1[1¬9]2]2}
* Ennugubrigoogol, {100,100[1[1¬10]2]2}
* Dekugubrigoogol, {100,100[1[1¬11]2]2}
* Centugubrigoogol, {100,100[1[1¬1,2]2]2}
* Big Bird, <math>\{100,100 [1 [1 \neg 1 \neg 2] 2] 2\}</math>
* Extremebixul, 200![1(1)[2200,200,200,200,200
* Kiloextremebixul, (200![1(1)[2200,200,200,200,200)![1(1)[2200,200,200,200,200
* Extremetrixul, 200![1(1)[2200,200,200,200,200,200
* Extremequaxul, 200![1(1)[2200,200,200,200,200,200,200
* Tria-hierarchaxis, {100,100[1[1[2\32]2]2]2}
* Bommthet, <math>f_{\theta(\Omega_2,0)}(10)</math>
* Gigantixul, 200![1(1)[3200,200,200
* Gigantibixul, 200![1(1)[3200,200,200,200
* Ultimate Omega Mega Super Even More Godder Tritri, 3 [3 {3 /// 3} 3] 3
* Gigantitrixul, 200![1(1)[3200,200,200,200,200
* Gigantiquaxul, 200![1(1)[3200,200,200,200,200,200
* Tetra-hierarchaxis, {100,100[1[1[1[2\42]2]2]2]2}
* Trommthet, <math>f_{\theta(\Omega_3,0)}(10)</math>
* Godly Ultimate Omega Mega Super Even More Godder Tritri, 3 [3 {3 <<<3 <<<3 /// 3>>> 3>>> 3} 3] 3
* Penta-hierarchaxis, {100,100[1[1[1[1[2\52]2]2]2]2]2}
* Quadrommthet, <math>f_{\theta(\Omega_4,0)}(10)</math>
* Hexa-hierarchaxis, {100,100[1[1[1[1[1[2\62]2]2]2]2]2]2}
* Quintommthet, <math>f_{\theta(\Omega_5,0)}(10)</math>
* Hepta-hierarchaxis, {100,100[1[1[1[1[1[1[2\72]2]2]2]2]2]2]2}
* Sextommthet, <math>f_{\theta(\Omega_6,0)}(10)</math>
* Octa-hierarchaxis, {100,100[1[1[1[1[1[1[1[2\82]2]2]2]2]2]2]2]2}
* Septommthet, <math>f_{\theta(\Omega_7,0)}(10)</math>
* Enna-hierarchaxis, {100,100[1[1[1[1[1[1[1[1[2\92]2]2]2]2]2]2]2]2]2}
* Octommthet, <math>f_{\theta(\Omega_8,0)}(10)</math>
* Deka-hierarchaxis, {100,100[1[1[1[1[1[1[1[1[1[2\102]2]2]2]2]2]2]2]2]2]2}
* Nonommthet, <math>f_{\theta(\Omega_9,0)}(10)</math>
* Dekommthet, <math>f_{\theta(\Omega_{10},0)}(10)</math>
* Corporalmax / hecta-hierarchaxis, {100,100[1[2\1,22]2]2}
* Hektommthet, <math>f_{\theta(\Omega_{100},0)}(10)</math>
* Kilommthet, <math>f_{\theta(\Omega_{1000},0)}(10)</math>
* Megommthet, <math>f_{\theta(\Omega_{10^6},0)}(10)</math>
* Gigommthet, <math>f_{\theta(\Omega_{10^9},0)}(10)</math>
* Terommthet, <math>f_{\theta(\Omega_{10^{12}},0)}(10)</math>
* Petommthet, <math>f_{\theta(\Omega_{10^{15}},0)}(10)</math>
* Exommthet, <math>f_{\theta(\Omega_{10^{18}},0)}(10)</math>
* Zettommthet, <math>f_{\theta(\Omega_{10^{21}},0)}(10)</math>
* Yottommthet, <math>f_{\theta(\Omega_{10^{24}},0)}(10)</math>
* '''SCG(13)''' (lower bound), <math>\approx f_{\psi(\Omega_\omega)}(13)</math>
* QZAZARZ (ɧ51), TREE(G64*(TREE(SCG(13))) + 1
* LoveDeath, SCG1521(7)
* ''Meeting point of the three hierarchies'', <math>f_{\theta(\Omega_{\omega})}(100)</math>
* Nucleabixul, 200![[200200]200]

=== Part 6.22: <math>f_{\psi_0(\Omega_\omega)}^2(10)</math> ~ <math>f_{\psi_0(\Phi(1,0))+1}(10)</math> ===

* Pair sequence number, <math>\approx f_{\psi(\Omega_\omega)+1}(10)</math>
* Stage array notation|Stage array number, <math>\approx f_{\psi(\Omega_{\omega})+1}(100)</math>
* Mulporalmax, {100,100[1[1[2\2,22]2]2]2}
* Big Chunk, {10,100 [1 [1 [1 \2,2 3] 2] 2] 2}
* Powporalmax, {100,100[1[1[1[2\3,22]2]2]2]2}
* Corplodalmax, {100,100[1[1[2\1,32]2]2]2}
* Absolutely Godly Ultimate Omega Mega Super Even More Godder Tritri, 3 [3 {3 \ 3, 3} 3] 3
* Cordetalmax, {100,100[1[1[1[2\1,42]2]2]2]2}
* Meg-Googolmax, {100,100[1[2\1,1,22]2]2}
* Dumeg-Googolmax, {100,100[1[1[2\1,1,32]2]2]2}
* Gig-Googolmax, {100,100[1[2\1,1,1,22]2]2}
* Dugig-Googolmax, {100,100[1[1[2\1,1,1,32]2]2]2}
* Ter-Googolmax, {100,100[1[2\1,1,1,1,22]2]2}
* Goobolmax, {100,100[1[2\1[2]22]2]2}
* Gibbolmax, {100,100[1[1[2\2[2]22]2]2]2}
* Gootrolmax, {100,100[1[1[2\1[2]32]2]2]2}
* Gooterolmax, {100,100[1[1[1[2\1[2]42]2]2]2]2}
* Diteralmax / dubolmax, {100,100[1[2\1[2]1[2]22]2]2}
* Xappolmax, {100,100[1[2\1[3]22]2]2}
* Colossolmax, {100,100[1[2\1[4]22]2]2}
* Goplexulusmax, {100,100[1[2\1[1[2]2]22]2]2}
* Bimixommwil, <math>f_{\psi(\Omega_{\psi(\Omega)})}(10)</math>
* Tethrinoogolmax, {100,100[1[2\1[1\2]22]2]2}
* Tethrinoofactimax / hecto-tethrinoogolmax, {100,100[1[2\1[2\2]22]2]2}
* Terrible tethrinoogolmax, {100,100[1[2\1[1\3]22]2]2}
* Terrible terrible tethrinoogolmax, {100,100[1[2\1[1\4]22]2]2}
* Tethrinoocrossmax, {100,100[1[2\1[1\1\2]22]2]2}
* Secundotethrated-tethrinoocrossmax, {100,100[1[2\1[1\1\3]22]2]2}
* Tethrinoocubormax, {100,100[1[2\1[1\1\1\2]22]2]2}
* Tethrinooteronmax, {100,100[1[2\1[1\1\1\1\2]22]2]2}
* Tethrinootopemax, {100,100[1[2\1[1[2\22]2]22]2]2}
* Mountommol, {100,100[1[2\1[1[2\32]2]22]2]2}
* Mountobbol, {100,100[1[2\1[1[2\42]2]22]2]2}
* Mountotrtrol, {100,100[1[2\1[1[2\52]2]22]2]2}
* Mountoquadquadol, {100,100[1[2\1[1[2\62]2]22]2]2}
* Mountoquinquinol, {100,100[1[2\1[1[2\72]2]22]2]2}
* Mountosextsextol, {100,100[1[2\1[1[2\82]2]22]2]2}
* Mountoseptseptol, {100,100[1[2\1[1[2\92]2]22]2]2}
* Mountooctoctol, {100,100[1[2\1[1[2\102]2]22]2]2}
* Mountononnonol, {100,100[1[2\1[1[2\112]2]22]2]2}
* Dimen-Mountommol, {100,100[1[2\1[1[2\122]2]22]2]2}
* Mountimmol, {100,100[1[2\1[1[2\1,22]2]22]2]2}
* Trimixommwil, <math>f_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega)})})}(10)</math>
* Quadrimixommwil, <math>f_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega)})})})}(10)</math>
* Quintimixommwil, <math>f_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega)})})})})}(10)</math>
* Sextimixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{6\ \Omega's}}(10)</math>
* Septimixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{7\ \Omega's}}(10)</math>
* Octimixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{8\ \Omega's}}(10)</math>
* Nonimixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{9\ \Omega's}}(10)</math>
* Dekomixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10\ \Omega's}}(10)</math>
* Hektomixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{100\ \Omega's}}(10)</math>
* Kilomixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{1000\ \Omega's}}(10)</math>
* Megomixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^6\ \Omega's}}(10)</math>
* Gigomixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^9\ \Omega's}}(10)</math>
* Teromixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^{12}\ \Omega's}}(10)</math>
* Petomixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^{15}\ \Omega's}}(10)</math>
* Exomixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^{18}\ \Omega's}}(10)</math>
* Zettomixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^{21}\ \Omega's}}(10)</math>
* Yottomixommwil, <math>f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^{24}\ \Omega's}}(10)</math>
* Binommwil, <math>f_{\psi(\Omega_\Omega)}(10)</math>
* The HUS, S(U(H(3)))
* Grand HUS, S(S(S(U(U(U(H(H(H(3)))))))))
* Great HUS, S(S(S( ... (S(U(U(U( ... (U(H(H(H( ... (H(3))) ... ))) (with the HUS number of S's, the HUS number of U's, and the HUS number of H's)
* Nucleatrixul, 200![[[200200]200]200]
* Trinommwil, <math>f_{\psi(\Omega_{\Omega_\Omega})}(10)</math>
* Nucleaquaxul, 200![[[[200200]200]200]200]
* Quadrinommwil, <math>f_{\psi(\Omega_{\Omega_{\Omega_\Omega}})}(10)</math>
* Quintinommwil, <math>f_{\psi(\Omega_{\Omega_{\Omega_{\Omega_\Omega}}})}(10)</math>
* Sextinommwil, <math>f_{\psi(\Omega_{\Omega_{\Omega_{\Omega_{\Omega_\Omega}}}})}(10)</math>
* Septinommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{7\ \Omega's})}(10)</math>
* Octinommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{8\ \Omega's})}(10)</math>
* Noninommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{9\ \Omega's})}(10)</math>
* Dekinommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10\ \Omega's})}(10)</math>
* Kilinommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{1000\ \Omega's})}(10)</math>
* Meginommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^6\ \Omega's})}(10)</math>
* Giginommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^9\ \Omega's})}(10)</math>
* Terinommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^{12}\ \Omega's})}(10)</math>
* Petinommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^{15}\ \Omega's})}(10)</math>
* Exinommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^{18}\ \Omega's})}(10)</math>
* Zettinommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^{21}\ \Omega's})}(10)</math>
* Yottinommwil, <math>f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^{24}\ \Omega's})}(10)</math>

=== Part 6.23: <math>> f_{\psi_0(\Phi_1(0))+1}(10)</math> ===

* Unimah, <math>f_{\psi(I)}(10)</math>
* Bitetrotos, <math>f_{\psi(I^I)}(10)</math>
* Tritetrotos, <math>f_{\psi(I^{I^I})}(10)</math>
* Quadritetrotos, <math>f_{\psi(I^{I^{I^I}})}(10)</math>
* Quintitetrotos, <math>f_{\psi(I^{I^{I^{I^I}}})}(10)</math>
* Sextitetrotos, <math>f_{\psi(I\uparrow\uparrow6)}(10)</math>
* Septitetrotos, <math>f_{\psi(I\uparrow\uparrow7)}(10)</math>
* Octitetrotos, <math>f_{\psi(I\uparrow\uparrow8)}(10)</math>
* Nonitetrotos, <math>f_{\psi(I\uparrow\uparrow9)}(10)</math>
* Dekotetrotos, <math>f_{\psi(I\uparrow\uparrow10)}(10)</math>
* Hektotetrotos, <math>f_{\psi(I\uparrow\uparrow100)}(10)</math>
* Kilotetrotos, <math>f_{\psi(I\uparrow\uparrow1000)}(10)</math>
* Megotetrotos, <math>f_{\psi(I\uparrow\uparrow10^6)}(10)</math>
* Gigotetrotos, <math>f_{\psi(I\uparrow\uparrow10^9)}(10)</math>
* Terotetrotos, <math>f_{\psi(I\uparrow\uparrow10^{12})}(10)</math>
* Petotetrotos, <math>f_{\psi(I\uparrow\uparrow10^{15})}(10)</math>
* Exotetrotos, <math>f_{\psi(I\uparrow\uparrow10^{18})}(10)</math>
* Zettotetrotos, <math>f_{\psi(I\uparrow\uparrow10^{21})}(10)</math>
* Yottotetrotos, <math>f_{\psi(I\uparrow\uparrow10^{24})}(10)</math>
* Uninotos, <math>f_{\psi(I_I)}(10)</math>
* Binotos, <math>f_{\psi(I_{I_I})}(10)</math>
* Trinotos, <math>f_{\psi(I_{I_{I_I}})}(10)</math>
* Sextinotos, <math>f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{7\ I's})}(10)</math>
* Dekinotos, <math>f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{11\ I's})}(10)</math>
* Hektinotos, <math>f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{101\ I's})}(10)</math>
* Kilinotos, <math>f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{1001\ I's})}(10)</math>
* Meginotos, <math>f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{10^6+1\ I's})}(10)</math>
* Giginotos, <math>f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{10^9+1\ I's})}(10)</math>
* Terinotos, <math>f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{10^{12}+1\ I's})}(10)</math>
* Petinotos, <math>f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{10^{15}+1\ I's})}(10)</math>
* Exinotos, <math>f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{10^{18}+1\ I's})}(10)</math>
* Zettinotos, <math>f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{10^{21}+1\ I's})}(10)</math>
* Yottinotos, <math>f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{10^{24}+1\ I's})}(10)</math>
* KumaKuma ψ function#Large Function and Large Number|Kumakuma 3 variables ψ number, F10100(10100)
* Bimah, <math>f_{\psi(I(2,0))}(10)</math>
* Trimah, <math>f_{\psi(I(3,0))}(10)</math>
* Quadrimah, <math>f_{\psi(I(4,0))}(10)</math>
* Quintimah, <math>f_{\psi(I(5,0))}(10)</math>
* Sextimah, <math>f_{\psi(I(6,0))}(10)</math>
* Septimah, <math>f_{\psi(I(7,0))}(10)</math>
* Octimah, <math>f_{\psi(I(8,0))}(10)</math>
* Nonimah, <math>f_{\psi(I(9,0))}(10)</math>
* Dekimah, <math>f_{\psi(I(10,0))}(10)</math>
* Hektimah, <math>f_{\psi(I(100,0))}(10)</math>
* Kilimah, <math>f_{\psi(I(1000,0))}(10)</math>
* Megimah, <math>f_{\psi(I(10^6,0))}(10)</math>
* Gigimah, <math>f_{\psi(I(10^9,0))}(10)</math>
* Terimah, <math>f_{\psi(I(10^{12},0))}(10)</math>
* Petimah, <math>f_{\psi(I(10^{15},0))}(10)</math>
* Eximah, <math>f_{\psi(I(10^{18},0))}(10)</math>
* Zettimah, <math>f_{\psi(I(10^{21},0))}(10)</math>
* Yottimah, <math>f_{\psi(I(10^{24},0))}(10)</math>
* Uninimah, <math>f_{\psi(I(I(0,0),0))}(10)</math>
* Binimah, <math>f_{\psi(I(I(I(0,0),0),0))}(10)</math>
* Trinimah, <math>f_{\psi(I(I(I(I(0,0),0),0),0))}(10)</math>
* Quadrinimah, <math>f_{\psi(I(I(I(I(I(0,0),0),0),0),0))}(10)</math>
* Quintinimah, <math>f_{\psi(\underbrace{I(I(\cdots I(0,0)\cdots,0),0)}_{6\ I's})}(10)</math>
* Sextinimah, <math>f_{\psi(\underbrace{I(I(\cdots I(0,0)\cdots,0),0)}_{7\ I's})}(10)</math>
* Septinimah, <math>f_{\psi(\underbrace{I(I(\cdots I(0,0)\cdots,0),0)}_{8\ I's})}(10)</math>
* Terinimah, <math>f_{\psi(\underbrace{I(I(\cdots I(0,0)\cdots,0),0)}_{10^{12}+1\ I's})}(10)</math>
* Zettinimah, <math>f_{\psi(\underbrace{I(I(\cdots I(0,0)\cdots,0),0)}_{10^{21}+1\ I's})}(10)</math>
* Yottinimah, <math>f_{\psi(\underbrace{I(I(\cdots I(0,0)\cdots,0),0)}_{10^{24}+1\ I's})}(10)</math>
* ε function#Large Number|グラハム数ver ε.0.1.0 (Graham's number version ε.0.1.0), G64(4)
* Tritetremar, <math>f_{\psi(M^{M^M})}(10)</math>
* Sextitetremar, <math>f_{\psi(M\uparrow\uparrow6)}(10)</math>
* Terotetremar, <math>f_{\psi(M\uparrow\uparrow10^{12})}(10)</math>
* Petotetremar, <math>f_{\psi(M\uparrow\uparrow10^{15})}(10)</math>
* Exotetremar, <math>f_{\psi(M\uparrow\uparrow10^{18})}(10)</math>
* Zettotetremar, <math>f_{\psi(M\uparrow\uparrow10^{21})}(10)</math>
* Yottotetremar, <math>f_{\psi(M\uparrow\uparrow10^{24})}(10)</math>
* Uninemar, <math>f_{\psi(M_M)}(10)</math>
* Trinemar, <math>f_{\psi(M_{M_{M_M}})}(10)</math>
* Quadrinemar, <math>f_{\psi(M_{M_{M_{M_M}}})}(10)</math>
* Quintinemar, <math>f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{6\ M's})}(10)</math>
* Sextinemar, <math>f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{7\ M's})}(10)</math>
* Kilinemar, <math>f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{1001\ M's})}(10)</math>
* Meginemar, <math>f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^6+1\ M's})}(10)</math>
* Giginemar, <math>f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^9+1\ M's})}(10)</math>
* Petinemar|TTerinemar|erinemar, <math>f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^{12}+1\ M's})}(10)</math>
* Petinemar, <math>f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^{15}+1\ M's})}(10)</math>
* Exinemar, <math>f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^{18}+1\ M's})}(10)</math>
* Zettinemar, <math>f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^{21}+1\ M's})}(10)</math>
* Yottinemar, <math>f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^{24}+1\ M's})}(10)</math>
* Uninamus, <math>f_{\psi(M(M(0;0);0))}(10)</math>
* Meginamus, <math>f_{\psi(\underbrace{M(M(\cdots M(0;0)\cdots;0);0)}_{10^{6}+1\ M's})}(10)</math>
* Exinamus, <math>f_{\psi(\underbrace{M(M(\cdots M(0;0)\cdots;0);0)}_{10^{18}+1\ M's})}(10)</math>
* Yottinamus, <math>f_{\psi(\underbrace{M(M(\cdots M(0;0)\cdots;0);0)}_{10^{24}+1\ M's})}(10)</math>
* SAN number, ~ (0,0,0)(1,1,1)(2,2,1)(3,0,0)(0,0,0)[64]
* Tritar, <math>f_{C(C(C(\Omega_{3}2,0),0),0)}(3) = Tar(3)</math>
* Quadritar, <math>f_{C(C(C(C(\Omega_{4}2,0),0),0),0)}(4) = Tar(4)</math>
* Quintitar, <math>f_{C(C(C(C(C(\Omega_{5}2,0),0),0),0),0)}(5) = Tar(5)</math>
* Sextitar, <math>f_{C(C(C(C(C(C(\Omega_{6}2,0),0),0),0),0),0)}(6) = Tar(6)</math>
* Septitar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{7}2,0),0),\cdots ),0)}_{7\text{ C's}}}(7) = Tar(7)</math>
* Octitar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{8}2,0),0),\cdots ),0)}_{8\text{ C's}}}(8) = Tar(8)</math>
* Nonitar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{9}2,0),0),\cdots ),0)}_{9\text{ C's}}}(9) = Tar(9)</math>
* Dekotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{10}2,0),0),\cdots ),0)}_{10\text{ C's}}}(10) = Tar(10)</math>
* Hektotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{100}2,0),0),\cdots ),0)}_{100\text{ C's}}}(100) = Tar(100)</math>
* Kilotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{1000}2,0),0),\cdots ),0)}_{1000\text{ C's}}}(1000) = Tar(1000)</math>
* Megotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{6}}2,0),0),\cdots ),0)}_{10^{6}\text{ C's}}}(10^{6}) = Tar(10^{6})</math>
* Gigotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{9}}2,0),0),\cdots ),0)}_{10^{9}\text{ C's}}}(10^{9}) = Tar(10^{9})</math>
* Terotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{12}}2,0),0),\cdots ),0)}_{10^{12}\text{ C's}}}(10^{12}) = Tar(10^{12})</math>
* Petotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{15}}2,0),0),\cdots ),0)}_{10^{15}\text{ C's}}}(10^{15}) = Tar(10^{15})</math>
* Exotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{18}}2,0),0),\cdots ),0)}_{10^{18}\text{ C's}}}(10^{18}) = Tar(10^{18})</math>
* Zettotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{21}}2,0),0),\cdots ),0)}_{10^{21}\text{ C's}}}(10^{21}) = Tar(10^{21})</math>
* Yottotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{24}}2,0),0),\cdots ),0)}_{10^{24}\text{ C's}}}(10^{24}) = Tar(10^{24})</math>
* Ronnotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{27}}2,0),0),\cdots ),0)}_{10^{27}\text{ C's}}}(10^{27}) = Tar(10^{27})</math>
* Quettotar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{30}}2,0),0),\cdots ),0)}_{10^{30}\text{ C's}}}(10^{30}) = Tar(10^{30})</math>
* Unintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{\text{Dekotar}}2,0),0),\cdots ),0)}_{\text{Dekotar C's}}}(\text{Dekotar}) = Tar(Dekotar) = Tar(Tar)</math>
* Bintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{\text{Unintar}}2,0),0),\cdots ),0)}_{\text{Unintar C's}}}(\text{Unintar}) = Tar(Tar(Tar)) = Tar(Tar(Dekotar))</math>
* Trintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{\text{Bintar}}2,0),0),\cdots ),0)}_{\text{Bintar C's}}}(\text{Bintar}) = Tar(Tar(Tar(Tar)))</math>
* Quadrintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{3\text{-intar}}2,0),0),\cdots ),0)}_{3\text{-intar C's}}}(3\text{-intar}) = Tar^{4}(Tar)</math>
* Quintintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{4\text{-intar}}2,0),0),\cdots ),0)}_{4\text{-intar C's}}}(4\text{-intar}) = Tar^{5}(Tar)</math>
* Sextintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{5\text{-intar}}2,0),0),\cdots ),0)}_{5\text{-intar C's}}}(5\text{-intar}) = Tar^{6}(Tar)</math>
* Septintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{6\text{-intar}}2,0),0),\cdots ),0)}_{6\text{-intar C's}}}(6\text{-intar}) = Tar^{7}(Tar)</math>
* Octintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{7\text{-intar}}2,0),0),\cdots ),0)}_{7\text{-intar C's}}}(7\text{-intar}) = Tar^{8}(Tar)</math>
* Nonintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{8\text{-intar}}2,0),0),\cdots ),0)}_{8\text{-intar C's}}}(8\text{-intar}) = Tar^{9}(Tar)</math>
* Dekintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{9\text{-intar}}2,0),0),\cdots ),0)}_{9\text{-intar C's}}}(9\text{-intar}) = Tar^{10}(Tar)</math>
* Hektintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{99\text{-intar}}2,0),0),\cdots ),0)}_{99\text{-intar C's}}}(99\text{-intar}) = Tar^{100}(Tar)</math>
* Kilintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{999\text{-intar}}2,0),0),\cdots ),0)}_{999\text{-intar C's}}}(999\text{-intar}) = Tar^{1000}(Tar)</math>
* Megintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{(10^{6}-1)\text{-intar}}2,0),0),\cdots ),0)}_{(10^{6}-1)\text{-intar C's}}}((10^{6}-1)\text{-intar}) = Tar^{10^{6}}(Tar)</math>
* Gigintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{(10^{9}-1)\text{-intar}}2,0),0),\cdots ),0)}_{(10^{9}-1)\text{-intar C's}}}((10^{9}-1)\text{-intar}) = Tar^{10^{9}}(Tar)</math>
* Terintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{(10^{12}-1)\text{-intar}}2,0),0),\cdots ),0)}_{(10^{12}-1)\text{-intar C's}}}((10^{12}-1)\text{-intar}) = Tar^{10^{12}}(Tar)</math>
* Petintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{(10^{15}-1)\text{-intar}}2,0),0),\cdots ),0)}_{(10^{15}-1)\text{-intar C's}}}((10^{15}-1)\text{-intar}) = Tar^{10^{15}}(Tar)</math>
* Exintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{(10^{18}-1)\text{-intar}}2,0),0),\cdots ),0)}_{(10^{18}-1)\text{-intar C's}}}((10^{18}-1)\text{-intar}) = Tar^{10^{18}}(Tar)</math>
* Zettintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{(10^{21}-1)\text{-intar}}2,0),0),\cdots ),0)}_{(10^{21}-1)\text{-intar C's}}}((10^{21}-1)\text{-intar}) = Tar^{10^{21}}(Tar)</math>
* Yottintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{(10^{24}-1)\text{-intar}}2,0),0),\cdots ),0)}_{(10^{24}-1)\text{-intar C's}}}((10^{24}-1)\text{-intar}) = Tar^{10^{24}}(Tar)</math>
* When the death metal music prevail to Armenian toddlers under five in certain isolated areas and cultural divisions during the clash
* Tarintar, <math>f_{\underbrace{C(C(\cdots(C(C(\Omega_{(Dekotar-1)\text{-intar}}2,0),0),\cdots ),0)}_{(Dekotar-1)\text{-intar C's}}}((Dekotar-1)\text{-intar}) = Tar^{Tar}(Tar)</math>
* '''[[Loader 数|Loader's number]]''' (output of loader.c), <math>D^5(99)</math>
* Stained Ouija, <math>D^{1729}(10)</math>
* Bashicu matrix number with respect to Bashicu matrix system version 2.3
* ６ (N primitive)
* [[Y序列|Y sequence]] number, <math>f^{2000}(1)</math>
* <math>\omega-Y</math> sequence number, <math>f^{2000}(1)</math> using <math>f(n) = \omega-Y\ (1,\omega)[n]</math>

【[[Googolism - Part 5|更小]] | [[Googolism|主页]] | 更大】

[[分类:经典大数]]

用户:Baixie01000a7

2026-02-22T09:14:39Z

Baixie01000a7：

拜谢

<chem>CO2 + C -> 2 CO</chem>

<math>\mathrm{Ciallo}\sim(\angle\cdot\omega<)\frown\bigstar</math>

DEN

2026-02-22T08:53:06Z

Baixie01000a7：重定向页面至iblp

#REDIRECT [[iblp]]

Y序列 VS TBMS

2026-02-21T09:53:15Z

Baixie01000a7：重定向页面至Y 序列 vs TBMS

#REDIRECT [[Y_序列_vs_TBMS]]

用户:Baixie01000a7/TON草稿

2026-02-20T13:53:06Z

Baixie01000a7：创建页面，内容为“Taranovsky 序数记号 (Taranovsky’s ordinal notation, TON) 是 Taranovsky 提出的一系列记号的总称。无反射配置的情况下，TON 具有如下的版本： * 反射度：Degrees of Reflection (DR)。 * 包含通过的自下而上：Built-from-below with Passthrough (BP)。 * 包含通过的反射度：Degrees of Reflection with Passthrough (DRP)。 * 主要序数体系：Main Ordinal Notation System (M)。 * 主要序数体系（通过扩展…”

Taranovsky 序数记号 (Taranovsky’s ordinal notation, TON) 是 Taranovsky 提出的一系列记号的总称。

无反射配置的情况下，TON 具有如下的版本：

* 反射度：Degrees of Reflection (DR)。
* 包含通过的自下而上：Built-from-below with Passthrough (BP)。
* 包含通过的反射度：Degrees of Reflection with Passthrough (DRP)。
* 主要序数体系：Main Ordinal Notation System (M)。
* 主要序数体系（通过扩展）：Main ordinal notation system (Passthrough extension)(MP)。
* ''n'' 自下而上迭代（无 4b 版本）：Iteration of ''n''-built from below (variation without 4b)(I)。
* ''n'' 自下而上迭代：Iteration of ''n''-built from below (IBP)。
* ''n'' 自下而上迭代（通过扩展）：Iteration of ''n''-built from below (Passthrough extension)(IP)。

有反射配置的情况下，TON 具有如下的版本：

* 反射配置版反射度：Reflection configuration version of Degrees of Reflection (DRC)。
* 反射配置版包含通过的反射度：Reflection configuration version of Degrees of Reflection with Passthrough (DRPC)。
* 反射配置版主要序数记号体系：Reflection configuration version of Main Ordinal Notation System (MC)。
* 反射配置版主要序数记号体系（通过扩展）：Reflection configuration version of Main ordinal notation system (Passthrough extension) (MPC)。

=== 共同定义 ===
大多数记号都是使用两个常数和一个函数构建的。常数包括 <math>0</math> ，以及 <math>\Omega</math> 或 <math>\Omega_n</math> 之一（其

中 ''n'' 是系统内的给定自然数）。函数通常用 ''C'' 表示，是二元的。

# <math>0</math> 或和 <math>\Omega</math> （或 <math>\Omega_n</math> ）是项。
# 如果 a 和 ''b'' 是项，则C(a,b)是项。

项可以用“''>''”、“''<''”或“=”进行比较和连接。

首先，以后缀形式写出项，即删除所有“(”、“)”和“'',''”，然后反转字符串。其次，按

字典序比较后缀形式，其中<math>C</math> < <math>0</math> < <math>\Omega</math> （或 <math>\Omega_n</math> 为最大单个字母）。

在体系之中，只有一部分项是标准的。

常数是标准的。

如果以下 3 项全部为真，则是标准的。

# a 和 b 都是标准的。
# 如果 b = C(c, d)，则 a ≤ c。
# 此条件在各个不同的体系之间有所不同，通常称之为“自下而上条件”。

要检查“自下而上条件”，我们需要检查 a 的语法树。在定义中：

# 量词不是在项上，而是在 a 内的位置上，因此不同位置的相同项会得到不同的处理。
# <math>x \sqsubseteq y</math> 表示 x 是 y 的子项（也是 <math>x \sqsupseteq y</math> ）。使用位置索引（例如，<math>C(C(C(C(C(\Omega, 0), C(\Omega, \Omega)), 0), 0)</math>中的三个 0 位于位置 (1, 1, 1, 2),(1, 2) 和 (2)），y 的位置索引是 x 的位置索引的初始子串。
# x <math>x \sqsubset y</math> y 表示 x 是 y 的真子项（也是 y <math>x \sqsupset y</math> x ）。即<math>x\subseteq y \wedge x \neq y</math>。

一个标准项表示一个序数，不同的标准项表示不同的序数。序数的序关系被定义为标准项的序关系。

因此，最小标准项 0 对应于最小序数 0 。大于 b1, b2, · · · 的标准项 a 对应于大于 b1, b2, · · ·对应的序数。

这些定义并不能确保良定义，因此需要证明。目前，只有一个体系被充分证明是良定义的。

Taranovsky 记号具有如下共同的性质：

1. <math>C(a,b)>b</math>。

2. <math>C(a,b)</math>在a和b上都是单调的，在a上是连续的。

3. <math>C(a,b)=b+\omega^{a}</math>当且仅当C(a,b)≥a。

第三个性质可以帮助我们进行标准项和 [[康托范式|Cantor 标准形式]] (CNF) 之间的转换。

由于 Ω是一个“大”序数，使得ωΩ= Ω，因此也可以在标准项和基数为 Ω 的 CNF 之间进行转换。

自下而上的条件是不同系统的不同之处。它由 3 个不同的概念组合而成：自下而上方法、通过和反射配置。自下而上方法最先引入，然后是通过，最后是反射配置。因此，这三个概念构成了 TON 的三代。

BSM

2026-02-20T13:30:30Z

Baixie01000a7：

Bashicu急矩阵(Bashicu Sudden Matrix,BSM)是Bashicu Hyudora发明的序数记号。它目前还未被证明[[良序]]。它被认为是[[急模式]]的源头。

== 定义 ==
''前排提示：请先阅读[[BMS]]和[[BHM]]的定义''

BSM只有找坏根规则和BMS不一致。以下介绍不一致的地方。

# 第0列：默认行、列标均从1开始，并在第1列之前加上一个额外的没有值的第0列。如果BHM中一个元素没有父项，则取其父项为同行第0列的元素。
# '''子项'''：如果项A的父项是项B，则称A是B的子项。
# '''待定坏根'''：待定坏根为末列最靠下的非0项(LNZ)的'''所有祖先项'''（包括第0列元素）的子项所在列。特别的，如果末列最下非0项不在第1行，则要求待定坏根正上方的元素应当是末列最下非0项正上方的元素的祖先项。我们称待定根集合中的一些根为“小根”，一些根为“大根”。大根与小根是不冲突的，这意味着，一个根可能既不是小根也不是大根，也可能同时是小根和大根。坏根的选择，和小根与大根息息相关。
# '''预展开'''：根据找到的待定坏根r，确定待定好部G'，待定坏部B'，末列L，待定阶差向量<math>\Delta'</math>，随后'''按照BMS的规则'''得到r对应的预展开式<math>S_r=G'\sim B'\sim (B'+\Delta') \sim (L+\Delta')</math>(其中~是序列连接)。特别的，我们称最右侧的待定坏根（即BMS意义的坏根）对应的预展开式为基准式。
# '''小根'''：至少满足下列两条件之一的根r是小根：①r的预展开式在字典序上小于基准式。②如果根r是最右侧待定坏根的祖先项，且第r列和最右侧待定坏根所处列的第t+1行到最后一行，'''不能完全对应相同'''(t是LNZ所处行号)。
# '''大根'''：如果根r是最右侧待定坏根的祖先项，且满足第r列和最右侧待定坏根所处列的第t+1行到最后一行，'''完全对应相同'''
#坏根：坏根定义为在所有“是小根但不是大根”的待定坏根右边的第一个待定坏根。特别的，如果不存在这样的这样的待定坏根，则坏根是最左侧待定坏根。

BSM的极限基本列是<math>\{(0)(1),(0,0)(1,1),(0,0,0)(1,1,1),\cdots\}</math>,因此从这里面的元素经过不断取基本列或取前驱所能得到的式子是BSM的标准式，否则不是标准式。

值得注意的是，单行BSM又称急序列(Sudden Sequence System,'''SSS'''),也是一个很有名的[[序数记号]]。

实例：

例1：<math>(0)(1)(2)</math>

可以发现LNZ的祖先是第0项、第1项、第2项。找到它们的所有子项，是第1项和第2项。于是给出预展开式<math>S_1=(0)(1)(1)(2)(3)</math>,<math>S_2=(0)(1)(1)(2)</math>.因此小根是第0项。因此坏根是第1项。得到展开式是<math>(0)(1)(1)(2)(2)(3)(3)(4)\cdots</math>.

例2：<math>(0,0)(1,1)(2,0)(3,1)(3,0)</math>

我们用红色标记其待定坏根：<math>({\color{red}0},0)({\color{red}1},1)({\color{red}2},0)(3,1)(3,0)</math>,前两个待定坏根均为最右侧待定坏根第三列第一行的2的祖先项，第一列第一行的0下方的元素和最右侧待定坏根下方的元素完全一致，因此它是一个大根。而第二列第一行的1下方的元素和最右侧待定坏根下方的元素不一致，因此它是一个小根。在这里我们很幸运，可以直接得出坏根是第三列第一行的2.于是展开式是<math>(0,0)(1,1)(2,0)(3,1)(2,0)(3,1)(2,0)(3,1)\cdots</math>

例3：<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(3,0)</math>

我们用红色标记其待定坏根：<math>({\color{red}0},0)({\color{red}1},1)({\color{red}1},0)({\color{red}1},0)({\color{red}2},0)(3,1)(3,0)</math>.其中第一列第一行的0和第四列第一行的1是最右侧待定坏根2的祖先项。可以发现它们都是大根。接下来是各个待定坏根的预展开式：<math>S_5=(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(3,1)(3,0)</math>,它是基准式。接下来有<math>S_4=(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(3,0)(4,1)(4,0)</math>然后是<math>S_3=(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(2,0)(3,0)(4,1)(4,0)</math>。然后是<math>S_2=(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,1)(2,0)(2,0)(3,0)(4,1)(4,0)</math>.然后是<math>S_1=(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(3,1)(3,0)(3,0)(4,0)(5,1)(5,0)</math>.比较字典序后发现，第二列第一行的1、第三列第一行的1、第四列第一行的1的预展开式都大于基准式，因此它们都不是小根。但因为第一列第一行的0和第四列第一行的1是大根，因此坏根是第四列第一行的1.于是得到展开式<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(3,0)(4,1)\cdots</math>

== 枚举和强度分析 ==
参见词条[[BSM分析]]

{{默认排序:序数记号}}
[[分类:记号]]

用户:Baixie01000a7

2026-02-20T13:26:04Z

Baixie01000a7：

拜谢

<chem>CO2 + C -> 2 CO</chem>

用户:Baixie01000a7

2026-02-20T13:25:35Z

Baixie01000a7：创建页面，内容为“拜谢”

拜谢

DcN

2026-02-20T12:25:23Z

Baixie01000a7：

DcN，是 318`4 创造的便于打字的记号，主要用于写 FOS 中作为序数的项，几乎不可能良定义，主要通过枚举列表来主观推算定义。DcN 的极限是 <math>\varphi(10,0)</math>，Y_cpper 将其扩展到 <math>\Gamma_0</math>，现在一般在 <math>\varphi(\omega,0)</math> 之后使用这个扩展。DcN 的所有符号都集中在电脑键盘左上方的一小片区域，qwerty13456789，456789 使用频率很低，Veblen 记号需要随时要输入括号下标希腊字母，1-Y 则有比 DcN 更长的常见表达式，所以 DcN 便于打字，是专为 FOS 中常见序数设计的记号；但因为可读性差，DcN 一直没能流传开来。

因为完全无r的 DcN 存在歧义，比如 wtw1wtww 可以是 <math>\omega^{\omega^2}+\omega^\omega</math>，也可以是 <math>\omega^{\omega^{\omega^2}+\omega}</math>，因此在表达 FOS 的项时，建议使用含 r 的 DcN，但是去掉所有位于表达式末尾的 r，如 <math>\omega^{\omega^{\omega^\omega}}</math>=wtwtwtwrrr 记作 wtwtwtw。

1-Y 不必多说，是 Yukito 在 2019 年创造的序列记号，首次引入山脉图，在 Y(1,3) 之前有非常优秀的性质，因此也常用于表达 FOS 中作为项的序数。不过为简便，写 1-Y 表达式时通常省略 Y( ) 外壳和逗号，超过 10 的数字用拉丁字母表示，超过 36 则无写法。

在研究 FOS 的定义、构造原理时，使用 1-Y 的情况更多，因为 1-Y 的山脉结构和 FOS 中项内部的山脉结构类似；而在研究 FOS 的分析、强度形成原理时，为简便起见，使用 DcN 更多。在阅读 FOS 的枚举列表之前，请务必将本文的枚举列表熟透于心中，否则用 Veblen 记号或 OCF 写 FOS 表达式费时费力。
{| class="wikitable"
|-
!序数（十进制 + Cantor 记号 + Veblen 记号）
!DcN
!1-Y
|-
|<math>0</math>
|0
|<math>\varnothing</math>
|-
|<math>1</math>
|1
|1
|-
|<math>2</math>
|11
|11
|-
|<math>3</math>
|111
|111
|-
|<math>\omega</math>
|w
|12
|-
|<math>\omega+1</math>
|1w
|121
|-
|<math>\omega+2</math>
|11w
|1211
|-
|<math>\omega2</math>
|w1
|1212
|-
|<math>\omega2+1</math>
|1w1
|12121
|-
|<math>\omega3</math>
|w11
|121212
|-
|<math>\omega3+1</math>
|1w11
|1212121
|-
|<math>\omega^2</math>
|ww
|122
|-
|<math>\omega^2+1</math>
|1ww
|1221
|-
|<math>\omega^2+\omega</math>
|w1ww
|12212
|-
|<math>\omega^2+\omega+1</math>
|1w1ww
|122121
|-
|<math>\omega^2+\omega2</math>
|w11ww
|1221212
|-
|<math>\omega^2+\omega2+1</math>
|1w11ww
|12212121
|-
|<math>\omega^2+\omega3</math>
|w111ww
|122121212
|-
|<math>\omega^22</math>
|ww1
|122122
|-
|<math>\omega^22+\omega</math>
|w1ww1
|12212212
|-
|<math>\omega^22+\omega2</math>
|w11ww1
|1221221212
|-
|<math>\omega^23</math>
|ww11
|122122122
|-
|<math>\omega^3</math>
|www
|1222
|-
|<math>\omega^3+\omega</math>
|w1www
|122212
|-
|<math>\omega^3+\omega^2</math>
|ww1www
|1222122
|-
|<math>\omega^3+\omega^2+1</math>
|1ww1www
|12221221
|-
|<math>\omega^3+\omega^2+\omega</math>
|w1ww1www
|122212212
|-
|<math>\omega^3+\omega^2+\omega+1</math>
|1w1ww1www
|1222122121
|-
|<math>\omega^3+\omega^2+\omega2</math>
|w11ww1www
|12221221212
|-
|<math>\omega^3+\omega^22+\omega</math>
|w1ww11www
|122212212212
|-
|<math>\omega^3+\omega^22+\omega2+1</math>
|1w11ww11www
|122212212212121
|-
|<math>\omega^32</math>
|www1
|12221222
|-
|<math>\omega^4</math>
|wwww
|12222
|-
|<math>\omega^5</math>
|wwwww
|122222
|-
|<math>\omega^\omega</math>
|wtw
|123
|-
|<math>\omega^\omega+1</math>
|1wtw
|1231
|-
|<math>\omega^\omega+\omega</math>
|w1wtw
|12312
|-
|<math>\omega^\omega+\omega2</math>
|w11wtw
|1231212
|-
|<math>\omega^\omega+\omega^2</math>
|ww1wtw
|123122
|-
|<math>\omega^\omega2</math>
|w1tw
|123123
|-
|<math>\omega^\omega2+\omega^2</math>
|ww1w1tw
|123123122
|-
|<math>\omega^\omega3</math>
|w11tw
|123123123
|-
|<math>\omega^{\omega+1}</math>
|wt1w
|1232
|-
|<math>\omega^{\omega+1}+\omega^2</math>
|ww1wt1w
|1232122
|-
|<math>\omega^{\omega+1}+\omega^\omega</math>
|wtwr1wt1w
|1232123
|-
|<math>\omega^{\omega+1}+\omega^\omega2</math>
|w1twr1wt1w
|1232123123
|-
|<math>\omega^{\omega+1}2+\omega^\omega</math>
|wtwr1w1t1w
|12321232123
|-
|<math>\omega^{\omega+1}2+\omega^\omega2</math>
|w1twr1w1t1w
|12321232123123
|-
|<math>\omega^{\omega+1}3</math>
|w11t1w
|123212321232
|-
|<math>\omega^{\omega+2}</math>
|wt11w
|12322
|-
|<math>\omega^{\omega+3}</math>
|wt111w
|123222
|-
|<math>\omega^{\omega2}</math>
|wtw1
|12323
|-
|<math>\omega^{\omega2+1}</math>
|wt1w1
|123232
|-
|<math>\omega^{\omega2+1}+\omega^{\omega2}</math>
|wtw1r1wt1w1
|12323212323
|-
|<math>\omega^{\omega2+1}+\omega^{\omega2}2</math>
|w1tw1r1wt1w1
|1232321232312323
|-
|<math>\omega^{\omega2+1}2+\omega^{\omega2}2</math>
|w1tw1r1w1t1w1
|1232321232321232312323
|-
|<math>\omega^{\omega2+1}2+\omega^{\omega2}2+\omega^{\omega+1}2+\omega^{\omega}2</math>
|w1twr1w1t1wr1w1tw1r1w1t1w1
|123232123232123231232312321232123123
|-
|<math>\omega^{\omega2+2}</math>
|wt11w1
|1232322
|-
|<math>\omega^{\omega2+2}+\omega^{\omega2+1}</math>
|wt1w1r1wt11w1
|1232322123232
|-
|<math>\omega^{\omega3}</math>
|wtw11
|1232323
|-
|<math>\omega^{\omega3+1}+\omega^{\omega3}</math>
|wtw11r1wt1w11
|123232321232323
|-
|<math>\omega^{\omega4}</math>
|wtw111
|123232323
|-
|<math>\omega^{\omega^2}</math>
|wtww
|1233
|-
|<math>\omega^{\omega^2+\omega+1}+\omega^{\omega^2+\omega}</math>
|wtw1wwr1wt1w1ww
|1233232123323
|-
|<math>\omega^{\omega^22}</math>
|wtww1
|1233233
|-
|<math>\omega^{\omega^3}</math>
|wtwww
|12333
|-
|<math>\omega^{\omega^\omega}</math>
|wtwtw
|1234
|-
|<math>\omega^{\omega^{\omega2+1}3}</math>
|wtw11t1w1
|1234343234343234343
|-
|<math>\omega^{\omega^{\omega2+2}}</math>
|wtwt11w1
|12343433
|-
|<math>\omega^{\omega^{\omega3}}</math>
|wtwtw11
|12343434
|-
|<math>\omega^{\omega^{\omega^2}}</math>
|wtwtww
|12344
|-
|<math>\omega^{\omega^{\omega^\omega}}</math>
|wtwtwtw
|12345
|-
|<math>\varepsilon_0</math>
|e
|124
|-
|<math>\varepsilon_0+\omega</math>
|w1e
|12412
|-
|<math>\varepsilon_0+\omega^\omega</math>
|wtwr1e
|124123
|-
|<math>\varepsilon_02</math>
|e1
|124124
|-
|<math>\varepsilon_02+\omega</math>
|w1e1
|12412412
|-
|<math>\varepsilon_0\omega=\omega^{\varepsilon_0+1}</math>
|wt1e
|1242
|-
|<math>\omega^{\varepsilon_0+1}+\varepsilon_0</math>
|e1wt1e
|1242124
|-
|<math>\omega^{\varepsilon_0+1}2</math>
|w1t1e
|12421242
|-
|<math>\omega^{\varepsilon_0+2}</math>
|wt11e
|12422
|-
|<math>\omega^{\varepsilon_0+\omega}</math>
|wtw1e
|12423
|-
|<math>\omega^{\varepsilon_0+\omega^\omega}</math>
|wtwtwr1e
|124234
|-
|<math>\omega^{\varepsilon_02}</math>
|wte1
|12424
|-
|<math>\omega^{\omega^{\varepsilon_0+1}}</math>
|wtwt1e
|1243
|-
|<math>\omega^{\omega^{\varepsilon_0 2}}</math>
|wtwte1
|12435
|-
|<math>\varepsilon_1</math>
|ee
|1244
|-
|<math>\omega^{\varepsilon_12}</math>
|wtee1
|1244244
|-
|<math>\varepsilon_2</math>
|eee
|12444
|-
|<math>\varepsilon_\omega</math>
|etw
|1245
|-
|<math>\varepsilon_\omega+\omega^\omega</math>
|wtwr1etw
|1245123
|-
|<math>\varepsilon_\omega+\varepsilon_0</math>
|e1etw
|1245124
|-
|<math>\varepsilon_\omega2</math>
|e1tw
|12451245
|-
|<math>\omega^{\varepsilon_\omega+1}</math>
|wt1etw
|12452
|-
|<math>\omega^{\varepsilon_\omega+\omega}</math>
|wtw1etw
|124523
|-
|<math>\omega^{\varepsilon_\omega2}</math>
|wte1tw
|1245245
|-
|<math>\varepsilon_{\omega+1}</math>
|et1w
|12454
|-
|<math>\varepsilon_{\omega2}</math>
|etw1
|124545
|-
|<math>\varepsilon_{\omega^\omega}</math>
|etwtw
|12456
|-
|<math>\varepsilon_{\varepsilon_0}</math>
|ete
|12457
|-
|<math>\varepsilon_{\varepsilon_0+1}</math>
|et1e
|12457
|-
|<math>\varepsilon_{\varepsilon_1}</math>
|etee
|12457
|-
|<math>\varepsilon_{\varepsilon_{\varepsilon_0}}</math>
|etete
|124578A
|-
|<math>\zeta_0</math>
|y
|1246
|-
|<math>\zeta_0+\varepsilon_0</math>
|e1y
|1246124
|-
|<math>\zeta_0+\varepsilon_{\varepsilon_0}</math>
|eter1y
|124612457
|-
|<math>\zeta_02</math>
|y1
|12461246
|-
|<math>\omega^{\zeta_0+1}</math>
|wt1y
|12462
|-
|<math>\omega^{\zeta_0+\varepsilon_\omega}</math>
|wtetwr1y
|1246245
|-
|<math>\omega^{\zeta_02}</math>
|wty1
|1246246
|-
|<math>\varepsilon_{\zeta_0+1}</math>
|ye=et1y
|12464
|-
|<math>\omega^{\varepsilon_{\zeta_0+1}+1}</math>
|wt1ye=wt1et1y
|124642
|-
|<math>\varepsilon_{\zeta_0+2}</math>
|yee=et11y
|124644
|-
|<math>\varepsilon_{\zeta_0+3}</math>
|yeee=et111y
|1246444
|-
|<math>\varepsilon_{\zeta_0+\omega}</math>
|etw1y
|124645
|-
|<math>\varepsilon_{\zeta_0+\omega^\omega}</math>
|etwtwr1y
|1246456
|-
|<math>\varepsilon_{\zeta_0+\varepsilon_0}</math>
|ete1y
|1246457
|-
|<math>\varepsilon_{\zeta_02}</math>
|ety1
|12464579
|-
|<math>\varepsilon_{\zeta_02+1}</math>
|et1y1
|124645794
|-
|<math>\varepsilon_{\zeta_03}</math>
|ety11
|124645794579
|-
|<math>\varepsilon_{\omega^{\zeta_0+1}}</math>
|etwt1y
|124645795
|-
|<math>\varepsilon_{\varepsilon_{\zeta_0+1}}</math>
|etet1y
|124645797
|-
|<math>\zeta_1</math>
|yy
|124646
|-
|<math>\varepsilon_{\zeta_1+1}</math>
|et1yy=yye
|1246464
|-
|<math>\zeta_2</math>
|yyy
|12464646
|-
|<math>\zeta_{\omega}</math>
|ytw
|12465
|-
|<math>\omega^{\zeta_{\omega}2}</math>
|wty1tw
|124652465
|-
|<math>\varepsilon_{\zeta_{\omega}+1}</math>
|et1ytw
|124654
|-
|<math>\varepsilon_{\zeta_{\omega}+\omega^{\varepsilon_0+1}}</math>
|etwt1er1ytw
|124654575
|-
|<math>\varepsilon_{\zeta_{\omega}+\varepsilon_\omega}</math>
|etetwr1ytw
|124654578
|-
|<math>\varepsilon_{\zeta_{\omega}+\zeta_0}</math>
|ety1ytw
|124654579
|-
|<math>\varepsilon_{\varepsilon_{\zeta_{\omega}2}}</math>
|etety1tw
|124654579878ACB
|-
|<math>\zeta_{\omega+1}</math>
|yt1w
|1246546
|-
|<math>\zeta_{\omega2}</math>
|ytw1
|124655
|-
|<math>\zeta_{\varepsilon_0}</math>
|yte
|124657
|-
|<math>\zeta_{\zeta_0}</math>
|yty
|1246579
|-
|<math>\eta_0</math>
|3
|12466
|-
|<math>\omega^{\eta_0+1}</math>
|wt13
|124662
|-
|<math>\omega^{\eta_0+\varepsilon_0}</math>
|wte13
|1246624
|-
|<math>\omega^{\eta_0+\zeta_0}</math>
|wty13
|12466246
|-
|<math>\omega^{\eta_02}</math>
|wt31
|124662466
|-
|<math>\varepsilon_{\eta_0+1}</math>
|3e=et13
|124664
|-
|<math>\varepsilon_{\eta_0+\omega}</math>
|etw13
|1246645
|-
|<math>\varepsilon_{\eta_0+\varepsilon_0}</math>
|ete13
|12466457
|-
|<math>\varepsilon_{\eta_0+\zeta_0}</math>
|ety13
|124664579
|-
|<math>\varepsilon_{\eta_02}</math>
|et31
|1246645799
|-
|<math>\zeta_{\eta_0+1}</math>
|3y=yt13
|1246646
|-
|<math>\zeta_{\eta_0+\omega}</math>
|ytw13
|12466465
|-
|<math>\zeta_{\eta_0+\varepsilon_0}</math>
|yte13
|124664657
|-
|<math>\zeta_{\eta_0+\zeta_0}</math>
|yty13
|1246646579
|-
|<math>\zeta_{\eta_02}</math>
|yt31
|12466465799
|-
|<math>\eta_1</math>
|33
|12466466
|-
|<math>\eta_\omega</math>
|3tw
|124665
|-
|<math>\eta_{\eta_0}</math>
|3t3
|124665799
|-
|<math>\varphi(4,0)</math>
|4
|124666
|-
|<math>\omega^{\varphi(4,0)2}</math>
|wt41
|1246662466
|-
|<math>\varepsilon_{\varphi(4,0)+1}</math>
|et41
|12466645799
|-
|<math>\zeta_{\varphi(4,0)+1}</math>
|yt41
|124666465799
|-
|<math>\eta_{\varphi(4,0)+1}</math>
|3t41
|1246664665799
|-
|<math>\varphi(4,1)</math>
|44
|1246664666
|-
|<math>\varphi(5,0)</math>
|5
|1246666
|-
|<math>\varphi(6,0)</math>
|6
|12466666
|-
|<math>\varphi(7,0)</math>
|7
|124666666
|-
|<math>\varphi(8,0)</math>
|8
|1246666666
|-
|<math>\varphi(4,\varphi(8,0)+1)+\eta_0</math>
|3184=314t18
|1246666666466657999999912466
|-
|<math>\varphi(9,0)</math>
|9
|12466666666
|-
|<math>\varphi(9,\varphi(9,0))</math>
|9t9
|124666666665799999999
|-
|<math>\varphi(10,0)</math>
|limit
|124666666666
|+
!序数（十进制 + Cantor 记号 + Veblen 记号）
!扩展DcN
!1-Y
|-
|<math>\varphi(10,0)</math>
|q1111111111r
|124666666666
|-
|<math>\varphi(11,0)</math>
|q11111111111r
|1246666666666
|-
|<math>\varphi(\omega,0)</math>
|qwr
|12467
|-
|<math>\varepsilon_{\varphi(\omega,0)+1}</math>
|et1qwr=qwre =q1rt1qwr=qwrq1r
|124674
|-
|<math>\varphi(\omega,1)</math>
|qwrqwr
|12467467
|-
|<math>\varphi(\omega,\omega)</math>
|qwrtw
|124675
|-
|<math>\varphi(\omega+1,0)</math>
|q1wr
|124676
|-
|<math>\varphi(\omega2,0)</math>
|qw1r
|1246767
|-
|<math>\varphi(\varepsilon_0,0)</math>
|qer
|124679
|-
|<math>\varphi(\varepsilon_0+\omega,\zeta_0)</math>
|qw1erty（qwerty）
|12467967579
|-
|<math>\varphi(\zeta_0,0)</math>
|qyr
|124679B
|-
|<math>\varphi(\varphi(\omega,0),0)</math>
|qqwrr
|124679BC
|-
|<math>\Gamma_0</math>
|limit
|12468
|}

{| class="wikitable"
!序数（十进制+BOCF）
!1-Y
|-
|<math>\psi(\Omega^{\Omega})</math>
|12468
|-
|<math>\psi(\Omega^{\Omega}+1)</math>
|124682
|-
|<math>\psi(\Omega^{\Omega}+\psi(\Omega^{\Omega}))</math>
|124682468
|-
|<math>\psi(\Omega^{\Omega}+\Omega)</math>
|124684
|-
|<math>\psi(\Omega^{\Omega}+\Omega^\omega)</math>
|12468467
|-
|<math>\psi(\Omega^{\Omega}+\Omega^{\psi(\Omega^\omega)})</math>
|124684679AB
|-
|<math>\psi(\Omega^{\Omega}+\Omega^{\psi(\Omega^\Omega)})</math>
|124684679AC
|-
|<math>\psi(\Omega^{\Omega}+\Omega^{\psi(\Omega^\Omega)+1})</math>
|124684679AC6
|-
|<math>\psi(\Omega^{\Omega}+\Omega^{\psi(\Omega^\Omega+1)})</math>
|124684679AC7
|-
|<math>\psi(\Omega^{\Omega}+\Omega^{\psi(\Omega^\Omega+\Omega)})</math>
|124684679AC9
|-
|<math>\psi(\Omega^{\Omega}+\Omega^{\psi(\Omega^\Omega+\Omega^\omega)})</math>
|124684679AC9AB
|-
|<math>\psi(\Omega^{\Omega}2)</math>
|12468468
|-
|<math>\psi(\Omega^{\Omega+1})</math>
|124686
|-
|<math>\psi(\Omega^{\Omega+\psi(\Omega^{\Omega})})</math>
|12468679BD
|-
|<math>\psi(\Omega^{\Omega2})</math>
|1246868
|-
|<math>\psi(\Omega^{\Omega\psi(\Omega^{\Omega})})</math>
|1246879BD
|-
|<math>\psi(\Omega^{\Omega^2})</math>
|124688
|-
|<math>\psi(\Omega^{\Omega^\omega})</math>
|124689
|-
|<math>\psi(\Omega^{\Omega^{\psi(\Omega^{\Omega^\omega})}})</math>
|124689BDFG
|-
|<math>\psi(\Omega^{\Omega^\Omega})</math>
|12468A
|-
|<math>\psi(\Omega_2)</math>
|1247
|-
|<math>\psi(\Omega_2+\Omega^\Omega)</math>
|1247468
|-
|<math>\psi(\Omega_2+\psi_1(\Omega_2))</math>
|124747
|-
|<math>\psi(\Omega_2+\psi_1(\Omega_2+\Omega))</math>
|12476
|-
|<math>\psi(\Omega_2+\psi_1(\Omega_2+\Omega^\Omega))</math>
|124768
|-
|<math>\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2)))</math>
|124769
|-
|<math>\psi(\Omega_22)</math>
|12477
|-
|<math>\psi(\Omega_2\omega)</math>
|12478
|-
|<math>\psi(\Omega_2\Omega)</math>
|12479
|-
|<math>\psi(\Omega_2^2)</math>
|1247A
|-
|<math>\psi(\Omega_2^{\Omega_2})</math>
|1247AD
|-
|<math>\psi(\Omega_3)</math>
|1247B
|-
|<math>\psi(\Omega_4)</math>
|1247BG
|-
|<math>\psi(\Omega_\omega)</math>
|1248
|}
再往后涉及项嵌套的提升效应，目前对此研究不清晰，故枚举列表暂时到此为止。

{{默认排序:个人记号}}
[[分类:分析]]
[[分类:记号]]

记号展开器

2026-02-20T11:03:43Z

Baixie01000a7：

[https://hypcos.github.io/notation-explorer/ NE]包含了许多常见记号的展开器。 
以下网址也包含了一些记号的展开器，各有不同，请依据实际情况使用：

* [https://0y.googology.top 0-Y展开器(带山脉图)，i0-Y(测试性)]
* [https://solarzone1010.github.io/ SSO内的BMS分析仪，cOCF及HSPN展开器，TONF及GON浏览器等]
* [https://gyafun.jp/ln/basmat.cgi Bashicu矩阵计算器]
* [https://waffle3z.github.io/notations/ BMS、Y序列、HPrSS、LPrSS、BrSS浏览器等]
* [https://fghdisplayer.onrender.com/ LVO内韦伯伦函数的FGH及基本列展开]
* [https://naruyoko.github.io/googology/ Y和ω-Y序列的展开和山脉图绘制、BMS的展开过程演示等]
* [https://koteitan.github.io/BeklemishevsWorms/ worm序列辅助展开程序] [https://gomen520.github.io/ X-Y展开程序]

BMS

2026-02-20T10:46:41Z

Baixie01000a7：/* 数学定义 */

Bashicu 矩阵系统（Bashicu Matrix System，'''BMS'''）是一个[[序数记号]]。Bashicu Hyudora 在 2018 年给出了它的定义。直至今日，BMS 依然是已经证明[[良序]]的最强的序数记号。

== 定义 ==

=== 原定义 ===
Bashicu 最初在他的未命名的 BASIC 编程语言改版上提交了 BMS 的定义。<ref name=":0"> Bashicu Hyudora (2015). [https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:BashicuHyudora/BASIC%E8%A8%80%E8%AA%9E%E3%81%AB%E3%82%88%E3%82%8B%E5%B7%A8%E5%A4%A7%E6%95%B0%E3%81%AE%E3%81%BE%E3%81%A8%E3%82%81#.E3.83.90.E3.82.B7.E3.82.AF.E8.A1.8C.E5.88.97.E6.95.B0.28Bashicu_matrix_number.29 Summary of large numbers in BASIC language] (BASIC言語による巨大数のまとめ). ''Googology Wiki''.</ref>BMS 的原定义是一个大数记号，理论的输出是一个大数。该程序并未设计为实际运行，原因在于语言修改的未定义性，同时也受限于内存与计算时间的现实约束，无法计算出这个大数的实际最终值。因此，Fish 编写了名为"Bashicu 矩阵计算器"的程序来演示预期的计算流程（该程序已得到 Bashicu 验证）。故 Bashicu 矩阵的正式定义可参考 Fish 程序的源代码。<ref>Kyodaisuu (2020). [https://github.com/kyodaisuu/basmat/blob/master/basmat.c basmat]. ''Gthub''.</ref>

=== 正式定义 ===
中文 googology 社区提到 BMS 默认是一个序数记号。以下是序数记号 BMS 的定义及说明：

首先是 BMS 合法式：BMS 的合法式是二维的自然数构成的序列，在外观上看是一个矩阵。如 <math>\begin{pmatrix} 0 & 1&2&1 \\ 0&1&1&1\\0&1&0&1 \end{pmatrix}</math> 就是一个 BMS 的合法式。在很多场合，这种二维的结构书写起来不是很方便，因此我们也常常把BMS从左到右、从上到下按列书写，每一列的不同行之间用逗号隔开，不同列之间用括号隔开。例如，上面的 BMS 也可以写成 <math>(0,0,0)(1,1,1)(2,1,0)(1,1,1)</math>。在很多情况下，除首列外，列末的 0 也可以省略不写，例如上面的 BMS 写为 <math>(0)(1,1,1)(2,1)(1,1,1)</math>。

理论上来说，只要是这样的式子就可以按照 BMS 的规则进行处理了。但实际操作过程中，我们还可以排除一些明显不标准的式子：

* 首列并非全 0
* 每一列并非不严格递减，即出现一列中下面的数大于上面的数
* 出现一个元素 a，它比它同行左边所有元素都大超过 1

在了解 BMS 的展开规则之前，需要先了解一些概念。

# 第一行元素的'''父项'''：对于位于第一行的元素 a，它的父项 b 是满足以下条件的项当中，位于最右边的项：1. 同样位于第一行且在 a 的左边；2. 小于 a。这里和 [[初等序列系统|PrSS]] 判定父项的规则是相同的。显然，0 没有父项。
# '''祖先项'''：一个元素自己，以及它的父项、父项的父项、父项的父项的父项……共同构成它的祖先项。
# 其余行元素的父项：对于不位于第一行的元素 c，它的父项 d 指满足以下条件的项当中，位于最右边的项：1. 与c位于同一行且在 c 的左边；2. 小于 c；3. d 正上方的项 e 是 c 正上方的项f的祖先项。0 没有父项。
# '''坏根'''：最后一列位于最下方的非零元素的父项所在列，称为坏根。如果最后一列所有元素为 0，则这个 BMS 表达式无坏根。值得一提的是，末列最靠下的非零元素记作 '''LNZ'''（Lowermost Non-Zero）
# '''好部'''、'''坏部'''：这两个概念与 PrSS 是相似的。位于坏根左边的所有列称为好部，记作 G，G 可以为空；从坏根到倒数第二列(包括坏根、倒数第二列)的部分称为坏部，记作B。
# '''阶差向量'''：在一个 n 行 BMS 中，我们把末列记为 <math>(\alpha_1,\alpha_2,\cdots,\alpha_n)</math>，把坏根列记为 <math>(\beta_1,\beta_2,\cdots,\beta_n)</math>，并且我们规定 <math>\alpha_{n+1}=0</math>。则阶差向量<math>\Delta=(\delta_1,\delta_2,\cdots,\delta_n)</math>按照这样的规则得到：<math>\delta_i = \begin{cases} \alpha_i-\beta_i, & \alpha_{i+1}\neq0 \\ 0, & \alpha_{i+1}=0 \end{cases}</math>。通俗的说，如果末列的第 <math>i+1</math> 项等于0，则 <math>\delta_i=0</math>，否则 <math>\delta_i</math> 等于末列第 i 行减去坏根列第 i 行。阶差向量记作 <math>\Delta</math>。
# <math>B_m</math>：<math>B_m</math>是 B 中每一列都加上 <math>\Delta</math> 的 m 倍所得到的新矩阵。但是有一点需要注意：如果 B 中某个元素 t 的祖先项不包含坏根中的元素，则在 <math>B_m</math> 对应位置的元素的值依然是 t，它不加 <math>\Delta</math>。

了解概念后，以下是 BMS 的展开规则：

# 空矩阵 = 0
# 如果表达式是非空矩阵 S，如果它没有坏根，那么 S 等于 S 去掉最后一列之后，剩余部分的后继。
# 否则，确定这个 BMS 表达式 S 的坏根、G、B、<math>\Delta</math>，S 的基本列第 n 项<math>S[n]=G\sim B\sim B_1 \sim B_2\sim B_3\sim\cdots\sim B_{n-1}</math>。其中 ~ 表示序列拼接。或者称 S 的展开式是 <math>G\sim B \underbrace{\sim B_1\sim B_2\sim \cdots}_{\omega}</math>。

BMS 的极限基本列是 <math>\{(0)(1),(0,0)(1,1),(0,0,0)(1,1,1),(0,0,0,0)(1,1,1,1),\cdots\}</math>，从这个基本列中元素开始取前驱或取基本列所能得到的表达式是 BMS 的标准式。

以下是 BMS 展开的一些实例：

例一：<math>(0,0,0)(1,1,1)(2,2,1)(3,2,0)(0,0,0)</math>

因为末列全都是 0，因此这个 BMS 没有坏根。根据规则 2，它是 <math>(0,0,0)(1,1,1)(2,2,1)(3,2,0)</math> 的后继。

例二：<math>(0,0,0)(1,1,1)(2,2,2)(3,3,3)(4,2,0)</math>

LNZ 是末列第二行的 2。首先确定末列第 1 行元素的祖先项，即标红的部分（末列本身不染色，下同）：<math>({\color{red}0},0,0)({\color{red}1},1,1)({\color{red}2},2,2)({\color{red}3},3,3)(4,2,0)</math>。因此末列第二行的 2 的父项只能在含有标红元素的这些列中选取。于是确定 LNZ 的父项为（标绿）：<math>({\color{red}0},0,0)({\color{red}1},{\color{green}1},1)({\color{red}2},2,2)({\color{red}3},3,3)(4,2,0)</math>。因此确定 <math>(1,1,1)</math> 是坏根。好部 G 是 <math>(0,0,0)</math>，坏部 B 是 <math>(1,1,1)(2,2,2)(3,3,3)</math>。计算出阶差向量 <math>\Delta=(3,0,0)</math>。检查 B 中是否存在祖先项不包含坏根中元素的项（当然，我们只需要检查 <math>\Delta</math> 非零的那些行），很幸运，没有。于是我们得到展开式是 <math>(0,0,0)(1,1,1)(2,2,2)(3,3,3)(4,1,1)(5,2,2)(6,3,3)(7,1,1)(8,2,2)(9,3,3)\cdots</math>

例三：<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)(4,2,0,0)(5,1,1,1)(6,2,2,1)(7,3,1,1)</math>

LNZ 是末列第四行的 1。首先确定末列第一行元素 7 的祖先项（标红）：<math>({\color{red}0},0,0,0)({\color{red}1},1,1,1)({\color{red}2},2,2,1)({\color{red}3},3,1,1)({\color{red}4},2,0,0)({\color{red}5},1,1,1)({\color{red}6},2,2,1)(7,3,1,1)</math>。在含有标红元素的列中寻找末列第二行元素 3 的祖先项（标绿）：<math>({\color{red}0},{\color{green}0},0,0)({\color{red}1},1,1,1)({\color{red}2},2,2,1)({\color{red}3},3,1,1)({\color{red}4},2,0,0)({\color{red}5},{\color{green}1},1,1)({\color{red}6},{\color{green}2},2,1)(7,3,1,1)</math>。在含有标绿元素的列中寻找末列第三行元素 1 的祖先项（标蓝）：<math>({\color{red}0},{\color{green}0},{\color{dodgerblue}0},0)({\color{red}1},1,1,1)({\color{red}2},2,2,1)({\color{red}3},3,1,1)({\color{red}4},2,0,0)({\color{red}5},{\color{green}1},1,1)({\color{red}6},{\color{green}2},2,1)(7,3,1,1)</math>。在含有标蓝元素的列中寻找 LNZ 的父项，即首列第四行的 0。于是得到坏根是 <math>(0,0,0,0)</math>，好部 G 是空矩阵，坏部 B 是 <math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)(4,2,0,0)(5,1,1,1)(6,2,2,1)</math>，计算阶差向量 <math>\Delta=(7,3,1,0)</math>。检查 B 中是否存在祖先项不包含坏根中元素的项（只检查 <math>\Delta</math> 非 0 的行）得到第五列第三行的 0 祖先项不经过坏根。于是我们得到展开式是

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)(4,2,{\color{red}0},0)(5,1,1,1)(6,2,2,1)(7,3,1,0)(8,4,2,1)(9,5,3,1)(10,6,2,1)(11,5,{\color{red}0},0)(12,4,2,1)(13,5,3,1)(14,6,2,0)(15,7,3,1)(16,8,4,1)(17,9,3,1)(18,8,{\color{red}0},0)(19,7,3,1)(20,8,4,1)\cdots</math>

展开 BMS 可以靠 [https://gyafun.jp/ln/basmat.cgi Bashicu Matrix Calculator] 或 [https://hypcos.github.io/notation-explorer/ Notation Explorer] 辅助。

=== 数学定义 ===
kotetian 给出 BMS 的数学定义，但是他给出的定义是大数记号版本的。以下是根据他的定义改写的序数记号版 BMS 的定义：

<math>\mathrm{Matrix:}{\boldsymbol S}={\boldsymbol S}_0{\boldsymbol S}_1\cdots{\boldsymbol S}_{X-1}</math>

<math>\mathrm{Vector:}~{\boldsymbol S}_x=(S_{x0},S_{x1},\cdots,S_{x(Y-1)})</math>

<math>\mathrm{parent~of}~{\boldsymbol S}_{xy}:~P_{y}(x)= \begin{cases} \max\{p|p<x\land {\boldsymbol S}_{py}<{\boldsymbol S}_{xy}\land \exists a(p=(P_{y-1})^a(x))\} & \text{if }y>0 \\ \max\{p|p<x\land {\boldsymbol S}_{py}<{\boldsymbol S}_{xy}\} & \text{if }y=0 \end{cases}</math>

<math>\mathrm{Lowermost~nonzero:}~t=\max\{y|{\boldsymbol S}_{(X-1)y}> 0\}</math>

<math>\mathrm{Bad~root:}~r = P_t(X-1)</math>

<math>\mathrm{Ascension~offset:}~\Delta_{y} = \begin{cases} {\boldsymbol S}_{(X-1)y}-{\boldsymbol S}_{ry} & \text{if }y < t \\ 0 & \text{if }y\geq t \end{cases}</math>

<math>\mathrm{Ascension~matrix:}~A_{xy}=\left\{\begin{array}{ll} 1 &(\mathrm{if}~ \exists a( r=(P_{y})^a(r+x)))\\ 0 &(\mathrm{otherwise}) \end{array}\right.</math>

<math>\mathrm{Good~part:}~{\boldsymbol G}={\boldsymbol S}_0{\boldsymbol S}_1\cdots{\boldsymbol S}_{r-1}</math>

<math>\mathrm{Bad~part:}~{\boldsymbol B}^{(a)}={\boldsymbol B}_0^{(a)}{\boldsymbol B}_1^{(a)}\cdots{\boldsymbol B}_{X-2-r}^{(a)}</math>

<math>{\boldsymbol B}_x^{(a)}=(B_{x0}^{(a)},B_{x1}^{(a)},\cdots,B_{x(Y-1)}^{(a)})</math>

<math>B_{xy}^{(a)}=S_{(r+x)y}+a\Delta_{y}A_{xy}</math>

<math>\varnothing=0</math>

<math>\boldsymbol{S} = \begin{cases} \boldsymbol{S}_0\boldsymbol{S}_1\boldsymbol{S}_2\cdots\boldsymbol{S}_{X-2}, & \text{if }\forall y,\boldsymbol{S}_{(X-1)y}=0 \\ \sup\{G,GB^{(0)},GB^{(0)}B^{(1)},GB^{(0)}B^{(1)}B^{(2)},\cdots\} & \text{otherwise} \end{cases}</math>

== 历史 ==
Bashicu 在2015年的时候给出了第一版 BMS 的定义，即 BM1。BM1 创建后的首个问题便是其是否必然终止。这一疑问直到 2016 年用户 KurohaKafka 在日本论坛 2ch.net 发表终止性证明才暂告段落。<ref>http://wc2014.2ch.net/test/read.cgi/math/1448211924/152-155n</ref>然而 Hyp cos 通过构造非终止序列推翻了该证明。<ref>Hyp cos (2016). [https://googology.fandom.com/wiki/Talk:Bashicu_matrix_system?oldid=118833#Something_wrong_happens Talk: Bashicu Matrix System, Something wrong happens]. ''Googology Wiki''.</ref>

为此，Bashicu 发布第二版（BM2），以 BASIC 语言重新实现算法。<ref name=":0" />2018年6月12日，他再次更新定义至 BM3，<ref>Kyodaisuu (2018). [https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:Kyodaisuu/%E3%83%90%E3%82%B7%E3%82%AF%E8%A1%8C%E5%88%97%E6%9C%80%E6%96%B0%E3%83%90%E3%83%BC%E3%82%B8%E3%83%A7%E3%83%B3 Bashiku Matrix Version 3] (バシク行列バージョン3). ''Googology Wiki''.</ref>但当月内 Alemagno12 便发现存在不终止的例证。<ref>Alemagno12 (2018). [https://googology.fandom.com/wiki/User_blog:Alemagno12/BM3_has_an_infinite_loop BM3 has an infinite loop]. ''Googology Wiki''.</ref>

2018 年 11 月 11 日，P進大好きbot 针对 PSS（即行数限制为 2 的 BMS）完成了终止性证明。<ref>P shin daisuki bot (P進大好きbot) (2018). [https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:P%E9%80%B2%E5%A4%A7%E5%A5%BD%E3%81%8Dbot/%E3%83%9A%E3%82%A2%E6%95%B0%E5%88%97%E3%81%AE%E5%81%9C%E6%AD%A2%E6%80%A7 Stopping property of pair sequences] (ペア数列の停止性). ''Googology Wiki''.</ref>

2018 年 8 月 28 日，Bubby3 确认 BM2 确实不会终止。<ref>Bubby3 (2018). [https://googology.fandom.com/wiki/User_blog:Bubby3/BM2_doesn%27t_terminate. BM2 doesn't terminate.]. ''Googology Wiki''.</ref>

Bashicu 最终修正官方定义推出 BM4，此为2018 年 9 月 1 日的最新版本。该版本最终在 2023 年 7 月 12 日被 Racheline（在 googology 社区中曾用名 Yto）证明停机。<ref>Rachel Hunter (2024). [https://arxiv.org/abs/2307.04606 Well-Orderedness of the Bashicu Matrix System]. ''arXiv''.</ref>

尽管 BM4 是最后官方修订版，但 googology 社区已衍生诸多非官方变体，如 BM2.2、BM2.5、BM2.6、BM3.1、BM3.1.1、BM3.2 及 PsiCubed2 版等。<ref>Ecl1psed276 (2018). [https://googology.fandom.com/wiki/User_blog:Ecl1psed276/A_list_of_all_BMS_versions_and_their_differences A list of all BMS versions and their differences]. ''Googology Wiki''.</ref>需注意的是，整数编号版本（1-4）均由 Bashicu 本人定义，其余版本均为他人修改。

由于 BMS 在三行之后出现提升效应造成分析上的极大困难，目前我们仍然在探索理想无提升 BMS（Idealized BMS，IBMS）的定义。[[BM3.3]]一度被认为是符合预期的 IBMS<ref>User blog:Rpakr/Bashicu Matrix Version 3.3 | Googology Wiki | Fandom</ref>，然而目前已经发现了 BM3.3 也具有提升。

=== 争议 ===
test_alpha0 声称 Yto（Racheline）剽窃了他的证明。据t est_alpha0 所说，他在 2022 年 2 月 16 日在 googology wiki 上发布了关于 BMS 停机证明的文章<ref>User blog:ReflectingOrdinal/A proof of termination of BMS | Googology Wiki | Fandom</ref>，并在 googology discord 社区回答了相关问题，Racheline 声称他的证明不严谨，但过了一段时间，Racheline 在 ArXiv上发了证明，框架与 test_alpha0 的证明完全一致。目前尚不清楚 Racheline 的回应。

== 强度分析 ==
主词条：[[BMS分析|BMS 分析]]，[[提升效应]]

BMS 的分析是一项浩大的工程，由于提升效应造成的困难。BMS的分析最初由Bubby3使用[[SAN]]进行，得出了<math>\text{lim(pDAN)}=(0,0,0)(1,1,1)(2,2,0)</math>，后来Yto接手了BMS的分析工作，使用[[稳定序数]]分析到了<math>(0,0,0)(1,1,1)(2,2,2)</math>。国内的YourCpper、bugit等人使用[[投影序数|投影]]进行BMS分析，达到了<math>(0,0,0,0)(1,1,1,1)(2,2,1,1)(3,0,0,0)</math>以上，但这些分析是错误的。后来FENG发现并修正了两人的分析错误，最终完成了BMS与向上投影的分析工作。

这里列举出一些关键节点：

<math>\varnothing=0</math>

<math>(0)=1</math>

<math>(0)(0)=2</math>

<math>(0)(1)=\omega</math>

<math>(0)(1)(1)=\omega^2</math>

<math>(0)(1)(2)=\omega^{\omega}</math>

<math>(0,0)(1,1)=\varepsilon_0</math>

<math>(0,0)(1,1)(1,1)=\varepsilon_1</math>

<math>(0,0)(1,1)(2,0)=\varepsilon_{\omega}</math>

<math>(0,0)(1,1)(2,1)=\zeta_0</math>

<math>(0,0)(1,1)(2,2)=\psi(\Omega_2)</math>

<math>(0,0,0)(1,1,1)=\psi(\Omega_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,1,0)=\psi(\Omega_{\omega}\times\Omega)</math>

<math>(0,0,0)(1,1,1)(2,1,0)(1,1,1)=\psi(\Omega_{\omega}^2)</math>

<math>(0,0,0)(1,1,1)(2,1,1)=\psi(\Omega_{\omega^2})</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)=\psi(I)</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,1)=\psi(I_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)=\psi(M_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,1)=\psi(K_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,2,0)=\psi(psd.\Pi_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,2,1)=\psi(\Pi_1(\lambda\alpha.(\Omega_{\alpha+2})-\Pi_1))</math>

<math>(0,0,0)(1,1,1)(2,2,1)(3,0,0)=\psi(\lambda\alpha.(\Omega_{\alpha+\omega})-\Pi_0)</math>

<math>(0,0,0)(1,1,1)(2,2,1)(3,2,1)=\psi(\Pi_1(\lambda\alpha.(I_{\alpha+1})-\Pi_1))</math>

<math>(0,0,0)(1,1,1)(2,2,1)(3,3,0)=\psi(\lambda\alpha.(\lambda\beta.\beta+1-\Pi_1[\alpha+1])-\Pi_1)</math>

<math>(0,0,0)(1,1,1)(2,2,2)=\psi(psd. \omega-\pi-\Pi_0)=\psi(\psi_\alpha(\alpha_{\omega}))</math>

<math>(0,0,0)(1,1,1)(2,2,2)(3,2,2)=\psi(\psi_\alpha(\alpha_{\omega^2}))</math>

<math>(0,0,0)(1,1,1)(2,2,2)(3,3,0)=\psi(\psi_\alpha(\psi_\beta(\varepsilon_{\alpha_{\beta+1}+1})))</math>

<math>(0,0,0)(1,1,1)(2,2,2)(3,3,3)=\psi(\beta_{\omega})</math>

<math>(0,0,0,0)(1,1,1,1)=\psi(\omega-\text{Projection})=\psi(\psi_S(\sigma S\times \omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,1,1,1)(3,1,0,0)(2,0,0,0)=\psi((1,0)-\text{Projection})=\psi(\psi_S(\sigma S\times S))</math>

<math>(0,0,0,0)(1,1,1,1)(2,1,1,1)(3,1,1,1)=\psi(\psi_S(\sigma S\times S\times\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,0,0)=\psi(\psi_S(\sigma S\times S\times\omega+S_2))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,1,1)=\psi(\psi_S(\sigma S\times S\times\omega+\psi_{S_3}(\sigma S\times S\times\omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,0)=\psi(\psi_S(\sigma S\times S\times\omega+S_\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)=\psi(\psi_S(\sigma S\times S\times\omega^2))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,2,0,0)(4,3,0,0)=\psi(\psi_S(\varepsilon_{\sigma S+1}))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,2,2,0)=\psi(\psi_S(\sigma S_\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,2,2,1)=\psi(\psi_S(\psi_{\sigma\sigma S}(\sigma S_{\sigma \sigma S+1}^2+1)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,0,0)=\psi(\psi_S(\psi_{\sigma\sigma S}(\sigma\sigma S_2)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)=\psi(\psi_S(\psi_{\sigma\sigma S}(S_{\sigma\sigma S_2+1}+\sigma S_{\sigma\sigma S+1}\times(S+1)+\sigma S\times S \times \omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,2,0)=\psi(\psi_S(\psi_{\sigma\sigma S}(S_{\sigma\sigma S_2+1}+\psi_{\sigma\sigma S_2}(S_{\sigma\sigma S_2+1}+1))))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,2,1)=\psi(\psi_S(\psi_{\sigma\sigma S}(S_{\sigma\sigma S_2+2}+1)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,0)=\psi(\psi_S(\psi_{\sigma\sigma S}(\sigma\sigma S_\omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,1)=\psi(\psi_S(\sigma\sigma S\times\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,1)(4,0,0,0)=\psi(\psi_S(\sigma\theta S\times\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,1)(4,4,4,0)=\psi(\psi_S(\psi_{\sigma\sigma\theta S}(\sigma\sigma\theta S_\omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,2)=\psi(\psi_X(\theta X\times\omega))</math>

<math>(0,0,0,0,0)(1,1,1,1,1)=\psi(\psi_H(H^{H^\omega}))</math>

<math>\text{Limit}=\psi(\psi_H(\varepsilon_{H+1}))</math>

<math>(0,0,0,0)(1,1,1,1)</math>被命名为 TSSO（Trio Sequence System Ordinal，三行序列系统序数），<math>(0,0,0,0,0)(1,1,1,1,1)</math>被命名为 QSSO（Quardo Sequence System Ordinal，四行序列系统序数）。BMS 的极限在中文 googology 社区被称为 SHO（Small Hydra Ordinal），但这一命名的起源不明（SHO 最早被用来指代 <math>\varepsilon_0</math>，后来不明不白的变成了 BMS 极限），也是非正式的，因此被部分人拒绝使用。也有人称 BMS 极限为 BMO。

== 来源 ==
{{默认排序:序数记号}}
[[分类:记号]]

BMS

2026-02-20T10:46:06Z

Baixie01000a7：sup -> \sup

Bashicu 矩阵系统（Bashicu Matrix System，'''BMS'''）是一个[[序数记号]]。Bashicu Hyudora 在 2018 年给出了它的定义。直至今日，BMS 依然是已经证明[[良序]]的最强的序数记号。

== 定义 ==

=== 原定义 ===
Bashicu 最初在他的未命名的 BASIC 编程语言改版上提交了 BMS 的定义。<ref name=":0"> Bashicu Hyudora (2015). [https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:BashicuHyudora/BASIC%E8%A8%80%E8%AA%9E%E3%81%AB%E3%82%88%E3%82%8B%E5%B7%A8%E5%A4%A7%E6%95%B0%E3%81%AE%E3%81%BE%E3%81%A8%E3%82%81#.E3.83.90.E3.82.B7.E3.82.AF.E8.A1.8C.E5.88.97.E6.95.B0.28Bashicu_matrix_number.29 Summary of large numbers in BASIC language] (BASIC言語による巨大数のまとめ). ''Googology Wiki''.</ref>BMS 的原定义是一个大数记号，理论的输出是一个大数。该程序并未设计为实际运行，原因在于语言修改的未定义性，同时也受限于内存与计算时间的现实约束，无法计算出这个大数的实际最终值。因此，Fish 编写了名为"Bashicu 矩阵计算器"的程序来演示预期的计算流程（该程序已得到 Bashicu 验证）。故 Bashicu 矩阵的正式定义可参考 Fish 程序的源代码。<ref>Kyodaisuu (2020). [https://github.com/kyodaisuu/basmat/blob/master/basmat.c basmat]. ''Gthub''.</ref>

=== 正式定义 ===
中文 googology 社区提到 BMS 默认是一个序数记号。以下是序数记号 BMS 的定义及说明：

首先是 BMS 合法式：BMS 的合法式是二维的自然数构成的序列，在外观上看是一个矩阵。如 <math>\begin{pmatrix} 0 & 1&2&1 \\ 0&1&1&1\\0&1&0&1 \end{pmatrix}</math> 就是一个 BMS 的合法式。在很多场合，这种二维的结构书写起来不是很方便，因此我们也常常把BMS从左到右、从上到下按列书写，每一列的不同行之间用逗号隔开，不同列之间用括号隔开。例如，上面的 BMS 也可以写成 <math>(0,0,0)(1,1,1)(2,1,0)(1,1,1)</math>。在很多情况下，除首列外，列末的 0 也可以省略不写，例如上面的 BMS 写为 <math>(0)(1,1,1)(2,1)(1,1,1)</math>。

理论上来说，只要是这样的式子就可以按照 BMS 的规则进行处理了。但实际操作过程中，我们还可以排除一些明显不标准的式子：

* 首列并非全 0
* 每一列并非不严格递减，即出现一列中下面的数大于上面的数
* 出现一个元素 a，它比它同行左边所有元素都大超过 1

在了解 BMS 的展开规则之前，需要先了解一些概念。

# 第一行元素的'''父项'''：对于位于第一行的元素 a，它的父项 b 是满足以下条件的项当中，位于最右边的项：1. 同样位于第一行且在 a 的左边；2. 小于 a。这里和 [[初等序列系统|PrSS]] 判定父项的规则是相同的。显然，0 没有父项。
# '''祖先项'''：一个元素自己，以及它的父项、父项的父项、父项的父项的父项……共同构成它的祖先项。
# 其余行元素的父项：对于不位于第一行的元素 c，它的父项 d 指满足以下条件的项当中，位于最右边的项：1. 与c位于同一行且在 c 的左边；2. 小于 c；3. d 正上方的项 e 是 c 正上方的项f的祖先项。0 没有父项。
# '''坏根'''：最后一列位于最下方的非零元素的父项所在列，称为坏根。如果最后一列所有元素为 0，则这个 BMS 表达式无坏根。值得一提的是，末列最靠下的非零元素记作 '''LNZ'''（Lowermost Non-Zero）
# '''好部'''、'''坏部'''：这两个概念与 PrSS 是相似的。位于坏根左边的所有列称为好部，记作 G，G 可以为空；从坏根到倒数第二列(包括坏根、倒数第二列)的部分称为坏部，记作B。
# '''阶差向量'''：在一个 n 行 BMS 中，我们把末列记为 <math>(\alpha_1,\alpha_2,\cdots,\alpha_n)</math>，把坏根列记为 <math>(\beta_1,\beta_2,\cdots,\beta_n)</math>，并且我们规定 <math>\alpha_{n+1}=0</math>。则阶差向量<math>\Delta=(\delta_1,\delta_2,\cdots,\delta_n)</math>按照这样的规则得到：<math>\delta_i = \begin{cases} \alpha_i-\beta_i, & \alpha_{i+1}\neq0 \\ 0, & \alpha_{i+1}=0 \end{cases}</math>。通俗的说，如果末列的第 <math>i+1</math> 项等于0，则 <math>\delta_i=0</math>，否则 <math>\delta_i</math> 等于末列第 i 行减去坏根列第 i 行。阶差向量记作 <math>\Delta</math>。
# <math>B_m</math>：<math>B_m</math>是 B 中每一列都加上 <math>\Delta</math> 的 m 倍所得到的新矩阵。但是有一点需要注意：如果 B 中某个元素 t 的祖先项不包含坏根中的元素，则在 <math>B_m</math> 对应位置的元素的值依然是 t，它不加 <math>\Delta</math>。

了解概念后，以下是 BMS 的展开规则：

# 空矩阵 = 0
# 如果表达式是非空矩阵 S，如果它没有坏根，那么 S 等于 S 去掉最后一列之后，剩余部分的后继。
# 否则，确定这个 BMS 表达式 S 的坏根、G、B、<math>\Delta</math>，S 的基本列第 n 项<math>S[n]=G\sim B\sim B_1 \sim B_2\sim B_3\sim\cdots\sim B_{n-1}</math>。其中 ~ 表示序列拼接。或者称 S 的展开式是 <math>G\sim B \underbrace{\sim B_1\sim B_2\sim \cdots}_{\omega}</math>。

BMS 的极限基本列是 <math>\{(0)(1),(0,0)(1,1),(0,0,0)(1,1,1),(0,0,0,0)(1,1,1,1),\cdots\}</math>，从这个基本列中元素开始取前驱或取基本列所能得到的表达式是 BMS 的标准式。

以下是 BMS 展开的一些实例：

例一：<math>(0,0,0)(1,1,1)(2,2,1)(3,2,0)(0,0,0)</math>

因为末列全都是 0，因此这个 BMS 没有坏根。根据规则 2，它是 <math>(0,0,0)(1,1,1)(2,2,1)(3,2,0)</math> 的后继。

例二：<math>(0,0,0)(1,1,1)(2,2,2)(3,3,3)(4,2,0)</math>

LNZ 是末列第二行的 2。首先确定末列第 1 行元素的祖先项，即标红的部分（末列本身不染色，下同）：<math>({\color{red}0},0,0)({\color{red}1},1,1)({\color{red}2},2,2)({\color{red}3},3,3)(4,2,0)</math>。因此末列第二行的 2 的父项只能在含有标红元素的这些列中选取。于是确定 LNZ 的父项为（标绿）：<math>({\color{red}0},0,0)({\color{red}1},{\color{green}1},1)({\color{red}2},2,2)({\color{red}3},3,3)(4,2,0)</math>。因此确定 <math>(1,1,1)</math> 是坏根。好部 G 是 <math>(0,0,0)</math>，坏部 B 是 <math>(1,1,1)(2,2,2)(3,3,3)</math>。计算出阶差向量 <math>\Delta=(3,0,0)</math>。检查 B 中是否存在祖先项不包含坏根中元素的项（当然，我们只需要检查 <math>\Delta</math> 非零的那些行），很幸运，没有。于是我们得到展开式是 <math>(0,0,0)(1,1,1)(2,2,2)(3,3,3)(4,1,1)(5,2,2)(6,3,3)(7,1,1)(8,2,2)(9,3,3)\cdots</math>

例三：<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)(4,2,0,0)(5,1,1,1)(6,2,2,1)(7,3,1,1)</math>

LNZ 是末列第四行的 1。首先确定末列第一行元素 7 的祖先项（标红）：<math>({\color{red}0},0,0,0)({\color{red}1},1,1,1)({\color{red}2},2,2,1)({\color{red}3},3,1,1)({\color{red}4},2,0,0)({\color{red}5},1,1,1)({\color{red}6},2,2,1)(7,3,1,1)</math>。在含有标红元素的列中寻找末列第二行元素 3 的祖先项（标绿）：<math>({\color{red}0},{\color{green}0},0,0)({\color{red}1},1,1,1)({\color{red}2},2,2,1)({\color{red}3},3,1,1)({\color{red}4},2,0,0)({\color{red}5},{\color{green}1},1,1)({\color{red}6},{\color{green}2},2,1)(7,3,1,1)</math>。在含有标绿元素的列中寻找末列第三行元素 1 的祖先项（标蓝）：<math>({\color{red}0},{\color{green}0},{\color{dodgerblue}0},0)({\color{red}1},1,1,1)({\color{red}2},2,2,1)({\color{red}3},3,1,1)({\color{red}4},2,0,0)({\color{red}5},{\color{green}1},1,1)({\color{red}6},{\color{green}2},2,1)(7,3,1,1)</math>。在含有标蓝元素的列中寻找 LNZ 的父项，即首列第四行的 0。于是得到坏根是 <math>(0,0,0,0)</math>，好部 G 是空矩阵，坏部 B 是 <math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)(4,2,0,0)(5,1,1,1)(6,2,2,1)</math>，计算阶差向量 <math>\Delta=(7,3,1,0)</math>。检查 B 中是否存在祖先项不包含坏根中元素的项（只检查 <math>\Delta</math> 非 0 的行）得到第五列第三行的 0 祖先项不经过坏根。于是我们得到展开式是

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)(4,2,{\color{red}0},0)(5,1,1,1)(6,2,2,1)(7,3,1,0)(8,4,2,1)(9,5,3,1)(10,6,2,1)(11,5,{\color{red}0},0)(12,4,2,1)(13,5,3,1)(14,6,2,0)(15,7,3,1)(16,8,4,1)(17,9,3,1)(18,8,{\color{red}0},0)(19,7,3,1)(20,8,4,1)\cdots</math>

展开 BMS 可以靠 [https://gyafun.jp/ln/basmat.cgi Bashicu Matrix Calculator] 或 [https://hypcos.github.io/notation-explorer/ Notation Explorer] 辅助。

=== 数学定义 ===
kotetian 给出 BMS 的数学定义，但是他给出的定义是大数记号版本的。以下是根据他的定义改写的序数记号版 BMS 的定义：

<math>\mathrm{Matrix:}{\boldsymbol S}={\boldsymbol S}_0{\boldsymbol S}_1\cdots{\boldsymbol S}_{X-1}</math>

<math>\mathrm{Vector:}~{\boldsymbol S}_x=(S_{x0},S_{x1},\cdots,S_{x(Y-1)})</math>

<math>\mathrm{parent~of}~{\boldsymbol S}_{xy}:~P_{y}(x)= \begin{cases} max\{p|p<x\land {\boldsymbol S}_{py}<{\boldsymbol S}_{xy}\land \exists a(p=(P_{y-1})^a(x))\} & \text{if }y>0 \\ max\{p|p<x\land {\boldsymbol S}_{py}<{\boldsymbol S}_{xy}\} & \text{if }y=0 \end{cases}</math>

<math>\mathrm{Lowermost~nonzero:}~t=\max\{y|{\boldsymbol S}_{(X-1)y}> 0\}</math>

<math>\mathrm{Bad~root:}~r = P_t(X-1)</math>

<math>\mathrm{Ascension~offset:}~\Delta_{y} = \begin{cases} {\boldsymbol S}_{(X-1)y}-{\boldsymbol S}_{ry} & \text{if }y < t \\ 0 & \text{if }y\geq t \end{cases}</math>

<math>\mathrm{Ascension~matrix:}~A_{xy}=\left\{\begin{array}{ll} 1 &(\mathrm{if}~ \exists a( r=(P_{y})^a(r+x)))\\ 0 &(\mathrm{otherwise}) \end{array}\right.</math>

<math>\mathrm{Good~part:}~{\boldsymbol G}={\boldsymbol S}_0{\boldsymbol S}_1\cdots{\boldsymbol S}_{r-1}</math>

<math>\mathrm{Bad~part:}~{\boldsymbol B}^{(a)}={\boldsymbol B}_0^{(a)}{\boldsymbol B}_1^{(a)}\cdots{\boldsymbol B}_{X-2-r}^{(a)}</math>

<math>{\boldsymbol B}_x^{(a)}=(B_{x0}^{(a)},B_{x1}^{(a)},\cdots,B_{x(Y-1)}^{(a)})</math>

<math>B_{xy}^{(a)}=S_{(r+x)y}+a\Delta_{y}A_{xy}</math>

<math>\varnothing=0</math>

<math>\boldsymbol{S} = \begin{cases} \boldsymbol{S}_0\boldsymbol{S}_1\boldsymbol{S}_2\cdots\boldsymbol{S}_{X-2}, & \text{if }\forall y,\boldsymbol{S}_{(X-1)y}=0 \\ \sup\{G,GB^{(0)},GB^{(0)}B^{(1)},GB^{(0)}B^{(1)}B^{(2)},\cdots\} & \text{otherwise} \end{cases}</math>

== 历史 ==
Bashicu 在2015年的时候给出了第一版 BMS 的定义，即 BM1。BM1 创建后的首个问题便是其是否必然终止。这一疑问直到 2016 年用户 KurohaKafka 在日本论坛 2ch.net 发表终止性证明才暂告段落。<ref>http://wc2014.2ch.net/test/read.cgi/math/1448211924/152-155n</ref>然而 Hyp cos 通过构造非终止序列推翻了该证明。<ref>Hyp cos (2016). [https://googology.fandom.com/wiki/Talk:Bashicu_matrix_system?oldid=118833#Something_wrong_happens Talk: Bashicu Matrix System, Something wrong happens]. ''Googology Wiki''.</ref>

为此，Bashicu 发布第二版（BM2），以 BASIC 语言重新实现算法。<ref name=":0" />2018年6月12日，他再次更新定义至 BM3，<ref>Kyodaisuu (2018). [https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:Kyodaisuu/%E3%83%90%E3%82%B7%E3%82%AF%E8%A1%8C%E5%88%97%E6%9C%80%E6%96%B0%E3%83%90%E3%83%BC%E3%82%B8%E3%83%A7%E3%83%B3 Bashiku Matrix Version 3] (バシク行列バージョン3). ''Googology Wiki''.</ref>但当月内 Alemagno12 便发现存在不终止的例证。<ref>Alemagno12 (2018). [https://googology.fandom.com/wiki/User_blog:Alemagno12/BM3_has_an_infinite_loop BM3 has an infinite loop]. ''Googology Wiki''.</ref>

2018 年 11 月 11 日，P進大好きbot 针对 PSS（即行数限制为 2 的 BMS）完成了终止性证明。<ref>P shin daisuki bot (P進大好きbot) (2018). [https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:P%E9%80%B2%E5%A4%A7%E5%A5%BD%E3%81%8Dbot/%E3%83%9A%E3%82%A2%E6%95%B0%E5%88%97%E3%81%AE%E5%81%9C%E6%AD%A2%E6%80%A7 Stopping property of pair sequences] (ペア数列の停止性). ''Googology Wiki''.</ref>

2018 年 8 月 28 日，Bubby3 确认 BM2 确实不会终止。<ref>Bubby3 (2018). [https://googology.fandom.com/wiki/User_blog:Bubby3/BM2_doesn%27t_terminate. BM2 doesn't terminate.]. ''Googology Wiki''.</ref>

Bashicu 最终修正官方定义推出 BM4，此为2018 年 9 月 1 日的最新版本。该版本最终在 2023 年 7 月 12 日被 Racheline（在 googology 社区中曾用名 Yto）证明停机。<ref>Rachel Hunter (2024). [https://arxiv.org/abs/2307.04606 Well-Orderedness of the Bashicu Matrix System]. ''arXiv''.</ref>

尽管 BM4 是最后官方修订版，但 googology 社区已衍生诸多非官方变体，如 BM2.2、BM2.5、BM2.6、BM3.1、BM3.1.1、BM3.2 及 PsiCubed2 版等。<ref>Ecl1psed276 (2018). [https://googology.fandom.com/wiki/User_blog:Ecl1psed276/A_list_of_all_BMS_versions_and_their_differences A list of all BMS versions and their differences]. ''Googology Wiki''.</ref>需注意的是，整数编号版本（1-4）均由 Bashicu 本人定义，其余版本均为他人修改。

由于 BMS 在三行之后出现提升效应造成分析上的极大困难，目前我们仍然在探索理想无提升 BMS（Idealized BMS，IBMS）的定义。[[BM3.3]]一度被认为是符合预期的 IBMS<ref>User blog:Rpakr/Bashicu Matrix Version 3.3 | Googology Wiki | Fandom</ref>，然而目前已经发现了 BM3.3 也具有提升。

=== 争议 ===
test_alpha0 声称 Yto（Racheline）剽窃了他的证明。据t est_alpha0 所说，他在 2022 年 2 月 16 日在 googology wiki 上发布了关于 BMS 停机证明的文章<ref>User blog:ReflectingOrdinal/A proof of termination of BMS | Googology Wiki | Fandom</ref>，并在 googology discord 社区回答了相关问题，Racheline 声称他的证明不严谨，但过了一段时间，Racheline 在 ArXiv上发了证明，框架与 test_alpha0 的证明完全一致。目前尚不清楚 Racheline 的回应。

== 强度分析 ==
主词条：[[BMS分析|BMS 分析]]，[[提升效应]]

BMS 的分析是一项浩大的工程，由于提升效应造成的困难。BMS的分析最初由Bubby3使用[[SAN]]进行，得出了<math>\text{lim(pDAN)}=(0,0,0)(1,1,1)(2,2,0)</math>，后来Yto接手了BMS的分析工作，使用[[稳定序数]]分析到了<math>(0,0,0)(1,1,1)(2,2,2)</math>。国内的YourCpper、bugit等人使用[[投影序数|投影]]进行BMS分析，达到了<math>(0,0,0,0)(1,1,1,1)(2,2,1,1)(3,0,0,0)</math>以上，但这些分析是错误的。后来FENG发现并修正了两人的分析错误，最终完成了BMS与向上投影的分析工作。

这里列举出一些关键节点：

<math>\varnothing=0</math>

<math>(0)=1</math>

<math>(0)(0)=2</math>

<math>(0)(1)=\omega</math>

<math>(0)(1)(1)=\omega^2</math>

<math>(0)(1)(2)=\omega^{\omega}</math>

<math>(0,0)(1,1)=\varepsilon_0</math>

<math>(0,0)(1,1)(1,1)=\varepsilon_1</math>

<math>(0,0)(1,1)(2,0)=\varepsilon_{\omega}</math>

<math>(0,0)(1,1)(2,1)=\zeta_0</math>

<math>(0,0)(1,1)(2,2)=\psi(\Omega_2)</math>

<math>(0,0,0)(1,1,1)=\psi(\Omega_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,1,0)=\psi(\Omega_{\omega}\times\Omega)</math>

<math>(0,0,0)(1,1,1)(2,1,0)(1,1,1)=\psi(\Omega_{\omega}^2)</math>

<math>(0,0,0)(1,1,1)(2,1,1)=\psi(\Omega_{\omega^2})</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)=\psi(I)</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,1)=\psi(I_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)=\psi(M_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,1)=\psi(K_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,2,0)=\psi(psd.\Pi_{\omega})</math>

<math>(0,0,0)(1,1,1)(2,2,1)=\psi(\Pi_1(\lambda\alpha.(\Omega_{\alpha+2})-\Pi_1))</math>

<math>(0,0,0)(1,1,1)(2,2,1)(3,0,0)=\psi(\lambda\alpha.(\Omega_{\alpha+\omega})-\Pi_0)</math>

<math>(0,0,0)(1,1,1)(2,2,1)(3,2,1)=\psi(\Pi_1(\lambda\alpha.(I_{\alpha+1})-\Pi_1))</math>

<math>(0,0,0)(1,1,1)(2,2,1)(3,3,0)=\psi(\lambda\alpha.(\lambda\beta.\beta+1-\Pi_1[\alpha+1])-\Pi_1)</math>

<math>(0,0,0)(1,1,1)(2,2,2)=\psi(psd. \omega-\pi-\Pi_0)=\psi(\psi_\alpha(\alpha_{\omega}))</math>

<math>(0,0,0)(1,1,1)(2,2,2)(3,2,2)=\psi(\psi_\alpha(\alpha_{\omega^2}))</math>

<math>(0,0,0)(1,1,1)(2,2,2)(3,3,0)=\psi(\psi_\alpha(\psi_\beta(\varepsilon_{\alpha_{\beta+1}+1})))</math>

<math>(0,0,0)(1,1,1)(2,2,2)(3,3,3)=\psi(\beta_{\omega})</math>

<math>(0,0,0,0)(1,1,1,1)=\psi(\omega-\text{Projection})=\psi(\psi_S(\sigma S\times \omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,1,1,1)(3,1,0,0)(2,0,0,0)=\psi((1,0)-\text{Projection})=\psi(\psi_S(\sigma S\times S))</math>

<math>(0,0,0,0)(1,1,1,1)(2,1,1,1)(3,1,1,1)=\psi(\psi_S(\sigma S\times S\times\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,0,0)=\psi(\psi_S(\sigma S\times S\times\omega+S_2))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,1,1)=\psi(\psi_S(\sigma S\times S\times\omega+\psi_{S_3}(\sigma S\times S\times\omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,0)=\psi(\psi_S(\sigma S\times S\times\omega+S_\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)=\psi(\psi_S(\sigma S\times S\times\omega^2))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,2,0,0)(4,3,0,0)=\psi(\psi_S(\varepsilon_{\sigma S+1}))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,2,2,0)=\psi(\psi_S(\sigma S_\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,2,2,1)=\psi(\psi_S(\psi_{\sigma\sigma S}(\sigma S_{\sigma \sigma S+1}^2+1)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,0,0)=\psi(\psi_S(\psi_{\sigma\sigma S}(\sigma\sigma S_2)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,1,1)=\psi(\psi_S(\psi_{\sigma\sigma S}(S_{\sigma\sigma S_2+1}+\sigma S_{\sigma\sigma S+1}\times(S+1)+\sigma S\times S \times \omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,2,0)=\psi(\psi_S(\psi_{\sigma\sigma S}(S_{\sigma\sigma S_2+1}+\psi_{\sigma\sigma S_2}(S_{\sigma\sigma S_2+1}+1))))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,2,1)=\psi(\psi_S(\psi_{\sigma\sigma S}(S_{\sigma\sigma S_2+2}+1)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,0)=\psi(\psi_S(\psi_{\sigma\sigma S}(\sigma\sigma S_\omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,1)=\psi(\psi_S(\sigma\sigma S\times\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,1)(4,0,0,0)=\psi(\psi_S(\sigma\theta S\times\omega))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,1)(3,3,3,1)(4,4,4,0)=\psi(\psi_S(\psi_{\sigma\sigma\theta S}(\sigma\sigma\theta S_\omega)))</math>

<math>(0,0,0,0)(1,1,1,1)(2,2,2,2)=\psi(\psi_X(\theta X\times\omega))</math>

<math>(0,0,0,0,0)(1,1,1,1,1)=\psi(\psi_H(H^{H^\omega}))</math>

<math>\text{Limit}=\psi(\psi_H(\varepsilon_{H+1}))</math>

<math>(0,0,0,0)(1,1,1,1)</math>被命名为 TSSO（Trio Sequence System Ordinal，三行序列系统序数），<math>(0,0,0,0,0)(1,1,1,1,1)</math>被命名为 QSSO（Quardo Sequence System Ordinal，四行序列系统序数）。BMS 的极限在中文 googology 社区被称为 SHO（Small Hydra Ordinal），但这一命名的起源不明（SHO 最早被用来指代 <math>\varepsilon_0</math>，后来不明不白的变成了 BMS 极限），也是非正式的，因此被部分人拒绝使用。也有人称 BMS 极限为 BMO。

== 来源 ==
{{默认排序:序数记号}}
[[分类:记号]]

fffz分析Part5:JO~TBO

2026-02-20T10:40:52Z

Baixie01000a7：

本条目展示[[Fake Fake Fake Zeta|fffz]]分析的第五部分。使用<math>MOCF</math>和[[BMS]]对照

<nowiki>\begin{align}s\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_0^{\varepsilon_0})=\psi(\psi_{\Omega_{I+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0},\varepsilon_0^{\varepsilon_0}+\omega](\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_0^{\varepsilon_0}))=\psi(\psi_{\Omega_{I+1}}(0))^2=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(1,0,0)(2,1,1)(3,1,0)(4,2,0)=\mathrm{JOJO(JO^2)}\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_1)=\psi(\psi_{\Omega_{I+1}}(1))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(4,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_2)=\psi(\psi_{\Omega_{I+1}}(2))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(4,2,0)(4,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_\omega)=\psi(\psi_{\Omega_{I+1}}(\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(5,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_\omega+\varepsilon_0)=\psi(\psi_{\Omega_{I+1}}(\Omega_\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(5,1,0)(1,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_{\varepsilon_0})=\psi(\psi_{\Omega_{I+1}}(\psi_{\Omega_{I+1}}(0)))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(5,1,0)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_{\varepsilon_{\varepsilon_0}})=\psi(\psi_{\Omega_{I+1}}(\psi_{\Omega_{I+1}}(\psi_{\Omega_{I+1}}(0))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(5,1,0)(6,2,0)(7,1,0)(8,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\zeta_0)=\psi(\Omega_{I+1})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(5,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0](\zeta_0))=\psi(\Omega_{I+2})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(5,3,0)(6,3,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0](\psi_Z[\varepsilon_0](\zeta_0)))=\psi(\Omega_{I+3})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(5,3,0)(6,4,0)(7,4,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0))=\psi(\Omega_{I+\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^2))=\psi(\Omega_{I+\omega^2})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^3))=\psi(\Omega_{I+\omega^3})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^\omega))=\psi(\Omega_{I+\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^\omega\times2))=\psi(\Omega_{\Omega_{I+1}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^\omega\times3))=\psi(\Omega_{\Omega_{\Omega_{I+1}}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(4,2,1)(5,2,1)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0},\psi_Z(\varepsilon_0^\omega\times\omega)](\psi_Z(\varepsilon_0^\omega\times\omega))=\psi(\psi_{I_2}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^\omega\times\omega))=\psi(\psi_{I_2}(0)\times\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}))=\psi(\Omega_{\Omega_{\psi_{I_2}(0)+1}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,0)(6,3,1)(7,3,1)(8,3,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}\times\omega))=\psi(\psi_{I_2}(1))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,0)(6,3,1)(7,3,1)(8,3,0)(7,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^{\omega+1}](\psi_Z[\varepsilon_0^{\omega+1}](\varepsilon_0^{\omega+1}\times\omega)))=\psi(\psi_{I_2}(2))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,0)(6,3,1)(7,3,1)(8,3,0)(7,3,0)(6,3,0)(7,4,1)(8,5,1)(9,4,0)(8,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega+1}))=\psi(\psi_{I_2}(\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega+2}))=\psi(\psi_{I_2}(\omega^2))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega+3}))=\psi(\psi_{I_2}(\omega^3))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(5,2,1)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega\times2}))=\psi(\psi_{I_2}(\Omega_{I+1}))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega\times2}\times\omega))=\psi(I_2)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega\times2+1}))=\psi(I_2\times\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega\times2+2}\times\omega))=\psi(I_2^2)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega^2}\times\omega))=\psi(I_2^{I_2})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega^{\omega^2}}\times\omega))=\psi(I_2^{I_2^{I_2}})=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(7,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^{\varepsilon_0}](\varepsilon_0^{\varepsilon_0}))=\psi(\psi_{\Omega_{I_2+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(7,3,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega\times2+1}\times\omega)))=\psi(I_3)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(7,3,1)(8,3,1)(9,3,0)(8,3,1)(9,3,0)(8,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^{\omega\times2+1}\times\omega))))=\psi(I_4)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(7,3,1)(8,3,1)(9,3,0)(10,4,1)(11,4,1)(12,4,0)(11,4,1)(12,4,0)(11,0,0)\\&\large\color{red}{\psi_Z(\varepsilon_0^{\varepsilon_0})=\psi(I_\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)=\mathrm{SIO}}\end{align}</nowiki>

<nowiki>\begin{align}s\\&\psi_Z(\varepsilon_0^{\varepsilon_0}+\varepsilon_0)=\psi(I_\omega+\Omega_\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0}+\varepsilon_0^2)=\psi(I_\omega+\Omega_{\omega^2})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0}\times2)=\psi(I_\omega\times2)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0}\times3)=\psi(I_\omega\times3)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0}\times\omega](\varepsilon_0^{\varepsilon_0}\times\omega)=\psi(I_\omega\times\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0}\times\omega)=\psi(I_\omega\times\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+1})=\psi(I_{\omega^2})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+2})=\psi(I_{\omega^3})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(2,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}](\varepsilon_0^{\varepsilon_0+\omega})=\psi(I_{\omega^\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega})=\psi(I_{\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0)=\psi(I_{\Omega_{\omega}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^2)=\psi(I_{\Omega_{\omega^2}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^\omega)=\psi(I_{\Omega_{\Omega}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\varepsilon_0}](\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\varepsilon_0})=\psi(I_{\psi_{\Omega_{I+1}}(0)})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^2))=\psi(I_{\Omega_{I+\omega^2}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\varepsilon_0}](\psi_Z(\varepsilon_0^3))=\psi(I_{\Omega_{I+\omega^3}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\varepsilon_0}](\psi_Z[\varepsilon_0^\omega](\varepsilon_0^\omega))=\psi(I_{\Omega_{I+\Omega}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\varepsilon_0},\psi_Z[\varepsilon_0^\omega](\varepsilon_0^\omega\times\omega)](\psi_Z[\varepsilon_0^\omega](\varepsilon_0^\omega\times\omega))=\psi(I_I)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,1,0)(2,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\varepsilon_0})=\psi(I_{I_\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega}\times2+\varepsilon_0^{\varepsilon_0})=\psi(I_{I_{I_\omega}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}\times\omega](\varepsilon_0^{\varepsilon_0+\omega}\times\omega)=\psi(\psi_{I(1,0)}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,0,0)\end{align}</nowiki>

<nowiki>\begin{align}s\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega}\times\omega)=\psi(\psi_{I(1,0)}(0)\times\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega+1})=\psi(\psi_{I(1,0)}(\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega+2})=\psi(\psi_{I(1,0)}(\omega^2))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega+3})=\psi(\psi_{I(1,0)}(\omega^3))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(2,1,1)(2,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega\times2})=\psi(\psi_{I(1,0)}(\omega^\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega\times2})=\psi(\psi_{I(1,0)}(\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega\times2}\times2)=\psi(\psi_{I(1,0)}(\psi_{I(1,0)}(\psi_{I(1,0)}(\Omega))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega)=\psi(I(1,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega+\varepsilon_0^\omega)=\psi(I(1,0)+\Omega_{\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega,\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega+\varepsilon_0^\omega\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega+\varepsilon_0^\omega\times\omega)=\psi(I(1,0)+\psi_I(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2+1},\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega)](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega))=\psi(I(1,0)\times2)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,1)(4,2,1)(5,2,0)(4,2,1)(5,2,0)(4,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2+1},\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega)](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2+1},\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega)](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega)))=\psi(I(1,0)\times3)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,1)(4,2,1)(5,2,0)(4,2,1)(5,2,0)(4,2,0)(5,3,1)(6,3,1)(7,3,1)(6,3,1)(7,3,0)(6,3,1)(7,3,0)(6,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2+1}](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega))=\psi(I(1,0)\times\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega\times3}\times\omega)=\psi(I(1,0)^2)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega\times3}\times\omega)=\psi(I(1,0)^3)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega^2}](\varepsilon_0^{\varepsilon_0+\omega^2})=\psi(I(1,0)^\omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(3,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0+\omega^2})=\psi(I(1,0)^\Omega)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega^2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega^2}\times\omega)=\psi(I(1,0)^{I(1,0)})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0+\omega^\omega}\times\omega](\varepsilon_0^{\varepsilon_0+\omega^\omega}\times\omega)=\psi(I(1,0)^{I(1,0)^{I(1,0)}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\varepsilon_0^{\varepsilon_0\times2})=\psi(\psi_{\Omega_{I(1,0)+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\zeta_0)=\psi(\Omega_{I(1,0)+1})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,0)(5,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0))=\psi(\Omega_{I(1,0)+\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,0)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^\omega))=\psi(\Omega_{I(1,0)+\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^\omega\times2))=\psi(\Omega_{\Omega_{I(1,0)+1}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^\omega\times3))=\psi(\Omega_{\Omega_{\Omega_{I(1,0)+1}}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(4,2,1)(5,2,1)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2},\psi_Z[\varepsilon_0^\omega\times\omega](\varepsilon_0^\omega\times\omega)](\psi_Z[\varepsilon_0^\omega\times\omega](\varepsilon_0^\omega\times\omega))=\psi(\psi_{I_{I(1,0)+1}}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^{\omega+1}))=\psi(\psi_{I_{I(1,0)+1}}(\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^{\omega+2}))=\psi(\psi_{I_{I(1,0)+1}}(\omega^2))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2},\psi_Z[\varepsilon_0^{\omega\times2}\times\omega](\varepsilon_0^{\omega\times2}\times\omega)](\psi_Z[\varepsilon_0^{\omega\times2}\times\omega](\varepsilon_0^{\omega\times2}\times\omega))=\psi(I_{I(1,0)+1})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^{\varepsilon_0}))=\psi(I_{I(1,0)+\omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^{\varepsilon_0+\omega}))=\psi(I_{I(1,0)+\Omega})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2},\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\omega\times2})\times\omega](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega}+\varepsilon_0^{\omega\times2})\times\omega)=\psi(I_{I_{I(1,0)+1}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2},\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}\times2+\varepsilon_0^{\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega}\times2+\varepsilon_0^{\omega\times2})\times\omega](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}\times2+\varepsilon_0^{\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega}\times2+\varepsilon_0^{\omega\times2})\times\omega)=\psi(I_{I_{I_{I(1,0)+1}}})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(4,2,1)(5,2,1)(6,2,0)(5,2,1)(6,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2},\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}\times\omega+\varepsilon_0^{\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega}\times\omega+\varepsilon_0^{\omega\times2})\times\omega](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega}\times\omega+\varepsilon_0^{\omega\times2}](\varepsilon_0^{\varepsilon_0+\omega}\times\omega+\varepsilon_0^{\omega\times2})\times\omega)=\psi(\psi_{I(1,1)}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z(\varepsilon_0^{\varepsilon_0+\omega+1}))=\psi(\psi_{I(1,1)}(\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(5,2,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega))=\psi(I(1,1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(5,2,1)(6,2,0)(5,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega)))=\psi(I(1,2))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(7,3,1)(8,3,1)(9,3,1)(8,3,1)(9,3,0)(8,3,1)(9,3,0)(8,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z[\varepsilon_0^{\varepsilon_0\times2}](\psi_Z[\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0+\omega\times2}\times\omega)))))=\psi(I(1,3))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(7,3,1)(8,3,1)(9,3,1)(8,3,1)(9,3,0)(10,4,1)(11,4,1)(12,4,1)(11,4,1)(12,4,0)(11,4,1)(12,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2})=\psi(I(1,\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+1})=\psi(I(1,\omega^2))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+2})=\psi(I(1,\omega^3))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+\omega})=\psi(I(1,\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+\omega}+\varepsilon_0^{\varepsilon_0\times2})=\psi(I(1,I_\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+\omega}\times2)=\psi(I(1,I(1,\Omega)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+\omega}\times3)=\psi(I(1,I(1,I(1,\Omega))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times2+\omega}\times\omega)=\psi(\psi_{I(2,0)}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+\omega+1})=\psi(\psi_{I(2,0)}(\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times2+\omega\times2})=\psi(\psi_{I(2,0)}(\Omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times2+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0\times2+\omega\times2}\times\omega)=\psi(I(2,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times3})=\psi(I(2,\omega))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times3+\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times3+\omega}\times\omega)=\psi(\psi_{I(3,0)}(0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times3+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0\times3+\omega\times2}\times\omega)=\psi(I(3,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times4+\omega\times2}\times\omega](\varepsilon_0^{\varepsilon_0\times4+\omega\times2}\times\omega)=\psi(I(4,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)\\&\large\color{blue}{\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}](\varepsilon_0^{\varepsilon_0\times\omega})=\psi(I(\omega,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,0,0)=\mathrm{MBO}}\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega})=\psi(I(\Omega,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0)=\psi(I(\Omega_\omega,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{2})=\psi(I(\Omega_{\omega^2},0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\omega}](\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\omega})=\psi(I(\Omega_{\omega^\omega},0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\omega})=\psi(I(\Omega_{\Omega},0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)\\&\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\omega}\times\omega)=\psi(I(\psi_I(0),0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\omega+1})=\psi(I(\psi_I(\omega),0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\varepsilon_0})=\psi(I(I_\omega,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\varepsilon_0+\omega})=\psi(I(I_\Omega,0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}+\varepsilon_0^{\varepsilon_0\times2})=\psi(I(I(1,\omega),0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}\times2+\varepsilon_0^{\varepsilon_0\times2})=\psi(I(I(I(1,\omega),0),0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)\\&\psi_Z(\varepsilon_0^{\varepsilon_0\times\omega}\times3+\varepsilon_0^{\varepsilon_0\times2})=\psi(I(I(I(I(1,\omega),0),0),0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)\\&\LARGE\color{purple}{\psi_Z[\varepsilon_0^{\varepsilon_0\times\omega}\times\omega](\varepsilon_0^{\varepsilon_0\times\omega}\times\omega)=\psi(\psi_{I(1,0,0)}(0))=\psi((2~~1-)^{1,0})=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,0,0)=\mathrm{TBO}}\end{align}</nowiki>

__静态重定向__
[[分类:分析]]