User:Ynought/Yallun

So this will hopefully be a series of number \(Y_1\) all the way too \(Y_?\)

Yallun 1
\(\#\) is a series of \(S\)'s

\(S_0(n)=n^2\)

\(\#S_0(n)=\#^n(n)\) \(^n\) denotes iteration.

\(\#S_j+1(n)=\#S_j...S_j^n(n)\) with \(n\) \(S_j\)'s

\(Y_1(n)=S_n(n)\)

Then \(Y_1=Y_1(99)\)

Size
It should be around \(f_{\omega 2}(99)\)

Yallun 2
\(°\) is any string seperated by \(,\)'s

\(b\) is the second number in the array

\((1,b,c,d...)=1\)

\((a,b)=a+b\)

\((°1)=(°)\)

\((a,b,c)=(a,(a,(...(a,b,c-1)...),c-1),c-1)\) with \(b\) nests

\((a,b...)\) gets solved by: "1.If there are no \(1\)'s in the array then:""1.1. Reduce the 3rd entry in the array by 1""2.1. Replace \(b\) by \(J_b\) where \(J_0\) is the new array (after the rule 1) and \(J_n\) is the new array after rule 1 but with \(b\) replaced with \(J_{n-1}\)""2.Otherwise:""1.2 Find the first 1 from the right and replace it by \(T_b\) where \(T_0\) is the array but with the 1 and the \(,\) to the left and \(T_b\) is the array but with the 1 replaced by \(T_{n-1}\) and the next entry is decreased by \(1\)""2.2 Decrease the entry after the 1 affected by rule 1.2 by 1"and \((a{1}b)=(a,a,a,a,a,a...,a)\) with the number of \(a\)'s being \(b\)

then \(Y_2=(99{1}99)\)

Size
the size of \(Y_2\) should be around \(f_{\omega^2}(99)\)