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Review of part 1:

SH(x)=39^x

SH(N,a,x)=SH(N,a-1,SH(N,a,x-1))

SH(N,a,0,M)=SH(N,a-1,SH(N,a-1,a,M),M)

SH(0,N)=SH(N)

(note: N,M can be nothing and 0 in the second formula is the leftmost zero.)

I repeat arguments themselves. I mean,

SH(1/x)=SH(x,x,...(x times)...,x)

And then,

SH(n/x)=SH(n-1/x,x,...(x times)...,x)

Also, this can be thought:

SH(1/x/n)=SH(x,x,...(x times)...,x/n)

If each slash have arrays, It must be 2D array.

Now, here is a 3D array notation:

SH(n//m)=SH(m,m,...(ntimes)...m/m,m,...(ntimes)...m/...(ntimes).../m,m,...(ntimes)...m)

Now it get complicated, so I will summarize my definitions.


SH(x)=39^x

SH(N,a,x)=SH(N,a-1,SH(N,a,x-1))

SH(N,a,0,M)=SH(N,a-1,SH(N,a-1,a,M),M)

SH(0,N)=SH(N)

SH(a/b/N)=SH(a-1/b,b,...(btimes)...,b/N)

SH(N,a/0/M)=SH(N,a-1/SH(N,a-1/a/M)/M)

I define a phrase n-dimensional array of m (nDm) : it is a notation of m's filled with n-dimensional cube with a size of n.

SH(N/^k a/^n b)=SH(N/^k a-1/^n (n-1Db))

SH(N,a/^k 0/^n b)=SH(N,a-1/^k SH(N,a-1/^k a/^n b)/^n b)

Are these definitions OK? Please leave a comment if these definition have any problems.


Last but not least, I will define a number.

Ita-Chihaya number (beta) = SH(72D72)

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