User blog:Nayuta Ito/Ita-Chihaya number(2)

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:

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

Now, there are some slashes and I repeat them.

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

I will summary these definitions:

N and M can have slashes. Also they can be nothing.

$$SH(x)=39^x$$

$$SH(0,N)=SH(N)$$

$$SH(N/^m 0/^n M)=SH(N/^m M)$$

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

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

(note: the 0 is the leftmost 0)

$$SH(N,p/x)=SH(N,p-1/x,x,...(x times)...x)$$

$$SH(N,p/ ^n x)=SH(N,p-1/^{\mathrm n+1} x /^{\mathrm n+1}x ... (x times) ...x/^{\mathrm n+1}x)$$