User blog:Nayuta Ito/Ita-Chihaya number(3)

Review of Part 2:

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

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

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

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

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

(note: the 0 is the leftmost 0)

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

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

Now, let's zip this!

$$SH(x,...(xtimes)...x/...(ytimes).../x,...(xtimes)...x)$$

What should I write for this? It looks like 2D notation, so I will write like this:

$$SH(x/_2 y)$$

This is nice and if I use the same rule as slashes, I may be able to have more extension.

Now, I will summarize my definitions:

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

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

$$SH(N/^m_a 0/^n_b M)=SH(N/^m_a M)$$

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

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

(note: the 0 is the leftmost 0)

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

$$SH(x/_n y)=SH(x,...(xtimes)...x/_{n-1}...(ytimes).../_{n-1}x,...(xtimes)...x)$$

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

...Actually, I don't know what to do next.

I will write a number for the end of this page.

$$KC(x)=SH(x/^x _x x)$$

Ita-Chihaya number(gamma)=$$Kc(72)$$