Kudi-Chan's Number

Kudi-Chan's Number is an example of a naive extension to Graham's number, and of a salad number. It is defined as follows:

\(k_0 &=& 4\)

\(k_1 &=& G \uparrow\uparrow\uparrow\uparrow G\) where \(G\) is Graham's number

\(k_2 &=& G \underbrace{\uparrow\uparrow\cdots\uparrow\uparrow}_{k_1 \text{ arrows}} G\)

\(k_n &=& G \underbrace{\uparrow\uparrow\cdots\uparrow\uparrow}_{k_n \text{ arrows}} G\)

\(k_G &=& \text{Kudi-Chan's number}\)

It can be shown that this number is upper-bounded by GG 64+64 in Graham's function.

It was named as such by Cookiefonster, and allegedly discovered by Sbiis Saibian (not sure where, can someone find where he mentions this?).