Sudan function

Sudan function is a fast growing function discovered by . It is similar to the Ackermann function (but less well-known) and formally defined as follows:
\(F_0(x,y) = x+y\)
\(F_{n+1}(x,0) = x\) (for \(n \geq 0\))
\(F_{n+1}(x,y+1) = F_n(F_{n+1}(x,y),F_{n+1}(x,y)+y+1)\) (for \(n \geq 0,y \geq 0\))
It has been proven that the function is not .
== Values ==
It can be shown that \(F_1(x,y) = F_1(0,y)+2^y \times x\). Below is the table for values of \(F_2(n)\).
y \ x	0 	1 	2 	3 	4 	5
0 	0 	1 	2 	3 	4 	5
1 	1 	8 	27 	74 	185 	440
2 	19	10,228	\(\approx 1.55 \times 10^{10}\)	\(\approx 5.74 \times 10^{24}\)	\(\approx 3.67 \times 10^{58}\)	\(\approx 5.08 \times 10^{135}\)
== Sources ==
* [https://en.wikipedia.org/wiki/Sudan_function
* How it is computed
* 
Category:Functions
Category:Eponymous functions