Stack-of-twos

The fourth function \(f_3\) of fast-growing hierarchy has been referred to as the stack-of-twos function from a paper discussing about Ramsey theorems. Prömel, H. J.; Thumser, W.; Voigt, B. "Fast growing functions based on Ramsey theorems", Discrete Mathematics, v.95 n.1-3, p. 343, Dec. 1991 . It has the growth rate equivalent to tetration, but no closed-form expression in terms of pentation or lower hyperoperators are known.
It is obtained by iterating \(f_2(n) = n2^n\) a total of \(n\) times. This expression is bounded below by \(2^nn((2^{2^nn})\uparrow\uparrow (n-1))\).
== Sources ==
Category:Functions
Category:Tetrational growth rate