Wow function

suggested that the fourth function \(f_4\) of fast-growing hierarchy as the wow-function. 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 pentation, and no closed-form expression in terms of pentation or lower hyperoperators are known.
Below are the first few outputs:
\(f_4(1)\) = 2
\(f_4(2)\) = \(f_3(f_3(2))\) = \(f_3(2048)\) ~ E619#2048
\(f_4(3)\) = \(f_3(f_3(f_3(3))) \approx 10\uparrow\uparrow(10\uparrow\uparrow(6.895 \times 10^{121210694}))\)
\(f_4(4)\) = \(f_3(f_3(f_3(f_3(4)))) \approx 10\uparrow\uparrow(10\uparrow\uparrow(10\uparrow\uparrow(10^{10^{10^{20}}})))\)
== Sources ==
ja:ワオ関数
Category:Functions
Category:Primitive recursive