
COMMENTS

The next term is too large to include.
The fastiteration (or extended Grzegorczyk hierarchy) function F[k]_n(x) is defined as follows:
F[k]_{n+1}(x) = (F[k]_n)^x(x) = F[k]_n(F[k]_n(...F[k]_n(x)) (with x iterations);
F[k]_0(x) = x+k.
The base case could be rewritten using n=1 rather than n=0. If so the definition would be:
F'[k]_n+1(x) = (F'[k]_n)^x(x);
F'[k]_1(x) = x+k.
Because of its clear definition, this function is a popular benchmark for large number functions.


MATHEMATICA

f[k_, 0, x_] := x + k; f[k_, n_, x_] := Nest[f[k, n  1, # ]&, x, x]; Table[f[n, n, 2], {n, 0, 3}]
