OFFSET
0,1
COMMENTS
Note that this could be extended backwards to a(-1), and any nonzero value x for a(-1) would work, since x^0 + 1 = 2.
LINKS
David Johnson-Davies, Recursive functions without a base case
MAPLE
a:= proc(n) option remember; `if`(n<0, %,
1 + a(n-1)^n)
end:
seq(a(n), n=0..5); # Alois P. Heinz, Dec 18 2019
MATHEMATICA
a[0] = 2; a[n_] := a[n] = a[n - 1]^n + 1; Array[a, 6, 0] (* Amiram Eldar, Dec 19 2019 *)
nxt[{n_, a_}]:={n+1, a^(n+1)+1}; NestList[nxt, {0, 2}, 5][[;; , 2]] (* Harvey P. Dale, Dec 10 2023 *)
PROG
(Lisp) (defun a (n) (+ (if (zerop n) 1 (expt (a (- n 1)) n)) 1))
(PARI) a(n) = if(n==0, 2, a(n-1)^n+1) \\ Felix Fröhlich, Dec 18 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
David Johnson-Davies, Dec 18 2019
EXTENSIONS
Edited by N. J. A. Sloane, Dec 27 2019
STATUS
approved