login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A330581 a(0) = 2; thereafter a(n) = a(n - 1)^n + 1. 0
2, 3, 10, 1001, 1004006004002, 1020191144865623440455270145683555422808365843606721760320033 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..5.

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 *)

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

Cf. A000522, A182242.

Sequence in context: A290638 A330294 A270442 * A184163 A218271 A128125

Adjacent sequences:  A330578 A330579 A330580 * A330582 A330583 A330584

KEYWORD

nonn

AUTHOR

David Johnson-Davies, Dec 18 2019

EXTENSIONS

Edited by N. J. A. Sloane, Dec 27 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 30 19:02 EST 2021. Contains 349424 sequences. (Running on oeis4.)