A163522 a(1)=2; for n>1, a(n) = sum of digits of a(n-1)^2.

2, 4, 7, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16, 13, 16

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..1001

Index entries for linear recurrences with constant coefficients, signature (0,1).

Formula

G.f.: x*(2 + 4*x + 5*x^2 + 9*x^3 + 9*x^4)/((1 - x)*(1 + x)). - Bruno Berselli, May 29 2014

Example

a(2)=4  because 2^2=4;
a(3)=7  because 4^2=16 and 6+1=7;
a(4)=13 because 7^2=49 and 4+9=13.
Other similar sequences, starting from 3, 5, 7 respectively:
. 3, 9 (9 repeated);
. 5, 7, 13, 16, 13 (13, 16 repeated);
. 8, 10, 1 (1 repeated).

Mathematica

Join[{2, 4, 7}, LinearRecurrence[{0, 1}, {13, 16}, 50]] (* or *) CoefficientList[Series[x*(2 + 4*x + 5*x^2 + 9*x^3 + 9*x^4)/((1 - x)*(1 + x)), {x, 0, 50}], x]  (* G. C. Greubel, Jul 27 2017 *)
PadRight[{2, 4, 7}, 120, {16, 13}] (* Harvey P. Dale, Aug 29 2021 *)

Prog

(PARI) x='x+O('x^50); Vec(x*(2 + 4*x + 5*x^2 + 9*x^3 + 9*x^4)/((1 - x)*(1 + x))) \\ G. C. Greubel, Jul 27 2017
(Scheme) (define (A163522 n) (cond ((<= n 2) (expt 2 n)) ((= 3 n) 7) ((even? n) 13) (else 16))) ;; Antti Karttunen, Sep 14 2017

Crossrefs

Cf. A007953.

Sequence in context: A177101 A018414 A002152 * A255173 A002466 A162842

Adjacent sequences: A163519 A163520 A163521 * A163523 A163524 A163525

Keyword

nonn,base,easy

Author

Vincenzo Librandi, Jul 30 2009

Extensions

Edited by N. J. A. Sloane, Aug 01 2009

Edited by Bruno Berselli, May 29 2014

Status

approved