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URL: https://oeis.org/A163522

⇱ A163522 - OEIS

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