A009967 Powers of 23.

1, 23, 529, 12167, 279841, 6436343, 148035889, 3404825447, 78310985281, 1801152661463, 41426511213649, 952809757913927, 21914624432020321, 504036361936467383, 11592836324538749809, 266635235464391245607, 6132610415680998648961, 141050039560662968926103, 3244150909895248285300369, 74615470927590710561908487, 1716155831334586342923895201

Offset

0,2

Comments

Same as Pisot sequences E(1, 23), L(1, 23), P(1, 23), T(1, 23). Essentially same as Pisot sequences E(23, 529), L(23, 529), P(23, 529), T(23, 529). See A008776 for definitions of Pisot sequences.

The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n>=1, a(n) equals the number of 23-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

Numbers n such that sigma(23*n) = 23*n + sigma(n). - Jahangeer Kholdi, Nov 23 2013

Links

T. D. Noe, Table of n, a(n) for n = 0..100

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (23).

Formula

G.f.: 1/(1-23*x). - Philippe Deléham, Nov 23 2008

a(n)=23^n; a(n)=23*a(n-1) n>0 a(0)=1. - Vincenzo Librandi, Nov 21 2010

Mathematica

23^Range[0, 20]  (* Harvey P. Dale, Apr 04 2011 *)

Prog

(Sage) [lucas_number1(n, 23, 0) for n in range(1, 17)]# - Zerinvary Lajos, Apr 29 2009
(Magma)[23^n: n in [0..100]] // Vincenzo Librandi, Nov 21 2010
(Maxima) A009967(n):=23^n$
makelist(A009967(n), n, 0, 30); /* Martin Ettl, Nov 07 2012 */
(PARI) a(n)=23^n \\ Charles R Greathouse IV, Sep 24 2015

Crossrefs

Sequence in context: A207223 A207010 A171297 * A147642 A057686 A042014

Adjacent sequences: A009964 A009965 A009966 * A009968 A009969 A009970

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved