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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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 k such that sigma(23*k) = 23*k + sigma(k). - 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).

Crossrefs

Cf. A000079, A008776, A009990.

Programs

Magma

[23^n: n in [0..100]]; // Vincenzo Librandi, Nov 21 2010

Mathematica

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

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

SageMath

[lucas_number1(n,23,0) for n in range(1, 17)] # Zerinvary Lajos, Apr 29 2009

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

From Elmo R. Oliveira, Jul 10 2025: (Start)

E.g.f.: exp(23*x).

a(n) = A009990(n)/A000079(n). (End)