A009981 Powers of 37.

1, 37, 1369, 50653, 1874161, 69343957, 2565726409, 94931877133, 3512479453921, 129961739795077, 4808584372417849, 177917621779460413, 6582952005840035281, 243569224216081305397, 9012061295995008299689

Offset

0,2

Comments

Same as Pisot sequences E(1, 37), L(1, 37), P(1, 37), T(1, 37). Essentially same as Pisot sequences E(37, 1369), L(37, 1369), P(37, 1369), T(37, 1369). 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 37-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

Numbers n such that sigma(37*n) = 37*n + sigma(n). - Jahangeer Kholdi, Nov 23 2013

References

C. W. Trigg, The Powers of 37, Journal of Recreational Mathematics, Vol. 12:3 (1979-80), 186-191.

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 (37).

Formula

G.f.: 1/(1-37*x). - Philippe Deléham, Nov 24 2008

a(n)=37^n; a(n)=37*a(n-1) n>0 a(0)=1. - Vincenzo Librandi, Nov 21 2010

Mathematica

37^Range[0, 20] (* or *)
NestList[37*# &, 1, 20] (* Paolo Xausa, Feb 21 2024 *)

Prog

(Magma)[37^n: n in [0..20]]; // Vincenzo Librandi, Nov 21 2010
(PARI) a(n)=37^n \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Sequence in context: A188771 A207185 A189061 * A370334 A097315 A158741

Adjacent sequences: A009978 A009979 A009980 * A009982 A009983 A009984

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Reference added by William Rex Marshall, Nov 13 2010

Status

approved