A009981 Powers of 37.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Programs

Magma

[37^n: n in [0..20]]; // Vincenzo Librandi, Nov 21 2010

Mathematica

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

PARI

a(n)=37^n \\ Charles R Greathouse IV, Oct 07 2015

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

Extensions

Reference added by William Rex Marshall, Nov 13 2010