A009981 - OEIS

%I #46 Feb 21 2024 08:18:11

%S 1,37,1369,50653,1874161,69343957,2565726409,94931877133,

%T 3512479453921,129961739795077,4808584372417849,177917621779460413,

%U 6582952005840035281,243569224216081305397,9012061295995008299689

%N Powers of 37.

%C 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.

%C 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

%C Numbers n such that sigma(37*n) = 37*n + sigma(n). - _Jahangeer Kholdi_, Nov 23 2013

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

%H T. D. Noe, <a href="/A009981/b009981.txt">Table of n, a(n) for n = 0..100</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (37).

%F G.f.: 1/(1-37*x). - _Philippe Deléham_, Nov 24 2008

%F a(n)=37^n; a(n)=37*a(n-1) n>0 a(0)=1. - _Vincenzo Librandi_, Nov 21 2010

%t 37^Range[0, 20] (* or *)

%t NestList[37*# &, 1, 20] (* _Paolo Xausa_, Feb 21 2024 *)

%o (Magma)[37^n: n in [0..20]]; // _Vincenzo Librandi_, Nov 21 2010

%o (PARI) a(n)=37^n \\ _Charles R Greathouse IV_, Oct 07 2015

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

%E Reference added by _William Rex Marshall_, Nov 13 2010