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A009981 Powers of 37.

%I A009981 #46 Feb 21 2024 08:18:11
%S A009981 1,37,1369,50653,1874161,69343957,2565726409,94931877133,
%T A009981 3512479453921,129961739795077,4808584372417849,177917621779460413,
%U A009981 6582952005840035281,243569224216081305397,9012061295995008299689
%N A009981 Powers of 37.
%C A009981 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 A009981 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 A009981 Numbers n such that sigma(37*n) = 37*n + sigma(n). - _Jahangeer Kholdi_, Nov 23 2013
%D A009981 C. W. Trigg, The Powers of 37, Journal of Recreational Mathematics, Vol. 12:3 (1979-80), 186-191.
%H A009981 T. D. Noe, <a href="/A009981/b009981.txt">Table of n, a(n) for n = 0..100</a>
%H A009981 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A009981 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (37).
%F A009981 G.f.: 1/(1-37*x). - _Philippe Deléham_, Nov 24 2008
%F A009981 a(n)=37^n; a(n)=37*a(n-1) n>0 a(0)=1. - _Vincenzo Librandi_, Nov 21 2010
%t A009981 37^Range[0, 20] (* or *)
%t A009981 NestList[37*# &, 1, 20] (* _Paolo Xausa_, Feb 21 2024 *)
%o A009981 (Magma)[37^n: n in [0..20]]; // _Vincenzo Librandi_, Nov 21 2010
%o A009981 (PARI) a(n)=37^n \\ _Charles R Greathouse IV_, Oct 07 2015
%K A009981 nonn,easy
%O A009981 0,2
%A A009981 _N. J. A. Sloane_
%E A009981 Reference added by _William Rex Marshall_, Nov 13 2010