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A085959 Multiples of 37. 2

%I

%S 0,37,74,111,148,185,222,259,296,333,370,407,444,481,518,555,592,629,

%T 666,703,740,777,814,851,888,925,962,999,1036,1073,1110,1147,1184,

%U 1221,1258,1295,1332,1369,1406,1443,1480,1517,1554,1591,1628,1665,1702,1739

%N Multiples of 37.

%C If a(k) = 100*u+10*v+w with 0 <= u, v, w < 10, then 100*v+10*w+u is also a term.

%C Numbers for which the sum of "digits" base 1000 is divisible by 37, since 999 = 3^3 * 37. For instance, 10089601558 gives 10 + 089 + 601 + 558 = 1258, 1 + 258 = 259 = 7 * 37. - _Daniel Forgues_, Feb 22 2016

%D David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books, 1986.

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

%H Luis Manuel Rivera, <a href="http://arxiv.org/abs/1406.3081">Integer sequences and k-commuting permutations</a>, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1).

%F a(n) = a(n-1)+37; a(0)=0.

%F G.f.: 37*x/(1-x)^2. - _Vincenzo Librandi_, Feb 23 2016

%t Range[0, 2000, 37] (* _Vladimir Joseph Stephan Orlovsky_, Jun 03 2011 *)

%t CoefficientList[Series[37 x / (1 - x)^2, {x, 0, 33}], x] (* _Vincenzo Librandi_, Feb 23 2016 *)

%o (MAGMA) [37*n: n in [0..50]]; // _Vincenzo Librandi_, Feb 23 2016

%Y Cf. A044102.

%K nonn,easy

%O 0,2

%A _Reinhard Zumkeller_, Aug 17 2003

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Last modified November 20 05:07 EST 2019. Contains 329323 sequences. (Running on oeis4.)