A085959 Multiples of 37.

0, 37, 74, 111, 148, 185, 222, 259, 296, 333, 370, 407, 444, 481, 518, 555, 592, 629, 666, 703, 740, 777, 814, 851, 888, 925, 962, 999, 1036, 1073, 1110, 1147, 1184, 1221, 1258, 1295, 1332, 1369, 1406, 1443, 1480, 1517, 1554, 1591, 1628, 1665, 1702, 1739

Offset

0,2

Comments

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

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

References

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

Links

Table of n, a(n) for n=0..47.

Tanya Khovanova, Recursive Sequences.

Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

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

G.f.: 37*x/(1-x)^2. - Vincenzo Librandi, Feb 23 2016

From Elmo R. Oliveira, Apr 10 2025: (Start)

E.g.f.: 37*x*exp(x).

a(n) = 37*n.

a(n) = 2*a(n-1) - a(n-2). (End)

Mathematica

Range[0, 2000, 37] (* Vladimir Joseph Stephan Orlovsky, Jun 03 2011 *)
CoefficientList[Series[37 x / (1 - x)^2, {x, 0, 33}], x] (* Vincenzo Librandi, Feb 23 2016 *)

Prog

(Magma) [37*n: n in [0..50]]; // Vincenzo Librandi, Feb 23 2016

Crossrefs

Cf. A044102.

Sequence in context: A289732 A087531 A283718 * A145936 A071884 A216287

Adjacent sequences: A085956 A085957 A085958 * A085960 A085961 A085962

Keyword

nonn,easy

Author

Reinhard Zumkeller, Aug 17 2003

Status

approved