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

Author

Reinhard Zumkeller, Aug 17 2003

Keywords

• nonn
• easy

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

• 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).

Crossrefs

Cf. A044102.

Programs

Magma

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

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 *)

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)