A135631 Multiples of 31.

0, 31, 62, 93, 124, 155, 186, 217, 248, 279, 310, 341, 372, 403, 434, 465, 496, 527, 558, 589, 620, 651, 682, 713, 744, 775, 806, 837, 868, 899, 930, 961, 992, 1023, 1054, 1085, 1116, 1147, 1178, 1209, 1240, 1271, 1302, 1333, 1364, 1395, 1426, 1457, 1488

Offset: 0

Author

Omar E. Pol, Nov 25 2007

Keywords

• easy
• nonn

Comments

a(1) = 31 is the third Mersenne prime. a(8) = 248 is the dimensions of E_8. a(16) = 496 is the third perfect number. - Pol

a(n)^340 = 155 mod 341 unless a(n) is also divisible by 11. - Alonso del Arte, Feb 15 2012

Number of sides on n triacontakaihenagons (31-gons). - Wesley Ivan Hurt, Oct 25 2016

Examples

			a(8) = 31 * 8 = 248. a(16) = 31 * 16 = 496.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081, 2014
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A135628.

Programs

Maple

with(numtheory):a:=proc(n) if n=0 then 0 else mcombine(7*n,3*n,5*n,11*n) fi end: seq(a(n), n=0..45); # Zerinvary Lajos, Apr 11 2008

Mathematica

Range[0, 3000, 31] (* Vladimir Joseph Stephan Orlovsky, Jun 03 2011 *)
LinearRecurrence[{2,-1},{0,31},25] (* G. C. Greubel, Oct 24 2016 *)

Formula

a(n) = 31*n.

From G. C. Greubel, Oct 24 2016: (Start)

G.f.: (31*x)/(1 - x)^2.

E.g.f.: 31*x*exp(x).

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