A153080 a(n) = 13*n + 2.

2, 15, 28, 41, 54, 67, 80, 93, 106, 119, 132, 145, 158, 171, 184, 197, 210, 223, 236, 249, 262, 275, 288, 301, 314, 327, 340, 353, 366, 379, 392, 405, 418, 431, 444, 457, 470, 483, 496, 509, 522, 535, 548, 561, 574, 587, 600, 613, 626, 639, 652, 665, 678, 691

Offset: 0

Author

Vincenzo Librandi, Feb 10 2009

Keywords

• nonn
• easy

Comments

Any square mod 13 is one of 0, 1, 3, 4, 9, 10 or 12 (A010376) but not 2, and for this reason there are no squares in the sequence. Likewise, any cube mod 13 is one of 0, 1, 5, 8 or 12, therefore no term is a cube. - Bruno Berselli, Feb 19 2016

Numbers k such that GCD(2*k^5+1, 3*k^3+2) > 1. This GCD is 13 if k == 2 (mod 13), or 1 otherwise. - Philippe Deléham, Jan 16 2024

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A008595, A010376, A141858, A190991.

Cf. A269100. - Bruno Berselli, Feb 22 2016

Programs

Magma

I:=[2, 15]; [n le 2 select I[n] else 2*Self(n-1)-1*Self(n-2): n in [1..60]]; // Vincenzo Librandi, Feb 25 2012

Maple

A153080:=n->13*n+2: seq(A153080(n), n=0..100); # Wesley Ivan Hurt, Oct 05 2017

Mathematica

Range[2, 1000, 13] (* Vladimir Joseph Stephan Orlovsky, May 29 2011 *)
LinearRecurrence[{2,-1},{2,15},30] (* Vincenzo Librandi, Feb 25 2012 *)

Formula

G.f.: (2+11*x)/(1-x)^2. - R. J. Mathar, Jan 05 2011

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 25 2012

E.g.f.: exp(x)*(2 + 13*x). - Elmo R. Oliveira, Apr 04 2025