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

0,1

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).

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

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 *)

Prog

(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

Crossrefs

Cf. A008595, A141858, A190991.

Cf. A269100. - Bruno Berselli, Feb 22 2016

Sequence in context: A300346 A370031 A338457 * A075312 A212975 A128828

Adjacent sequences: A153077 A153078 A153079 * A153081 A153082 A153083

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 10 2009

Status

approved