This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A153080 #46 Apr 04 2025 14:30:52
%S A153080 2,15,28,41,54,67,80,93,106,119,132,145,158,171,184,197,210,223,236,
%T A153080 249,262,275,288,301,314,327,340,353,366,379,392,405,418,431,444,457,
%U A153080 470,483,496,509,522,535,548,561,574,587,600,613,626,639,652,665,678,691
%N A153080 a(n) = 13*n + 2.
%C A153080 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
%C A153080 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
%H A153080 Vincenzo Librandi, <a href="/A153080/b153080.txt">Table of n, a(n) for n = 0..1000</a>
%H A153080 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A153080 G.f.: (2+11*x)/(1-x)^2. - _R. J. Mathar_, Jan 05 2011
%F A153080 a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Feb 25 2012
%F A153080 E.g.f.: exp(x)*(2 + 13*x). - _Elmo R. Oliveira_, Apr 04 2025
%p A153080 A153080:=n->13*n+2: seq(A153080(n), n=0..100); # _Wesley Ivan Hurt_, Oct 05 2017
%t A153080 Range[2, 1000, 13] (* _Vladimir Joseph Stephan Orlovsky_, May 29 2011 *)
%t A153080 LinearRecurrence[{2,-1},{2,15},30] (* _Vincenzo Librandi_, Feb 25 2012 *)
%o A153080 (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
%Y A153080 Cf. A008595, A010376, A141858, A190991.
%Y A153080 Cf. A269100. - _Bruno Berselli_, Feb 22 2016
%K A153080 nonn,easy
%O A153080 0,1
%A A153080 _Vincenzo Librandi_, Feb 10 2009