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 A165721 #13 Jul 26 2024 08:57:51
%S A165721 4,14,22,25,35,55,69,74,90,120,140,147,169,209,235,244,272,322,354,
%T A165721 365,399,459,497,510,550,620,664,679,725,805,855,872,924,1014,1070,
%U A165721 1089,1147,1247,1309,1330,1394,1504,1572,1595,1665,1785,1859,1884,1960,2090
%N A165721 Integers of the form k*(k+13)/12.
%C A165721 Integers of the form k+k*(k+1)/12 = k+A000217(k)/6 (see A069497). - R. J. Mathar, Sep 25 2009
%C A165721 Are all terms composite numbers?
%C A165721 Contribution from _Zak Seidov_, Sep 25 2009: (Start)
%C A165721 Integers of form n(13+n)/12, n=0,1,2,...
%C A165721 Each four terms of the sequence are composite numbers of forms:
%C A165721 {(4+3 m) (1+4 m), (2+3 m) (7+4 m), (2+m) (11+12 m), m (13+12 m)}, m=0,1,2,...
%C A165721 m=0: {4,14,22,25}; m=1: {35,55,69,74}; m=2: {90,120,140,147}, etc. (End)
%H A165721 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-5,7,-7,5,-3,1).
%F A165721 From _R. J. Mathar_, Sep 25 2009: (Start)
%F A165721 a(n) = 3*a(n-1) - 5*a(n-2) + 7*a(n-3) - 7*a(n-4) + 5*a(n-5) - 3*a(n-6) + a(n-7).
%F A165721 G.f.: x*(-4-2*x-x^3+x^5)/((x^2+1)^2*(x-1)^3). (End)
%F A165721 Sum_{n>=1} 1/a(n) = 712/507 - (3 + 4*sqrt(3))*Pi/39. - _Amiram Eldar_, Jul 26 2024
%t A165721 q=6;s=0;lst={};Do[s+=((n+q)/q);If[IntegerQ[s],AppendTo[lst,s]],{n,6!}];lst
%t A165721 Select[Table[k (k+13)/12,{k,200}],IntegerQ] (* or *) LinearRecurrence[ {3,-5,7,-7,5,-3,1},{4,14,22,25,35,55,69},50] (* _Harvey P. Dale_, Jan 30 2013 *)
%Y A165721 Cf. A000217, A069497, A165717, A165718, A165719, A165720.
%K A165721 nonn,easy
%O A165721 1,1
%A A165721 _Vladimir Joseph Stephan Orlovsky_, Sep 24 2009
%E A165721 Definition simplified by _R. J. Mathar_, Sep 25 2009