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 A165719 #17 Jul 26 2024 08:58:04
%S A165719 14,17,45,50,92,99,155,164,234,245,329,342,440,455,567,584,710,729,
%T A165719 869,890,1044,1067,1235,1260,1442,1469,1665,1694,1904,1935,2159,2192,
%U A165719 2430,2465,2717,2754,3020,3059,3339,3380,3674,3717,4025,4070,4392,4439,4775
%N A165719 Integers of the form k*(k+9)/8.
%C A165719 Only one term is a prime number (17). Are all others composite?
%C A165719 There is no prime other than 17 in the first 1 million terms. - _Harvey P. Dale_, Jan 07 2020
%C A165719 Integers of the form k+k*(k+1)/8 = k+A000217(k)/4; for k see A047521, for A000217(k)/4 see A154260.
%H A165719 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A165719 From _R. J. Mathar_, Sep 25 2009: (Start)
%F A165719 a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).
%F A165719 a(n) = 2*n^2 + 6*n + 9/4 - 3*(-1)^n*(2*n+3)/4.
%F A165719 G.f.: x*(-14-3*x+x^3)/((1+x)^2 * (x-1)^3 ). (End)
%F A165719 Sum_{n>=1} 1/a(n) = 89/81 - (sqrt(2)+1)*Pi/9. - _Amiram Eldar_, Jul 26 2024
%e A165719 for k = 1,2,..., k(k+9)/8 is 5/4, 11/4, 9/2, 13/2, 35/4, 45/4, 14, 17,.. and the integer values out of these become the sequence.
%t A165719 q=4;s=0;lst={};Do[s+=((n+q)/q);If[IntegerQ[s],AppendTo[lst,s]],{n,6!}];lst
%t A165719 Select[Table[(n(n+9))/8,{n,200}],IntegerQ] (* or *) Rest[Flatten[Table[ {9n+8n^2,14+23n+8n^2},{n,0,30}]]] (* or *) LinearRecurrence[{1,2,-2,-1,1},{14,17,45,50,92},60] (* _Harvey P. Dale_, Jan 07 2020 *)
%Y A165719 Cf. A000217, A047521, A154260, A165717, A165718.
%K A165719 nonn,easy
%O A165719 1,1
%A A165719 _Vladimir Joseph Stephan Orlovsky_, Sep 24 2009
%E A165719 Definition simplified by _R. J. Mathar_, Sep 25 2009