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 A165720 #13 Jul 26 2024 08:58:00
%S A165720 6,8,18,21,35,39,57,62,84,90,116,123,153,161,195,204,242,252,294,305,
%T A165720 351,363,413,426,480,494,552,567,629,645,711,728,798,816,890,909,987,
%U A165720 1007,1089,1110,1196,1218,1308,1331,1425,1449,1547,1572,1674,1700,1806
%N A165720 Integers of the form k*(k+11)/10.
%C A165720 Integers of the form k + k*(k+1)/10 = k + A000217(k)/5. For k see A047208, for A000217(k)/5 see A057569. - _R. J. Mathar_, Sep 25 2009
%C A165720 Are all terms composite numbers?
%C A165720 Yes. They are alternately of the form (h+2)*(5*h-1)/2 and h*(5*h+11)/2, with h>0. - _Bruno Berselli_, Dec 22 2016
%H A165720 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A165720 From _R. J. Mathar_, Sep 25 2009: (Start)
%F A165720 a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).
%F A165720 a(n) = 5*(2*n^2 + 10*n + 3)/16 - 3*(-1)^n*(5 + 2*n)/16.
%F A165720 G.f.: x*(-6 - 2*x + 2*x^2 + x^3) / ((1 + x)^2*(x - 1)^3). (End)
%F A165720 Sum_{n>=1} 1/a(n) = 514/363 - 2*Pi*sqrt(1+2/sqrt(5))/11. - _Amiram Eldar_, Jul 26 2024
%t A165720 Select[k = Range[0, 130]; k (k + 11)/10, IntegerQ] (* _Bruno Berselli_, Dec 22 2016 *)
%Y A165720 Cf. A000217, A047208, A057569, A165717, A165718, A165719, A279895.
%K A165720 nonn,easy
%O A165720 1,1
%A A165720 _Vladimir Joseph Stephan Orlovsky_, Sep 24 2009
%E A165720 Definition simplified by _R. J. Mathar_, Sep 25 2009
%E A165720 Corrected A-number in my comment - _R. J. Mathar_, Oct 30 2009