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 A274579 #22 Apr 27 2025 09:08:23 %S A274579 0,1,7,27,540,2002,10660,39501,779247,2887450,15372280,56960982, %T A274579 1123674201,4163701465,22166817667,82137697110,1620337419162, %U A274579 6004054625647,31964535704101,118442502272205,2336525434757970,8657842606482076,46092838318496542 %N A274579 Values of k such that 2*k+1 and 5*k+1 are both triangular numbers. %C A274579 Intersection of A074377 and A085787. %H A274579 Colin Barker, <a href="/A274579/b274579.txt">Table of n, a(n) for n = 1..1000</a> %H A274579 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1442,-1442,0,0,-1,1). %F A274579 G.f.: x^2*(1+6*x+20*x^2+513*x^3+20*x^4+6*x^5+x^6) / ((1-x)*(1+6*x-x^2)*(1-6*x-x^2)*(1+38*x^2+x^4)). %e A274579 7 is in the sequence because 2*7+1 = 15, 5*7+1 = 36, and 15 and 36 are both triangular numbers. %o A274579 (PARI) concat(0, Vec(x^2*(1+6*x+20*x^2+513*x^3+20*x^4+6*x^5+x^6)/((1-x)*(1+6*x-x^2)*(1-6*x-x^2)*(1+38*x^2+x^4)) + O(x^30))) %o A274579 (PARI) isok(n) = ispolygonal(2*n+1, 3) && ispolygonal(5*n+1, 3); \\ _Michel Marcus_, Jun 29 2016 %Y A274579 Cf. A000217, A074377, A085787, A124174. %K A274579 nonn,easy %O A274579 1,3 %A A274579 _Colin Barker_, Jun 29 2016