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 A230044 #36 Mar 27 2021 23:33:26 %S A230044 0,1,2,3,5,6,9,10,11,12,14,15,17,19,20,21,24,27,28,29,30,32,35,36,39, %T A230044 41,42,44,45,46,50,51,53,54,55,56,57,62,65,66,69,71,72,74,75,77,78,80, %U A230044 82,84,87,89,90,91,95,96,100,101,104,105,107,109,110,111,116,117,119,120,122,126,127,128 %N A230044 Nonnegative numbers k such that k plus a perfect square is a triangular number. %C A230044 Negative k are in A175035. %C A230044 Numbers such that the Diophantine equation y^2 + y - 2x^2 = 2n, y > 0 has a solution. Empirically, solutions (x,y) don't exceed (5n,5n) for n < 10^5. Record quotients y/n are at n = 2, 3, 12, 45, 1225, 6806, ... %C A230044 Conjecture: these are the sorted distinct terms of A064784. %C A230044 n is in this sequence iff 8n+1 is in A035251, that is, every prime p == 3 or 5 (mod 8) dividing 8n+1 appears to an even power. - _Max Alekseyev_, Oct 14 2013 %H A230044 Charles R Greathouse IV, <a href="/A230044/b230044.txt">Table of n, a(n) for n = 1..10000</a> %e A230044 28 is triangular, and 25 is a square <= 28, and 28-25=3, so 3 is in sequence. %o A230044 (PARI) B=bnfinit(z^2-8); is(n)=#bnfisintnorm(B,8*n+1) \\ _Max Alekseyev_, Oct 13 2013 %Y A230044 Cf. A035251, A064784, A175035. %K A230044 nonn %O A230044 1,3 %A A230044 _Ralf Stephan_, Oct 06 2013