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 A260647 #22 Jul 26 2020 12:40:22
%S A260647 4,7,9,11,13,16,18,21,22,24,25,27,29,31,34,36,37,38,39,42,43,46,48,49,
%T A260647 51,55,56,57,58,60,61,64,65,66,67,69,70,72,73,76,79,81,83,84,87,88,91,
%U A260647 92,93,94,97,99,100,101,102,106,108,111,112,114,115,119,120
%N A260647 Numbers that are the sum of two distinct nonzero triangular numbers.
%C A260647 The sequence contains every square greater than 1.
%C A260647 Conjecture: the sequence contains infinitely many primes.
%F A260647 {k: A307597(k) > 0 }. - _R. J. Mathar_, Apr 28 2020
%e A260647 24 = 3 + 21, so 24 is in the sequence.
%t A260647 r = 120; lst = Table[0, {r}]; lim = Floor[Sqrt[8*r - 7]]; Do[num = (i^2 + i)/2 + (j^2 + j)/2; If[num <= r, lst[[num]]++], {i, lim}, {j, i - 1}]; Flatten@Position[lst, n_ /; n > 0]
%t A260647 With[{nn=20},Select[Union[Total/@Subsets[Accumulate[Range[nn]],{2}]],#<= (nn(nn+1))/2+1&]] (* _Harvey P. Dale_, Jul 26 2020 *)
%Y A260647 Cf. A000217, A265140 (exactly one way), A262749 (more than one way), A265134 (exactly two ways), A265135 (more than two ways), A265136 (exactly three ways), A265137 (more than three ways), A265138 (exactly four ways).
%Y A260647 Subsequence of A051533.
%K A260647 nonn
%O A260647 1,1
%A A260647 _Arkadiusz Wesolowski_, Dec 02 2015