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 A188891 #15 Feb 16 2025 08:33:14
%S A188891 3,36,210,6,55,21,325,10,0,105,36,1275,15,45,231,0,946,276,21,11935,
%T A188891 66,136,351,1596,78,28,1225,595,820,58653,190,325,1335795,36,6670,0,
%U A188891 561,4005,120,1128,1485,203841,45,666,6903,465,4950,20910,741,153,10731,8911,55,1953
%N A188891 Least triangular n-gonal number greater than 1, or 0 if none exists.
%C A188891 See A188893 and A188894 for the corresponding indices of these terms. Note that a(n) is zero for n = 11, 18, 38 (numbers in A188892). Although the Mathematica program searches only the first 20000 triangular numbers for n-gonal numbers, the Reduce function can show that there are no triangular n-gonal numbers (other than 0 and 1) for these n.
%H A188891 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/PolygonalNumber.html">MathWorld: Polygonal Number</a>
%H A188891 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/TriangularNumber.html">MathWorld: Triangular Number</a>
%t A188891 NgonIndex[n_, v_] := (-4 + n + Sqrt[16 - 8*n + n^2 - 16*v + 8*n*v])/(n - 2)/2; Table[k = 2; While[tr = k*(k+1)/2; i = NgonIndex[n, tr]; k < 20000 && ! IntegerQ[i], k++]; If[k==20000, tr=0]; tr, {n, 3, 50}]
%t A188891 Table[SelectFirst[PolygonalNumber[n,Range[2,1000]],OddQ[Sqrt[8#+1]]&],{n,3,100}]/.Missing["NotFound"]->0 (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Nov 10 2019 *)
%Y A188891 Cf. A000217 (triangular numbers), A100252 (similar sequence for squares).
%K A188891 nonn
%O A188891 3,1
%A A188891 _T. D. Noe_, Apr 13 2011