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 A216269 #20 Nov 14 2024 10:59:02
%S A216269 1,6,11,45,51,209,660099
%N A216269 Numbers n such that n^2 - 1 is a tetrahedral number (A000292).
%C A216269 Corresponding tetrahedral numbers are in A216268.
%C A216269 The curve 6*(x^2-1)-y*(y+1)*(y+2)=0 is elliptic, and has finitely many integral points by Siegel's theorem. - _Robert Israel_, Apr 22 2021
%H A216269 Wikipedia, <a href="https://en.wikipedia.org/wiki/Siegel%27s_theorem_on_integral_points">Siegel's theorem on integral points</a>
%t A216269 t = {}; Do[tet = n (n + 1) (n + 2)/6; If[IntegerQ[s = Sqrt[tet + 1]], AppendTo[t, s]], {n, 0, 100000}]; t (* _T. D. Noe_, Mar 18 2013 *)
%o A216269 (Python)
%o A216269 import math
%o A216269 for i in range(1<<30):
%o A216269 t = i*(i+1)*(i+2)//6 + 1
%o A216269 sr = int(math.sqrt(t))
%o A216269 if sr*sr == t:
%o A216269 print(sr)
%Y A216269 Cf. A000292, A216268.
%Y A216269 Cf. A003556 (both square and tetrahedral).
%K A216269 nonn,fini
%O A216269 1,2
%A A216269 _Alex Ratushnyak_, Mar 15 2013