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 A309009 #30 Jan 17 2025 19:35:10 %S A309009 0,1,6,231 %N A309009 Numbers that are both triangular and octahedral. %C A309009 Similar to the list of triangular and tetrahedral numbers (A027568). It would appear that the similar sequence of pentagonal-dodecahedral numbers contains only the trivial cases 0 and 1. %C A309009 Terms n*(n+1)/2 = m*(2*m^2+1)/3 corresponds to integral points (X,Y) = (12*m,36*n+18) on the elliptic curve Y^2 = X^3 + 72*X + 324, which can be computed efficiently. There are none besides those already listed. - _Max Alekseyev_, Feb 12 2024 %C A309009 Is 1156 the only nontrivial number that is both octahedral and square? - _Kelvin Voskuijl_, Jan 07 2025 %t A309009 triQ[n_] := IntegerQ[Sqrt[8n + 1]]; oct[n_] := n(2n^2 + 1)/3 ; Select[oct@Range[0, 10], triQ] (* _Amiram Eldar_, Jul 15 2019 *) %o A309009 (PARI) lista(nn) = for (n=0, nn, if (ispolygonal(k=n*(2*n^2 + 1)/3, 3), print1(k, ", "))); \\ _Michel Marcus_, Jul 06 2019 %Y A309009 Intersection of A000217 and A005900. - _A.H.M. Smeets_, Aug 19 2019 %Y A309009 Cf. A000217, A005900, A027568, A307174. %K A309009 nonn,fini,full %O A309009 1,3 %A A309009 _William C. Laursen_, Jul 05 2019 %E A309009 Keyword "full" added by _Max Alekseyev_, Feb 12 2024