cp's OEIS Frontend

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.

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A309009 Numbers that are both triangular and octahedral.

Original entry on oeis.org

0, 1, 6, 231
Offset: 1

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Author

William C. Laursen, Jul 05 2019

Keywords

Comments

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.
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
Is 1156 the only nontrivial number that is both octahedral and square? - Kelvin Voskuijl, Jan 07 2025

Crossrefs

Intersection of A000217 and A005900. - A.H.M. Smeets, Aug 19 2019
Cf. A000217, A005900, A027568, A307174.

Programs

  • Mathematica
    triQ[n_] := IntegerQ[Sqrt[8n + 1]]; oct[n_] := n(2n^2 + 1)/3 ; Select[oct@Range[0, 10], triQ] (* Amiram Eldar, Jul 15 2019 *)
  • PARI
    lista(nn) = for (n=0, nn, if (ispolygonal(k=n*(2*n^2 + 1)/3, 3), print1(k, ", "))); \\ Michel Marcus, Jul 06 2019

Extensions

Keyword "full" added by Max Alekseyev, Feb 12 2024
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