A216269 Numbers n such that n^2 - 1 is a tetrahedral number (A000292).

1, 6, 11, 45, 51, 209, 660099

Offset: 1

Author

Alex Ratushnyak, Mar 15 2013

Keywords

• nonn
• fini

Comments

Corresponding tetrahedral numbers are in A216268.

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

Links

• Wikipedia, Siegel's theorem on integral points

Crossrefs

Cf. A000292, A216268.

Cf. A003556 (both square and tetrahedral).

Programs

Mathematica

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 *)

Python

import math
for i in range(1<<30):
    t = i*(i+1)*(i+2)//6 + 1
    sr = int(math.sqrt(t))
    if sr*sr == t:
        print(sr)