A215795 Numbers n such that 2^n-1 is a triangular number (A000217).

0, 1, 2, 4, 12

Offset: 1

Author

V. Raman, Aug 23 2012

Keywords

• nonn
• fini
• full

Comments

Aside from a(2), all terms are even. Probably complete; no more terms up to 10^6. - Charles R Greathouse IV, Sep 07 2012

This sequence maps to the Ramanujan-Nagell squares (8*(2^n - 1) + 1) and is therefore complete. - Raphie Frank, Sep 10 2012

Define equivalence classes on a specified real interval with respect to the symmetric transitive closure of R(x,y) = "x is an integer multiple of y". If any equivalence class is finite (the conditions for which are given in A328129), then a smallest equivalence class has cardinality 1, 2, 4 or 12. - Peter Munn, Jun 02 2021

Links

• Eric Weisstein's World of Mathematics, Ramanujan's Square Equation

Crossrefs

Cf. A000217, A060728, A038198.

Cf. A076046 (triangular numbers of the form 2^n - 1).

Cf. A060728 (a(n) + 3).

Cf. A038198 (sqrt(8*(2^n - 1)+1)).

Cf. A215797 ((sqrt(8*(2^n - 1)+1) - 1)/2).

Cf. A328129.

Programs

Mathematica

Select[Range[0,15],OddQ[Sqrt[8(2^#-1)+1]]&] (* Harvey P. Dale, Dec 13 2024 *)

PARI

is(n)=issquare(8<Charles R Greathouse IV, Sep 07 2012

Extensions

Four cross-references to the Ramanujan-Nagell problem added by Raphie Frank, Sep 10 2012