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

0, 1, 2, 4, 12

Offset

1,3

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

Table of n, a(n) for n=1..5.

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

Mathematica

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

Prog

(PARI) is(n)=issquare(8<<n-7) \\ Charles R Greathouse IV, Sep 07 2012

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.

Sequence in context: A227530 A218129 A156519 * A070314 A075554 A365000

Adjacent sequences: A215792 A215793 A215794 * A215796 A215797 A215798

Keyword

nonn,fini,full

Author

V. Raman, Aug 23 2012

Extensions

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

Status

approved