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Numbers n such that 2^n-1 is a triangular number (A000217).
5

%I #35 Jun 02 2021 22:09:17

%S 0,1,2,4,12

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

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

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

%C 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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RamanujansSquareEquation.html">Ramanujan's Square Equation</a>

%o (PARI) is(n)=issquare(8<<n-7) \\ _Charles R Greathouse IV_, Sep 07 2012

%Y Cf. A000217, A060728, A038198.

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

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

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

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

%Y Cf. A328129.

%K nonn,fini,full

%O 1,3

%A _V. Raman_, Aug 23 2012

%E Four cross-references to the Ramanujan-Nagell problem added by _Raphie Frank_, Sep 10 2012