A215797 Numbers k such that k*(k+1)/2 + 1 is a power of 2.

0, 1, 2, 5, 90

Offset: 1

Author

V. Raman, Aug 23 2012

Keywords

• nonn
• fini
• full

Comments

No other terms < 10^6. - T. D. Noe, Aug 25 2012

This sequence maps to the Ramanujan-Nagell squares (8*(k*(k+1)/2)+1) and is therefore complete. - Raphie Frank, Aug 26 2012

All terms in this sequence follow form floor[2^((2*x - 1)/2)]; x = {0, 1, 2, 3, 7}. - Raphie Frank, Mar 03 2013

Links

• Eric W. Weisstein, MathWorld: Ramanujan's Square Equation

Crossrefs

Cf. A060728, A038198 (two references to the Ramanujan-Nagell problem).

Programs

Mathematica

Select[Range[0,1000], IntegerQ[Log[2, 1 + #(#+1)/2]]&] (* T. D. Noe, Aug 25 2012 *)

PARI

for(n=0,100,if(ispolygonal(2^n-1,3),print1(sqrtint(2*2^n-2)", "))) \\ Charles R Greathouse IV, Mar 04 2013

Formula

a(n) = -1 + ceiling[sqrt(2^(A060728(n) - 2) - 1)]. - Raphie Frank, Mar 31 2013

a(n) = (|(((1+i*sqrt(7))/2)^(A060728(n) - 2) + ((1-i*sqrt(7))/2)^(A060728(n) - 2))| - 1)/2. - Raphie Frank, Dec 25 2013