A106332 Decimal expansion of the constant x that satisfies: 1 = Sum_{n>=1} x^(n*(n+1)/2).

6, 4, 5, 2, 2, 2, 7, 0, 3, 2, 3, 6, 0, 2, 0, 9, 7, 9, 1, 3, 4, 2, 5, 1, 6, 6, 3, 9, 4, 4, 0, 2, 6, 3, 3, 2, 2, 5, 4, 7, 2, 7, 4, 4, 3, 6, 4, 0, 5, 7, 1, 2, 2, 1, 0, 7, 4, 2, 2, 0, 1, 8, 3, 9, 0, 1, 3, 6, 5, 4, 6, 7, 1, 5, 7, 3, 9, 6, 4, 9, 9, 7, 2, 0, 1, 4, 4, 6, 9, 3, 6, 9, 3, 5, 0, 0, 2, 6, 6, 1, 3, 4, 5, 5, 1

Offset: 0

Author

Paul D. Hanna, Apr 29 2005

Keywords

• cons
• nonn

Comments

Equals the radius of convergence of the g.f. of A023361 (number of compositions into sums of triangular numbers).

Examples

			1 = x + x^3 + x^6 + x^10 + x^15 + x^21 + x^28 + x^36 + ...
x = 0.6452227032360209791342516639440263322547274436405712210742201839013654671
		

Crossrefs

Cf. A023361.

Programs

Mathematica

x /. FindRoot[ EllipticTheta[2, 0, Sqrt[x]] == 4*x^(1/8), {x, 1/2}, WorkingPrecision -> 110] // RealDigits[#, 10, 105]& // First (* Jean-François Alcover, Feb 13 2013 *)

PARI

solve(x=0.6,0.7,1-sum(n=1,60,x^(n*(n+1)/2)))