|
%I #8 Feb 17 2017 08:37:53
%S 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,
%T 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,
%U 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
%N Decimal expansion of the constant x that satisfies: 1 = Sum_{n>=1} x^(n*(n+1)/2).
%C Equals the radius of convergence of the g.f. of A023361 (number of compositions into sums of triangular numbers).
%e 1 = x + x^3 + x^6 + x^10 + x^15 + x^21 + x^28 + x^36 + ...
%e x = 0.6452227032360209791342516639440263322547274436405712210742201839013654671
%t 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 *)
%o (PARI) solve(x=0.6,0.7,1-sum(n=1,60,x^(n*(n+1)/2)))
%Y Cf. A023361.
%K cons,nonn
%O 0,1
%A _Paul D. Hanna_, Apr 29 2005
|
