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%I #11 Aug 06 2017 22:28:13
%S 2,9,6,6,7,5,1,3,4,7,4,3,5,9,1,0,3,4,5,7,0,1,5,5,0,2,0,2,1,9,1,4,2,8,
%T 6,4,8,6,4,8,3,1,5,1,9,1,7,8,9,4,7,8,9,0,8,1,6,7,3,5,7,3,3,1,6,5,9,0,
%U 6,1,6,2,9,1,5,1,9,6,0,8,8,8,3,6,6,7,4,8,1,6,4,0,2,1,2,6,2,2,1,4,5,4,1,7,7
%N Decimal expansion of Product_{n>=2} (1 - 1/(n*(n-1))).
%C Product of Artin's constant A005596 and the equivalent almost-prime products.
%H M. Chamberland, A. Straub, <a href="http://arxiv.org/abs/1309.3455">On gamma constants and infinite products</a>, arXiv:1309.3455
%H R. J. Mathar, <a href="http://arxiv.org/abs/0903.2514">Hardy-Littlewood constants embedded into infinite products over all positive integers</a>, arXiv:0903.2514 [math.NT], first line Table 3.
%F The logarithm is -Sum_{s>=2} Sum_{j=1..floor(s/(1+r))} binomial(s-r*j-1, j-1)*(1-Zeta(s))/j at r=1.
%F s*Sum_{j=1..floor(s/2)} binomial(s-j-1, j-1)/j = A001610(s-1).
%F Equals 1/Product_{k=1..2} Gamma(1-x_k) = -sin(A094886)/A000796, where x_k are the 2 roots of the polynomial x*(x+1)-1. [_R. J. Mathar_, Feb 20 2009]
%e 0.2966751347435910345... = (1 - 1/2)*(1 - 1/6)*(1 - 1/12)*(1 - 1/20)*...
%p phi := (1+sqrt(5))/2; evalf(-sin(Pi*phi)/Pi) ; # _R. J. Mathar_, Feb 20 2009
%t RealDigits[-Cos[Pi*Sqrt[5]/2]/Pi, 10, 105] // First (* _Jean-François Alcover_, Feb 11 2013 *)
%Y Cf. A005596.
%K nonn,cons
%O 0,1
%A _R. J. Mathar_, Feb 13 2009
%E More terms from _Jean-François Alcover_, Feb 11 2013
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