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%I #10 May 08 2023 02:26:59
%S 4,3,8,7,9,6,8,3,7,2,0,3,6,3,8,5,3,1,2,6,6,7,2,9,9,9,7,1,7,7,2,5,8,3,
%T 5,9,6,0,4,5,7,4,6,3,1,2,3,9,3,5,1,1,6,5,4,1,7,7,3,6,7,5,6,4,3,6,7,9,
%U 1,0,6,6,5,6,9,8,6,6,5,0,0,6,9,2,8,9,6,6,7,2,3,8,9,8,5,4,4,0,0,6,0,2,8
%N Decimal expansion of Product_{k>=0} 1-1/(2*5^k).
%F Equals lim inf_{n->oo} Product_{k=0..floor(log_5(n))} floor(n/5^k)*5^k/n.
%F Equals lim inf_{n->oo} A132029(n)/n^(1+floor(log_5(n)))*5^(1/2*(1+floor(log_5(n)))*floor(log_5(n))).
%F Equals lim inf_{n->oo} A132029(n)/n^(1+floor(log_5(n)))*5^A000217(floor(log_5(n))).
%F Equals (1/2)*exp(-Sum_{n>0} 5^(-n)*Sum_{k|n} 1/(k*2^k)).
%F Equals lim inf_{n->oo} A132029(n)/A132029(n+1).
%F Equals Product_{n>=0} (1 - 1/A020729(n)). - _Amiram Eldar_, May 08 2023
%e 0.438796837203638531...
%t digits = 103; NProduct[1-1/(2*5^k), {k, 0, Infinity}, NProductFactors -> 100, WorkingPrecision -> digits+5] // N[#, digits+5]& // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Feb 18 2014 *)
%t RealDigits[QPochhammer[1/2, 1/5], 10, 120][[1]] (* _Amiram Eldar_, May 08 2023 *)
%Y Cf. A048651, A098844, A067080, A132019, A132026, A132029, A100222, A000217, A020729.
%K nonn,cons
%O 0,1
%A _Hieronymus Fischer_, Aug 14 2007
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