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%I #18 May 09 2023 08:56:36
%S 4,7,2,3,6,2,4,4,3,8,1,6,5,7,2,2,3,6,5,5,1,4,1,3,3,8,3,3,3,2,3,2,7,3,
%T 5,3,3,4,9,6,6,4,2,9,5,8,5,0,2,2,1,9,4,6,2,1,8,8,9,0,9,6,1,1,7,7,8,7,
%U 1,9,9,4,4,2,6,0,1,3,0,7,7,9,5,4,2,9,4,3,2,5,3,0,7,2,3,0,7,8,1,1,8,1,2
%N Decimal expansion of Product_{k>=0} (1 - 1/(2*10^k)).
%F Equals lim inf_{n->oo} Product_{k=0..floor(log_10(n))} floor(n/10^k)*10^k/n.
%F Equals lim inf_{n->oo} A067080(n)/n^(1+floor(log_10(n)))*10^(1/2*(1+floor(log_10(n)))*floor(log_10(n))).
%F Equals lim inf_{n->oo} A067080(n)/n^(1+floor(log_10(n)))*10^A000217(floor(log_10(n))).
%F Equals lim inf_{n->oo} A067080(n)/A067080(n+1).
%F Equals 1/2*exp(-Sum_{n>0} 10^(-n)*Sum_{k|n} 1/(k*2^k)).
%F Equals Product_{n>=1} (1 - 1/A093136(n)). - _Amiram Eldar_, May 09 2023
%e 0.472362443816572236551413383332...
%t digits = 103; Product[1-1/(2*10^k), {k, 0, Infinity}] // N[#, digits+1]& // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Feb 18 2014 *)
%t RealDigits[QPochhammer[1/2, 1/10], 10, 100][[1]] (* _Jan Mangaldan_, Jan 04 2017 *)
%o (PARI) prodinf(k=0, 1 - 1/(2*10^k)) \\ _Amiram Eldar_, May 09 2023
%Y Cf. A000217, A067080, A093136, A098844, A132019.
%K nonn,cons
%O 0,1
%A _Hieronymus Fischer_, Jul 28 2007
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