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%I #14 May 08 2023 02:26:46
%S 3,8,2,6,6,3,1,9,6,6,7,9,0,3,3,0,2,3,2,8,8,9,5,5,0,3,3,5,3,3,1,9,1,3,
%T 2,2,7,9,5,3,7,7,1,9,7,3,1,2,7,6,7,1,1,8,0,5,5,1,4,9,5,3,5,4,6,7,8,6,
%U 8,7,5,2,4,4,0,8,2,7,5,9,9,2,7,0,3,5,3,6,4,7,1,8,8,7,4,2,5,1,6,5,6,4,6
%N Decimal expansion of Product_{k>=0} 1-1/(2*3^k).
%F Equals lim inf_{n->oo} Product_{k=0..floor(log_3(n))} floor(n/3^k)*3^k/n.
%F Equals lim inf_{n->oo} A132027(n)/n^(1+floor(log_3(n)))*3^(1/2*(1+floor(log_3(n)))*floor(log_3(n))).
%F Equals lim inf_{n->oo} A132027(n)/n^(1+floor(log_3(n)))*3^A000217(floor(log_3(n))).
%F Equals (1/2)*exp(-Sum_{n>0} 3^(-n)*Sum_{k|n} 1/(k*2^k)).
%F Equals lim inf_{n->oo} A132027(n)/A132027(n+1).
%F Equals Product_{n>=1} (1 - 1/A025192(n)). - _Amiram Eldar_, May 08 2023
%e 0.3826631966790330232889550...
%t digits = 103; NProduct[1-1/(2*3^k), {k, 0, Infinity}, NProductFactors -> 100, WorkingPrecision -> digits+3] // N[#, digits+3]& // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Feb 18 2014 *)
%t RealDigits[QPochhammer[1/2, 1/3], 10, 120][[1]] (* _Amiram Eldar_, May 08 2023 *)
%Y Cf. A098844, A067080, A132026, A132027, A000217, A025192.
%K nonn,cons
%O 0,1
%A _Hieronymus Fischer_, Aug 13 2007
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