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A132023 Decimal expansion of Product_{k>=0} 1-1/(2*7^k).

%I A132023 #10 May 08 2023 02:27:16
%S A132023 4,5,8,7,6,6,7,2,6,6,9,9,7,6,8,9,8,5,0,2,0,0,0,5,1,5,3,3,6,9,7,4,3,7,
%T A132023 2,1,7,8,2,5,4,6,6,8,8,7,1,4,7,3,1,8,7,0,0,7,8,2,4,4,0,1,3,8,5,0,6,9,
%U A132023 9,7,4,4,0,3,2,6,5,9,3,0,3,6,5,2,3,7,8,1,7,1,0,9,0,4,0,5,8,4,7,5,9,8,2
%N A132023 Decimal expansion of Product_{k>=0} 1-1/(2*7^k).
%F A132023 Equals lim inf_{n->oo} Product_{k=0..floor(log_7(n))} floor(n/7^k)*7^k/n.
%F A132023 Equals lim inf_{n->oo} A132031(n)/n^(1+floor(log_7(n)))*7^(1/2*(1+floor(log_7(n)))*floor(log_7(n))).
%F A132023 Equals lim inf_{n->oo} A132031(n)/n^(1+floor(log_7(n)))*7^A000217(floor(log_7(n))).
%F A132023 Equals 1/2*exp(-Sum_{n>0} 7^(-n)*Sum_{k|n} 1/(k*2^k)).
%F A132023 Equals lim inf_{n->oo} A132031(n)/A132031(n+1).
%F A132023 Equals Product_{n>=1} (1 - 1/A109808(n)). - _Amiram Eldar_, May 08 2023
%e A132023 0.4587667266997689850200...
%t A132023 digits = 103; NProduct[1-1/(2*7^k), {k, 0, Infinity}, NProductFactors -> 200, WorkingPrecision -> digits+5] // N[#, digits+5]& // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Feb 18 2014 *)
%t A132023 RealDigits[QPochhammer[1/2, 1/7], 10, 120][[1]] (* _Amiram Eldar_, May 08 2023 *)
%Y A132023 Cf. A048651, A098844, A067080, A132019, A132026, A132031, A132035, A000217, A109808.
%K A132023 nonn,cons
%O A132023 0,1
%A A132023 _Hieronymus Fischer_, Aug 14 2007