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A132019
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Decimal expansion of Product_{k>=0} 1-1/(2*3^k).
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26
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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, 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, 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
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OFFSET
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0,1
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LINKS
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FORMULA
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Equals lim inf_{n->oo} Product_{k=0..floor(log_3(n))} floor(n/3^k)*3^k/n.
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))).
Equals lim inf_{n->oo} A132027(n)/n^(1+floor(log_3(n)))*3^A000217(floor(log_3(n))).
Equals (1/2)*exp(-Sum_{n>0} 3^(-n)*Sum_{k|n} 1/(k*2^k)).
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EXAMPLE
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0.3826631966790330232889550...
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MATHEMATICA
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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 *)
RealDigits[QPochhammer[1/2, 1/3], 10, 120][[1]] (* Amiram Eldar, May 08 2023 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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