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A132024
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Decimal expansion of Product_{k>=0} (1-1/(2*8^k)).
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4
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4, 6, 4, 5, 6, 8, 8, 8, 3, 6, 8, 6, 4, 7, 6, 3, 9, 0, 9, 8, 1, 9, 5, 9, 5, 6, 9, 7, 4, 8, 4, 7, 8, 0, 1, 0, 8, 7, 0, 0, 5, 8, 5, 1, 5, 4, 9, 5, 1, 2, 3, 0, 6, 5, 5, 6, 6, 0, 8, 5, 6, 0, 5, 9, 7, 0, 6, 0, 9, 9, 5, 7, 6, 2, 7, 4, 4, 1, 5, 4, 3, 8, 4, 8, 7, 8, 8, 8, 1, 2, 5, 0, 7, 6, 2, 1, 9, 4, 7, 0, 8, 1, 7
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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_8(n))} floor(n/8^k)*8^k/n.
Equals lim inf_{n->oo} A132032(n)/n^(1+floor(log_8(n)))*8^(1/2*(1+floor(log_8(n)))*floor(log_8(n))).
Equals lim inf_{n->oo} A132032(n)/n^(1+floor(log_8(n)))*8^A000217(floor(log_8(n))).
Equals (1/2)*exp(-Sum_{n>0} 8^(-n)*Sum_{k|n} 1/(k*2^k)).
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EXAMPLE
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0.46456888368647639098...
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MATHEMATICA
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RealDigits[QPochhammer[1/2, 1/8], 10, 120][[1]] (* Harvey P. Dale, May 23 2011 *)
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PROG
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(PARI) prodinf(k=0, 1 - 1/(2*8^k)) \\ Amiram Eldar, May 09 2023
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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