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A132020
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Decimal expansion of Product{k>0, 1-1/(2*4^k)}.
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4
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4, 1, 9, 4, 2, 2, 4, 4, 1, 7, 9, 5, 1, 0, 7, 5, 9, 7, 7, 0, 9, 9, 5, 6, 1, 0, 7, 7, 0, 2, 9, 7, 4, 2, 5, 2, 2, 3, 3, 9, 5, 3, 2, 3, 4, 3, 9, 2, 6, 6, 6, 7, 4, 9, 0, 8, 0, 4, 4, 9, 9, 1, 6, 6, 3, 1, 7, 7, 2, 0, 5, 0, 8, 7, 2, 7, 0, 9, 1, 9, 3, 9, 1, 0, 0, 2, 3, 2, 4, 5, 4, 7, 4, 2, 3, 8, 1, 9, 5, 5, 0, 2, 8, 5, 8
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Also the Product_k>0, 1-1/(2^k+1). - Robert G. Wilson v, May 25 2011.
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FORMULA
| lim inf product{0<=k<=floor(log_4(n)), floor(n/4^k)*4^k/n} for n-->oo.
lim inf A132028(n)/n^(1+floor(log_4(n)))*4^(1/2*(1+floor(log_4(n)))*floor(log_4(n))) for n-->oo.
lim inf A132028(n)/n^(1+floor(log_4(n)))*4^A000217(floor(log_4(n))) for n-->oo.
(1/2)*exp(-sum{n>0, 4^(-n)*sum{k|n, 1/(k*2^k))}}).
lim inf A132028(n)/A132028(n+1)=0.4194224417951075977... for n-->oo.
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EXAMPLE
| 0.41942244179510759770995610770297425223395323439266674908044991663177205087270919... - Robert G. Wilson v, May 25 2011.
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MATHEMATICA
| RealDigits[ Product[1 - 1/(2*4^i), {i, 0, 175}], 10, 111][[1]] (* Robert G. Wilson v, May 25 2011 *)
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CROSSREFS
| Cf. A048651, A098844, A067080, A132019, A132026, A132028, A100221, A000217.
Sequence in context: A085691 A055461 A104796 * A175643 A143864 A073364
Adjacent sequences: A132017 A132018 A132019 * A132021 A132022 A132023
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KEYWORD
| nonn,cons
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AUTHOR
| Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Aug 14 2007
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