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A248582
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Decimal expansion of product_{n>=1} (2n/(2n+1))^((-1)^t(n-1)), a probabilistic counting constant, where t(n) = A010060(n) is the Thue-Morse sequence.
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0
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8, 7, 1, 1, 5, 7, 0, 4, 6, 4, 1, 4, 8, 9, 3, 7, 4, 1, 6, 1, 7, 8, 5, 7, 6, 5, 6, 4, 5, 9, 1, 9, 1, 6, 0, 6, 2, 6, 0, 3, 9, 2, 3, 2, 6, 3, 9, 7, 5, 2, 4, 1, 8, 9, 1, 2, 9, 0, 2, 2, 7, 1, 3, 8, 0, 0, 9, 3, 1, 8, 2, 4, 6, 6, 1, 2, 4, 7, 5, 4, 1, 7, 0, 8, 7, 8, 3
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OFFSET
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0,1
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 6.8 Prouhet-Thue-Morse constant, p. 438.
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LINKS
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Table of n, a(n) for n=0..86.
J.-P. Allouche and Jeffrey Shallit, The Ubiquitous Prouhet-Thue-Morse Sequence, in C. Ding. T. Helleseth and H. Niederreiter, eds., Sequences and Their Applications: Proceedings of SETA '98, Springer-Verlag, 1999, pp. 1-16. See the constant Q on page 6.
Philippe Flajolet and G. Nigel Martin, Probabilistic counting algorithms for data base applications, Journal of Computer and System Sciences. Vol. 31, No. 2, October 1985, p. 193.
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EXAMPLE
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0.871157046414893741617857656459191606260392326397524189129...
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MATHEMATICA
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digits = 60; t[n_] := Mod[DigitCount[n, 2, 1], 2]; Clear[p]; p[1] = 5/6; p[k_] := p[k] = Product[(2*n/(2*n+1))^(-1)^t[n-1], {n, 2^(k-1)+1, 2^k}] // N[#, digits + 40]&; pp = Table[Print["k = ", k]; p[k], {k, 1, 23}]; RealDigits[Times @@ pp, 10, digits] // First
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CROSSREFS
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Cf. A010060, A086744, A244256, A248342, A248581.
Sequence in context: A348728 A255702 A154401 * A255699 A343965 A201768
Adjacent sequences: A248579 A248580 A248581 * A248583 A248584 A248585
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KEYWORD
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nonn,cons
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AUTHOR
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Jean-François Alcover, Oct 09 2014
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EXTENSIONS
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Error beginning at the 15th digit detected by Jon E. Schoenfield and corrected by Jean-François Alcover, Oct 22 2014
More terms from Jon E. Schoenfield, Oct 22 2014
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STATUS
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approved
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