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 A248582 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. 0
 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 6.8 Prouhet-Thue-Morse constant, p. 438. LINKS 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. EXAMPLE 0.871157046414893741617857656459191606260392326397524189129... MATHEMATICA 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 CROSSREFS Cf. A010060, A086744, A244256, A248342, A248581. Sequence in context: A348728 A255702 A154401 * A255699 A343965 A201768 Adjacent sequences:  A248579 A248580 A248581 * A248583 A248584 A248585 KEYWORD nonn,cons AUTHOR Jean-François Alcover, Oct 09 2014 EXTENSIONS 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 STATUS approved

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Last modified May 19 18:35 EDT 2022. Contains 353847 sequences. (Running on oeis4.)