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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
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
KEYWORD
nonn,cons
AUTHOR
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