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A248581
Decimal expansion of product_{n>=1} (n/(n+1))^((-1)^t(n-1)), a probabilistic counting constant, where t(n) = A010060(n) is the Thue-Morse sequence.
1
8, 1, 1, 6, 8, 6, 9, 2, 1, 5, 4, 4, 7, 7, 9, 3, 1, 0, 0, 8, 8, 7, 6, 9, 4, 5, 4, 7, 7, 6, 9, 1, 4, 4, 4, 0, 8, 1, 1, 9, 3, 4, 9, 3, 5, 0, 0, 9, 9, 8, 5, 6, 5, 4, 3, 1, 2, 9, 8, 3, 0, 3, 7, 4, 3, 7, 0, 3, 1, 6, 2, 2, 9, 4, 3, 9, 6, 1, 1, 9, 2, 1, 9, 4, 3, 8, 9
OFFSET
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 6.8 Prouhet-Thue-Morse constant, p. 438.
LINKS
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
0.811686921544779310088769454776914440811934935...
MATHEMATICA
digits = 60; t[n_] := Mod[DigitCount[n, 2, 1], 2]; Clear[p]; p[1] = 3/4; p[k_] := p[k] = Product[(n/(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 14th digit detected by Jon E. Schoenfield and corrected by Jean-François Alcover, Oct 17 2014
A few more digits from Jon E. Schoenfield, Oct 17 2014
STATUS
approved