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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 (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 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 Cf. A010060, A086744, A244256, A248342. Sequence in context: A010151 A021556 A172428 * A178163 A197110 A109571 Adjacent sequences:  A248578 A248579 A248580 * A248582 A248583 A248584 KEYWORD nonn,cons AUTHOR Jean-François Alcover, Oct 09 2014 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

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Last modified June 22 20:39 EDT 2021. Contains 345389 sequences. (Running on oeis4.)