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 A248342 Decimal expansion of product_{n>=1} (n/(n+1))^((-1)^t(n)), a probabilistic counting constant, where t(n) = A010060(n) is the Thue-Morse sequence. 2
 2, 3, 0, 2, 5, 6, 6, 1, 3, 7, 1, 6, 3, 6, 3, 0, 5, 0, 4, 2, 9, 3, 5, 8, 1, 2, 5, 1, 2, 4, 1, 8, 1, 5, 5, 9, 3, 6, 4, 0, 1, 2, 3, 5, 9, 6, 5, 0, 5, 9, 1, 1, 0, 1, 1, 4, 6, 1, 6, 7, 0, 9, 0, 4, 1, 3, 9, 7, 6, 6, 3, 3, 9, 9, 5, 0, 2, 6, 2, 4, 3, 2, 9, 0, 9, 9, 2 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 2.302566137163630504293581251241815593640123596505911... MATHEMATICA digits = 80; t[n_] := Mod[DigitCount[n, 2, 1], 2]; p[k_] := p[k] = Product[(n/(n+1))^((-1)^t[n]), {n, 2^k, 2^(k+1)-1}] // N[#, digits + 20]&; pp = Table[Print["k = ", k]; p[k], {k, 0, 24}]; RealDigits[ Times @@ pp , 10, digits] // First CROSSREFS Cf. A010060, A086744, A244256. Sequence in context: A219864 A257844 A194745 * A002392 A002708 A167925 Adjacent sequences:  A248339 A248340 A248341 * A248343 A248344 A248345 KEYWORD nonn,cons AUTHOR Jean-François Alcover, Oct 08 2014 EXTENSIONS A few more digits from Jon E. Schoenfield, Oct 13 2014 STATUS approved

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Last modified October 17 12:21 EDT 2019. Contains 328111 sequences. (Running on oeis4.)