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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
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
KEYWORD
nonn,cons
AUTHOR
EXTENSIONS
A few more digits from Jon E. Schoenfield, Oct 13 2014
STATUS
approved