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A244256
Decimal expansion of exp(gamma)/sqrt(2)*Product_{n>=1} ((2n+1)/(2n))^((-1)^t(n)), a probabilistic counting constant, where gamma is Euler's constant and t(n) = A010060(n) the Thue-Morse sequence.
3
7, 7, 3, 5, 1, 6, 2, 9, 0, 9, 0, 8, 4, 4, 5, 3, 0, 4, 0, 7, 3, 3, 0, 2, 5, 8, 5, 7, 0, 7, 4, 0, 1, 2, 0, 0, 3, 5, 6, 7, 4, 4, 4, 7, 6, 2, 3, 5, 0, 2, 0, 7, 6, 1, 2, 7, 0, 2, 8, 6, 4, 2, 8, 7, 5, 8, 7, 4, 0, 1, 5, 8, 1, 7, 9, 8, 7, 9, 0, 1, 0, 0, 5, 5, 6, 8, 7
OFFSET
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 6.8 Prouhet-Thue-Morse constant, p. 437.
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 phi 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.
FORMULA
exp(gamma)/(sqrt(2)*A086744).
EXAMPLE
0.7735162909084453040733025857074...
MATHEMATICA
digits = 80; t[n_] := Mod[DigitCount[n, 2, 1], 2]; p[k_] := p[k] = Product[(2*n/(2*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[E^EulerGamma / (Sqrt[2] * Times @@ pp), 10, digits] // First
CROSSREFS
Sequence in context: A211074 A204067 A291364 * A197846 A153102 A155959
KEYWORD
nonn,cons
AUTHOR
EXTENSIONS
A few more digits from Jon E. Schoenfield, Oct 13 2014
STATUS
approved