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.

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

Table of n, a(n) for n=0..86.

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.

Wikipedia, Flajolet-Martin algorithm

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

Cf. A010060, A086744.

Sequence in context: A211074 A204067 A291364 * A197846 A153102 A155959

Adjacent sequences: A244253 A244254 A244255 * A244257 A244258 A244259

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 24 2014

Extensions

A few more digits from Jon E. Schoenfield, Oct 13 2014

Status

approved