A248582 Decimal expansion of product_{n>=1} (2n/(2n+1))^((-1)^t(n-1)), a probabilistic counting constant, where t(n) = A010060(n) is the Thue-Morse sequence.

8, 7, 1, 1, 5, 7, 0, 4, 6, 4, 1, 4, 8, 9, 3, 7, 4, 1, 6, 1, 7, 8, 5, 7, 6, 5, 6, 4, 5, 9, 1, 9, 1, 6, 0, 6, 2, 6, 0, 3, 9, 2, 3, 2, 6, 3, 9, 7, 5, 2, 4, 1, 8, 9, 1, 2, 9, 0, 2, 2, 7, 1, 3, 8, 0, 0, 9, 3, 1, 8, 2, 4, 6, 6, 1, 2, 4, 7, 5, 4, 1, 7, 0, 8, 7, 8, 3

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 6.8 Prouhet-Thue-Morse constant, p. 438.

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 Q 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.

Example

0.871157046414893741617857656459191606260392326397524189129...

Mathematica

digits = 60; t[n_] := Mod[DigitCount[n, 2, 1], 2]; Clear[p]; p[1] = 5/6; p[k_] := p[k] = Product[(2*n/(2*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, A248581.

Sequence in context: A348728 A255702 A154401 * A362120 A362122 A255699

Adjacent sequences: A248579 A248580 A248581 * A248583 A248584 A248585

Keyword

nonn,cons

Author

Jean-François Alcover, Oct 09 2014

Extensions

Error beginning at the 15th digit detected by Jon E. Schoenfield and corrected by Jean-François Alcover, Oct 22 2014

More terms from Jon E. Schoenfield, Oct 22 2014

Status

approved