A248581 Decimal expansion of product_{n>=1} (n/(n+1))^((-1)^t(n-1)), a probabilistic counting constant, where t(n) = A010060(n) is the Thue-Morse sequence.

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

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.

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

0.811686921544779310088769454776914440811934935...

Mathematica

digits = 60; t[n_] := Mod[DigitCount[n, 2, 1], 2]; Clear[p]; p[1] = 3/4; p[k_] := p[k] = Product[(n/(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.

Sequence in context: A010151 A021556 A172428 * A178163 A197110 A109571

Adjacent sequences: A248578 A248579 A248580 * A248582 A248583 A248584

Keyword

nonn,cons

Author

Jean-François Alcover, Oct 09 2014

Extensions

Error beginning at the 14th digit detected by Jon E. Schoenfield and corrected by Jean-François Alcover, Oct 17 2014

A few more digits from Jon E. Schoenfield, Oct 17 2014

Status

approved