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, 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

Table of n, a(n) for n=1..87.

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

Cf. A010060, A086744, A244256.

Sequence in context: A219864 A257844 A194745 * A002392 A002708 A167925

Adjacent sequences: A248339 A248340 A248341 * A248343 A248344 A248345

Keyword

nonn,cons

Author

Jean-François Alcover, Oct 08 2014

Extensions

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

Status

approved