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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
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 (list; constant; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Oct 08 2014

EXTENSIONS

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

STATUS

approved

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Last modified October 17 12:21 EDT 2019. Contains 328111 sequences. (Running on oeis4.)