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A340543
Decimal expansion of log(Pi/2)/log(2).
2
6, 5, 1, 4, 9, 6, 1, 2, 9, 4, 7, 2, 3, 1, 8, 7, 9, 8, 0, 4, 3, 2, 7, 9, 2, 9, 5, 1, 0, 8, 0, 0, 7, 3, 3, 5, 0, 1, 8, 4, 7, 6, 9, 2, 6, 7, 6, 3, 0, 4, 1, 5, 2, 9, 4, 0, 6, 7, 8, 8, 5, 1, 5, 4, 8, 8, 1, 0, 2, 9, 6, 3, 5, 8, 4, 5, 4, 1, 4, 3, 8, 9, 6, 0, 2, 6, 4
OFFSET
0,1
COMMENTS
Probability of a coefficient in the continued fraction being odd, where the continued fraction coefficients satisfy the Gauss-Kuzmin distribution.
LINKS
V. N. Nolte, Some probabilistic results on the convergents of continued fractions, Indagationes Mathematicae, Vol. 1, No. 3 (1990), pp. 381-389.
FORMULA
Equals A216582 - 1.
Equals log_2(A019669).
Equals Sum_{k >= 0} -log_2(1-1/(2*k+2)^2).
Equals 1-A340533.
EXAMPLE
0.65149612947231879804327929510800733501847692676304...
MATHEMATICA
RealDigits[Log2[Pi/2], 10, 120][[1]] (* Amiram Eldar, May 29 2023 *)
PROG
(PARI) log(Pi/2)/log(2)
CROSSREFS
Cf. A019669. Essentially the same as A216582.
Cf. A340533.
Sequence in context: A195774 A320833 A216582 * A177824 A242000 A238181
KEYWORD
nonn,cons
AUTHOR
A.H.M. Smeets, Jan 11 2021
STATUS
approved