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A340533
Decimal expansion of log_2(4/Pi).
2
3, 4, 8, 5, 0, 3, 8, 7, 0, 5, 2, 7, 6, 8, 1, 2, 0, 1, 9, 5, 6, 7, 2, 0, 7, 0, 4, 8, 9, 1, 9, 9, 2, 6, 6, 4, 9, 8, 1, 5, 2, 3, 0, 7, 3, 2, 3, 6, 9, 5, 8, 4, 7, 0, 5, 9, 3, 2, 1, 1, 4, 8, 4, 5, 1, 1, 8, 9, 7, 0, 3, 6, 4, 1, 5, 4, 5, 8, 5, 6, 1, 0, 3, 9, 7, 3, 5
OFFSET
0,1
COMMENTS
Probability of a coefficient in the continued fraction being even, 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 2 - A216582.
Equals log_2(A088538).
Equals -Sum_{k >= 1} log_2(1-1/(2*k+1)^2).
Equals 1-A340543.
EXAMPLE
0.348503870527681201956720704891992664981523...
MATHEMATICA
RealDigits[Log[4/Pi]/Log[2], 10, 100][[1]] (* Amiram Eldar, Jan 10 2021 *)
PROG
(PARI) log(4/Pi)/log(2)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
A.H.M. Smeets, Jan 10 2021
STATUS
approved