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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 (list; constant; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..86.

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

Cf. A088538, A216582, A340543.

Sequence in context: A127122 A086850 A245598 * A050274 A262951 A288091

Adjacent sequences:  A340530 A340531 A340532 * A340534 A340535 A340536

KEYWORD

nonn,cons

AUTHOR

A.H.M. Smeets, Jan 10 2021

STATUS

approved

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Last modified July 30 00:57 EDT 2021. Contains 346346 sequences. (Running on oeis4.)