A340533 Decimal expansion of log_2(4/Pi).

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

Author

A.H.M. Smeets, Jan 10 2021

Keywords

• nonn
• cons

Comments

Probability of a coefficient in the continued fraction being even, where the continued fraction coefficients satisfy the Gauss-Kuzmin distribution.

Examples

			0.348503870527681201956720704891992664981523...
		

Links

• V. N. Nolte, Some probabilistic results on the convergents of continued fractions, Indagationes Mathematicae, Vol. 1, No. 3 (1990), pp. 381-389.

Crossrefs

Cf. A088538, A216582, A340543.

Programs

Mathematica

RealDigits[Log[4/Pi]/Log[2], 10, 100][[1]] (* Amiram Eldar, Jan 10 2021 *)

PARI

log(4/Pi)/log(2)

Formula

Equals 2 - A216582.

Equals log_2(A088538).

Equals -Sum_{k >= 1} log_2(1-1/(2*k+1)^2).

Equals 1-A340543.