A340543 Decimal expansion of log(Pi/2)/log(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

Author

A.H.M. Smeets, Jan 11 2021

Keywords

• nonn
• cons

Comments

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

Examples

			0.65149612947231879804327929510800733501847692676304...
		

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. A019669. Essentially the same as A216582.

Cf. A340533.

Programs

Mathematica

RealDigits[Log2[Pi/2], 10, 120][[1]] (* Amiram Eldar, May 29 2023 *)

PARI

log(Pi/2)/log(2)

Formula

Equals A216582 - 1.

Equals log_2(A019669).

Equals Sum_{k >= 0} -log_2(1-1/(2*k+2)^2).

Equals 1-A340533.