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

0,1

Comments

Probability of a coefficient in the continued fraction being odd, 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 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

Adjacent sequences: A340540 A340541 A340542 * A340544 A340545 A340546

Keyword

nonn,cons

Author

A.H.M. Smeets, Jan 11 2021

Status

approved