A340543 - OEIS

%I #14 May 29 2023 01:47:30

%S 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,

%T 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,

%U 2,9,6,3,5,8,4,5,4,1,4,3,8,9,6,0,2,6,4

%N Decimal expansion of log(Pi/2)/log(2).

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

%H V. N. Nolte, <a href="https://doi.org/10.1016/0019-3577(90)90025-I">Some probabilistic results on the convergents of continued fractions</a>, Indagationes Mathematicae, Vol. 1, No. 3 (1990), pp. 381-389.

%F Equals A216582 - 1.

%F Equals log_2(A019669).

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

%F Equals 1-A340533.

%e 0.65149612947231879804327929510800733501847692676304...

%t RealDigits[Log2[Pi/2], 10, 120][[1]] (* _Amiram Eldar_, May 29 2023 *)

%o (PARI) log(Pi/2)/log(2)

%Y Cf. A019669. Essentially the same as A216582.

%Y Cf. A340533.

%K nonn,cons

%O 0,1

%A _A.H.M. Smeets_, Jan 11 2021