A340533 - OEIS

%I #22 Feb 13 2021 15:03:07

%S 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,

%T 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,

%U 7,0,3,6,4,1,5,4,5,8,5,6,1,0,3,9,7,3,5

%N Decimal expansion of log_2(4/Pi).

%C Probability of a coefficient in the continued fraction being even, 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 2 - A216582.

%F Equals log_2(A088538).

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

%F Equals 1-A340543.

%e 0.348503870527681201956720704891992664981523...

%t RealDigits[Log[4/Pi]/Log[2], 10, 100][[1]] (* _Amiram Eldar_, Jan 10 2021 *)

%o (PARI) log(4/Pi)/log(2)

%Y Cf. A088538, A216582, A340543.

%K nonn,cons

%O 0,1

%A _A.H.M. Smeets_, Jan 10 2021