A392067 - OEIS

%I #31 Feb 06 2026 09:07:05

%S 2,3,9,2,4,8,5,9,8,3,3,9,0,8,3,2,9,8,5,6,7,9,0,9,4,8,7,6,1,8,8,3,6,8,

%T 4,5,5,1,5,7,8,0,1,4,9,1,4,8,4,1,1,6,0,4,7,0,5,2,0,9,4,1,3,9,2,6,1,5,

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

%N Decimal expansion of the limit mean of the number of continued fraction coefficients required per decimal digit for the golden ratio.

%C This limiting mean is the worst case possible.

%C The limiting mean of the continued fraction with some number k being infinitely repeated is given by 1/(2*log_10((k+sqrt(k^2+4))/2)).

%C The limiting mean of the continued fraction for almost all other real numbers is given by the Lochs's constant A086819.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lochs%27s_theorem">Lochs's theorem</a>.

%F Equals 1/(2*log_10(phi)) = 1/log_10(1+phi).

%e 2.39248598339083298567909487618836845515...

%t N[1 / Log10[1 + GoldenRatio], 120]

%Y Cf. A001622, A086819.

%K nonn,cons

%O 1,1

%A _Jwalin Bhatt_, Jan 27 2026