A392729 - OEIS

%I #12 Jul 14 2026 22:49:06

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

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

%U 7,2,1,9,0,7,5,9,7,4,9,8,5,9,0,8,9,8,1

%N Decimal expansion of the number whose continued fraction coefficients are given in A391217.

%C This constant does not appear to be normal in the continued fraction sense although its continued fraction coefficients follow the Gauss-Kuzmin distribution by construction. This is because normality requires all blocks of partial quotients (not just the individual terms) to follow the Gauss measure. - Corrected by _Jwalin Bhatt_, Jul 08 2026

%H Jwalin Bhatt, <a href="/A392729/b392729.txt">Table of n, a(n) for n = 0..10000</a>

%F Equals lim_{n->oo} A392258(n) / A392259(n).

%e 0.736303159771936859899914347521211324683806567245696217281218736449407...

%o (Python) # Using sample_gauss_kuzmin_distribution function from A391217.

%o from sympy import floor, continued_fraction_convergents

%o from collections import deque

%o from os.path import commonprefix

%o def reliable_digits_from_cf(coeffs, prec):

%o     frac_lower, frac_upper = deque(tqdm(continued_fraction_convergents(coeffs+[1])), maxlen=2)

%o     trunc_lower, trunc_upper = floor(frac_lower * 10**prec), floor(frac_upper * 10**prec)

%o     return commonprefix([str(trunc_lower), str(trunc_upper)])

%o coeffs = [0] + sample_gauss_kuzmin_distribution(250)

%o num = reliable_digits_from_cf(coeffs, prec=200)

%o A392729 = [int(d) for d in num]

%Y Cf. A391217 (continued fraction), A392258, A392259.

%K nonn,cons,changed

%O 0,1

%A _Jwalin Bhatt_, Jan 21 2026