login
Numerators of the convergents given by treating A084580 as continued fraction coefficients after the leading 0.
4

%I #18 Jun 18 2026 00:29:44

%S 0,1,1,3,4,7,25,57,82,139,221,1023,2267,3290,12137,15427,42991,58418,

%T 335081,393499,728580,1850659,2579239,9588376,60109495,69697871,

%U 338900979,747499829,1086400808,1833900637,2920301445,7674503527,25943812026,33618315553

%N Numerators of the convergents given by treating A084580 as continued fraction coefficients after the leading 0.

%C Limit_{n->oo} a(n)^(1/n) seems to approach a value between Pi and Lévy's constant (A086702). - Corrected by _Jwalin Bhatt_, Jun 13 2026

%H Jwalin Bhatt, <a href="/A390651/b390651.txt">Table of n, a(n) for n = 0..2000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/L%C3%A9vy%27s_constant">Lévy's constant</a>

%o (Python) # Using sample_gauss_kuzmin_distribution function from A084580.

%o from sympy import continued_fraction_convergents

%o coeffs = [0] + sample_gauss_kuzmin_distribution(100)

%o convergent_generator = continued_fraction_convergents(coeffs)

%o A390651 = [frac.numerator for frac in convergent_generator]

%Y Cf. A084580, A086702, A372869, A390652.

%K nonn,frac

%O 0,4

%A _Jwalin Bhatt_, Nov 14 2025