A390651 Numerators of the convergents given by treating A084580 as continued fraction coefficients after the leading 0.

0, 1, 1, 3, 4, 7, 25, 57, 82, 139, 221, 1023, 2267, 3290, 12137, 15427, 42991, 58418, 335081, 393499, 728580, 1850659, 2579239, 9588376, 60109495, 69697871, 338900979, 747499829, 1086400808, 1833900637, 2920301445, 7674503527, 25943812026, 33618315553

Offset

0,4

Comments

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

Links

Jwalin Bhatt, Table of n, a(n) for n = 0..2000

Wikipedia, Lévy's constant

Prog

(Python) # Using sample_gauss_kuzmin_distribution function from A084580.
from sympy import continued_fraction_convergents
coeffs = [0] + sample_gauss_kuzmin_distribution(100)
convergent_generator = continued_fraction_convergents(coeffs)
A390651 = [frac.numerator for frac in convergent_generator]

Crossrefs

Cf. A084580, A086702, A372869, A390652.

Sequence in context: A288049 A145593 A042037 * A041091 A270373 A117764

Adjacent sequences: A390648 A390649 A390650 * A390652 A390653 A390654

Keyword

nonn,frac

Author

Jwalin Bhatt, Nov 14 2025

Status

approved