A391714 Numerators of the convergents given by treating A072193 as continued fraction coefficients after the leading 0.

1, 3, 4, 11, 48, 107, 155, 572, 3015, 6602, 16219, 22821, 39040, 100901, 139941, 660665, 4103931, 12972458, 30048847, 43021305, 116091457, 159112762, 911655267, 6540699631, 20533754160, 47608207951, 115750170062, 394858718137, 510608888199, 905467606336

Offset

1,2

Comments

a(n)^(1/n) approaches the Lévy's constant (A086702) as n tends to infinity since A072193 samples the Gauss-Kuzmin distribution by construction.

Links

Jwalin Bhatt, Table of n, a(n) for n = 1..2192

Wikipedia, Lévy's constant

Prog

(Python)
from sympy import Rational, continued_fraction_iterator, continued_fraction_convergents
coeffs = [cf for i in range(2, 12) for j in range(1, i) for cf in continued_fraction_iterator(Rational(i, j))]
convergent_generator = continued_fraction_convergents([0] + coeffs)
next(convergent_generator)
A391714 = [frac.numerator for frac in convergent_generator]

Crossrefs

Cf. A072193, A086702, A391715 (denominators).

Sequence in context: A351510 A101982 A041947 * A327081 A201970 A102013

Adjacent sequences: A391711 A391712 A391713 * A391715 A391716 A391717

Keyword

nonn,frac

Author

Jwalin Bhatt, Dec 18 2025

Status

approved