A391715 Denominators of the convergents given by treating A072193 as continued fraction coefficients after the leading 0.

2, 7, 9, 25, 109, 243, 352, 1299, 6847, 14993, 36833, 51826, 88659, 229144, 317803, 1500356, 9319939, 29460173, 68240285, 97700458, 263641201, 361341659, 2070349496, 14853788131, 46631713889, 108117215909, 262866145707, 896715653030, 1159581798737, 2056297451767

Offset

1,1

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)
A391715 = [frac.denominator for frac in convergent_generator]

Crossrefs

Cf. A072193, A086702, A391714 (numerators).

Sequence in context: A042929 A082962 A041197 * A080157 A203801 A081999

Adjacent sequences: A391712 A391713 A391714 * A391716 A391717 A391718

Keyword

nonn,frac

Author

Jwalin Bhatt, Dec 18 2025

Status

approved