A391906 Numerators of the convergents given by treating A390946 as continued fraction coefficients after the leading 0.

1, 2, 5, 12, 17, 29, 75, 254, 583, 1420, 4843, 6263, 17369, 41001, 222374, 485749, 1679621, 2165370, 6010361, 14186092, 76940821, 91126913, 168067734, 259194647, 945651675, 5933104697, 12811861069, 57180548973, 184353507988, 425887564949, 610241072937

Offset

1,2

Comments

a(n)^(1/n) approaches the Lévy's constant (A086702) as n tends to infinity since A390946 samples the Gauss-Kuzmin distribution by construction.

Links

Jwalin Bhatt, Table of n, a(n) for n = 1..1999

Wikipedia, Lévy's constant

Prog

(Python)
from sympy import prime, 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(prime(i), prime(j)))]
convergent_generator = continued_fraction_convergents([0] + coeffs)
next(convergent_generator)
A391906 = [frac.numerator for frac in convergent_generator]

Crossrefs

Cf. A086702, A390946, A391907 (numerators).

Sequence in context: A084122 A381834 A042143 * A042467 A024465 A041889

Adjacent sequences: A391903 A391904 A391905 * A391907 A391908 A391909

Keyword

nonn,frac

Author

Jwalin Bhatt, Dec 23 2025

Status

approved