A391906 - OEIS

%I #9 Jun 22 2026 22:33:33

%S 1,2,5,12,17,29,75,254,583,1420,4843,6263,17369,41001,222374,485749,

%T 1679621,2165370,6010361,14186092,76940821,91126913,168067734,

%U 259194647,945651675,5933104697,12811861069,57180548973,184353507988,425887564949,610241072937

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

%C Conjecture: Limit_{n->oo} a(n)^(1/n) = Lévy's constant (A086702). - Corrected by _Jwalin Bhatt_, Jun 18 2026

%H Jwalin Bhatt, <a href="/A391906/b391906.txt">Table of n, a(n) for n = 1..1999</a>

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

%o (Python)

%o from sympy import prime, Rational, continued_fraction_iterator, continued_fraction_convergents

%o 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)))]

%o convergent_generator = continued_fraction_convergents([0] + coeffs)

%o next(convergent_generator)

%o A391906 = [frac.numerator for frac in convergent_generator]

%Y Cf. A086702, A390946, A391907 (denominators).

%K nonn,frac

%O 1,2

%A _Jwalin Bhatt_, Dec 23 2025