A391714 - OEIS

%I #12 Jun 28 2026 21:16:39

%S 1,3,4,11,48,107,155,572,3015,6602,16219,22821,39040,100901,139941,

%T 660665,4103931,12972458,30048847,43021305,116091457,159112762,

%U 911655267,6540699631,20533754160,47608207951,115750170062,394858718137,510608888199,905467606336

%N Numerators of the convergents given by treating A072193 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 23 2026

%H Jwalin Bhatt, <a href="/A391714/b391714.txt">Table of n, a(n) for n = 1..2192</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 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(i, j))]

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

%o next(convergent_generator)

%o A391714 = [frac.numerator for frac in convergent_generator]

%Y Cf. A072193, A086702, A391715 (denominators).

%K nonn,frac

%O 1,2

%A _Jwalin Bhatt_, Dec 18 2025