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Denominators of the convergents given by treating A072193 as continued fraction coefficients after the leading 0.
3

%I #12 Jun 28 2026 21:16:46

%S 2,7,9,25,109,243,352,1299,6847,14993,36833,51826,88659,229144,317803,

%T 1500356,9319939,29460173,68240285,97700458,263641201,361341659,

%U 2070349496,14853788131,46631713889,108117215909,262866145707,896715653030,1159581798737,2056297451767

%N Denominators 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="/A391715/b391715.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 A391715 = [frac.denominator for frac in convergent_generator]

%Y Cf. A072193, A086702, A391714 (numerators).

%K nonn,frac,changed

%O 1,1

%A _Jwalin Bhatt_, Dec 18 2025