OFFSET
0,1
LINKS
Ivan Panchenko, Table of n, a(n) for n = 0..1000
Corey Martinsen and Pantelimon Stănică, Asymptotic Behavior of Gaps Between Roots of Weighted Factorials, Fibonacci Quart. 53 (2015), no. 3, 213-218. See Corollary 2.4 p. 216.
FORMULA
From Michel Marcus, Jan 11 2022: (Start)
Equals lim_{n->oo} ((n+1)!*F(n+1))^(1/(n+1)) - (n!*F(n))^(1/n).
Equals lim_{n->oo} ((n+1)!*L(n+1))^(1/(n+1)) - (n!*L(n))^(1/n). (End)
EXAMPLE
0.59524143957771110901803082077425172857166421077832...
MATHEMATICA
RealDigits[GoldenRatio/E, 10, 105][[1]] (* Amiram Eldar, May 02 2023 *)
PROG
(PARI) ((1+sqrt(5))/2)/exp(1) \\ Michel Marcus, Jan 11 2022
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
N. J. A. Sloane, Jun 15 2004
STATUS
approved