A094880 - OEIS

A094880

Decimal expansion of phi/e, where phi = (1+sqrt(5))/2.

5, 9, 5, 2, 4, 1, 4, 3, 9, 5, 7, 7, 7, 1, 1, 1, 0, 9, 0, 1, 8, 0, 3, 0, 8, 2, 0, 7, 7, 4, 2, 5, 1, 7, 2, 8, 5, 7, 1, 6, 6, 4, 2, 1, 0, 7, 7, 8, 3, 2, 3, 2, 5, 3, 2, 9, 0, 2, 4, 0, 7, 8, 2, 6, 4, 0, 0, 4, 6, 7, 1, 0, 2, 8, 6, 9, 5, 3, 5, 2, 5, 4, 4, 2, 7, 6, 9, 9, 3, 9, 6, 0, 3, 8, 1, 8, 9, 0, 4

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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 A001622/A001113.

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