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

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

Cf. A001113 (e), A001622 (phi), A094868 (reciprocal).

Cf. A000032 (Lucas), A000045 (Fibonacci).

Sequence in context: A135169 A335840 A021172 * A351216 A256593 A275810

Adjacent sequences: A094877 A094878 A094879 * A094881 A094882 A094883

Keyword

cons,nonn

Author

N. J. A. Sloane, Jun 15 2004

Status

approved