A019762 Decimal expansion of 2*e.

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

Offset

1,1

Comments

Simple continued fraction is A081750. - Michael Somos, May 07 2012

2*e - 3 = 2.436563... is the expected number of real numbers that are independently and uniformly selected at random from the interval (0, 1) until they are no longer monotonically increasing or monotonically decreasing (Shultz and Leonard, 1989). - Amiram Eldar, Jun 09 2026

Links

Ivan Panchenko, Table of n, a(n) for n = 1..1000

Harris S. Shultz and Bill Leonard, Unexpected Occurrences of the Number e, Mathematics Magazine, Vol. 62, No. 4 (1989), pp. 269-271.

Index entries for transcendental numbers.

Formula

Equals Sum_{n>=1} n^2/n!. - Arkadiusz Wesolowski, Mar 11 2013

From Richard R. Forberg, Dec 23 2014: (Start)

Equals lim_{x->1} (x*e^x - e)/(x-1).

Equals Sum_{n>=0} Sum_{k=0..n} 1/n!. (End)

Equals 1 + (2/1) + (3/2/1) + (4/3/2/1) + (5/4/3/2/1) + (6/5/4/3/2/1) + ... . - Davide Rotondo, Apr 07 2024

Example

5.43656365691809047072057494270532499551449418739991914993...

Mathematica

RealDigits[N[2*E, 105]][[1]] (* Arkadiusz Wesolowski, Mar 11 2013 *)

Prog

(PARI) 2*exp(1) \\ Charles R Greathouse IV, Oct 02 2022

Crossrefs

Cf. A001113, A081750 (continued fraction), A081749 (continued fraction of e/5 = 0.543...).

Sequence in context: A164360 A183164 A364490 * A328015 A256099 A192918

Adjacent sequences: A019759 A019760 A019761 * A019763 A019764 A019765

Keyword

nonn,cons

Author

N. J. A. Sloane

Status

approved