A092426 Decimal expansion of e^4.

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

Offset: 2

Author

Mohammad K. Azarian, Mar 22 2004

Keywords

• easy
• nonn
• cons

Examples

			54.598150033144239078110261202860878402790737038614....
		

Links

• Harry J. Smith, Table of n, a(n) for n = 2..20000
• Index entries for transcendental numbers

Crossrefs

Cf. A001113, A072334, A091933, A092511, A092512, A092513.

Cf. A058283 (continued fraction).

Programs

Maple

Digits:=100: evalf(exp(4)); # Wesley Ivan Hurt, Sep 01 2014

Mathematica

RealDigits[E^4, 10, 100][[1]] (* Alonso del Arte, Aug 31 2014 *)

PARI

default(realprecision, 20080); x=exp(1)^4/10; for (n=2, 20000, d=floor(x); x=(x-d)*10; write("b092426.txt", n, " ", d)); \\ Harry J. Smith, Jun 22 2009

Formula

From Peter Bala, Jan 12 2022: (Start)

e^4 = 45 + 2*Sum_{n >= 0} 4^(n+4)/((n+4)^2*(n+5)^2*n!).

45/e^4 = 1 - 3*Sum_{n >= 0} (-4)^(n+3)*n^2/(n+4)!. (End)

Largest solution to sqrt(log(x)) = log(sqrt(x)), the other solution being x = 1. - Andrea Pinos, Jan 23 2024