%I #32 Feb 15 2024 12:32:32

%S 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,

%T 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,

%U 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

%N Decimal expansion of e^4.

%H Harry J. Smith, <a href="/A092426/b092426.txt">Table of n, a(n) for n = 2..20000</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F From _Peter Bala_, Jan 12 2022: (Start)

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

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

%F Largest solution to sqrt(log(x)) = log(sqrt(x)), the other solution being x = 1. - _Andrea Pinos_, Jan 23 2024

%e 54.598150033144239078110261202860878402790737038614....

%p Digits:=100: evalf(exp(4)); # _Wesley Ivan Hurt_, Sep 01 2014

%t RealDigits[E^4, 10, 100][[1]] (* _Alonso del Arte_, Aug 31 2014 *)

%o (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

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

%Y Cf. A058283 (continued fraction).

%K easy,nonn,cons

%O 2,1

%A _Mohammad K. Azarian_, Mar 22 2004