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A092426 Decimal expansion of e^4.

%I A092426 #32 Feb 15 2024 12:32:32
%S A092426 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 A092426 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 A092426 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 A092426 Decimal expansion of e^4.
%H A092426 Harry J. Smith, <a href="/A092426/b092426.txt">Table of n, a(n) for n = 2..20000</a>
%H A092426 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A092426 From _Peter Bala_, Jan 12 2022: (Start)
%F A092426 e^4 = 45 + 2*Sum_{n >= 0} 4^(n+4)/((n+4)^2*(n+5)^2*n!).
%F A092426 45/e^4 = 1 - 3*Sum_{n >= 0} (-4)^(n+3)*n^2/(n+4)!. (End)
%F A092426 Largest solution to sqrt(log(x)) = log(sqrt(x)), the other solution being x = 1. - _Andrea Pinos_, Jan 23 2024
%e A092426 54.598150033144239078110261202860878402790737038614....
%p A092426 Digits:=100: evalf(exp(4)); # _Wesley Ivan Hurt_, Sep 01 2014
%t A092426 RealDigits[E^4, 10, 100][[1]] (* _Alonso del Arte_, Aug 31 2014 *)
%o A092426 (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 A092426 Cf. A001113, A072334, A091933, A092511, A092512, A092513.
%Y A092426 Cf. A058283 (continued fraction).
%K A092426 easy,nonn,cons
%O A092426 2,1
%A A092426 _Mohammad K. Azarian_, Mar 22 2004