A019741 - OEIS

%I #37 May 02 2024 17:33:15

%S 6,7,9,5,7,0,4,5,7,1,1,4,7,6,1,3,0,8,8,4,0,0,7,1,8,6,7,8,3,8,1,6,5,6,

%T 2,4,4,3,9,3,1,1,7,7,3,4,2,4,9,8,9,8,9,3,7,4,1,7,4,1,9,0,6,9,3,1,0,1,

%U 9,1,5,7,5,8,8,3,8,6,8,9,8,6,4,2,8,4,5

%N Decimal expansion of e/4.

%C Also (with offset = 1) 2.5*e = Sum_{n>=1} A000326(n)/n!. - _Richard R. Forberg_, Jul 15 2013

%C Also abscissa of minimum of f(x) = 2*Pi/(4x)^(1/(2x)) = (Product_{k=1..x} Gamma(k/(2x))*Gamma(1 - k/(2x)))^(1/x). - _Andrea Pinos_, Nov 22 2023

%H Harry J. Smith, <a href="/A019741/b019741.txt">Table of n, a(n) for n = 0..20000</a>

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

%e 0.679570457114761308840071867838165624439311773424989893741741906931019....

%t First[RealDigits[E/4, 10, 100]] (* _Paolo Xausa_, May 02 2024 *)

%o (PARI) default(realprecision, 20080); x=10*exp(1)/4; for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b019741.txt", n, " ", d)); \\ _Harry J. Smith_, May 10 2009

%Y Cf. A000326, A001113, A006085 (continued fraction).

%K nonn,cons

%O 0,1

%A _N. J. A. Sloane_