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%I #20 Oct 02 2022 23:05:18
%S 6,0,6,5,3,0,6,5,9,7,1,2,6,3,3,4,2,3,6,0,3,7,9,9,5,3,4,9,9,1,1,8,0,4,
%T 5,3,4,4,1,9,1,8,1,3,5,4,8,7,1,8,6,9,5,5,6,8,2,8,9,2,1,5,8,7,3,5,0,5,
%U 6,5,1,9,4,1,3,7,4,8,4,2,3,9,9,8,6,4,7,6,1,1,5,0,7,9,8,9,4,5,6,0,2,6,4,2,3
%N Decimal expansion of e^(-1/2) or 1/sqrt(e).
%C For x = e^(-1/2), the largest prime factor of a random integer n is equally likely to be above or below n^x. - _Charles R Greathouse IV_, May 25 2009
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Equals Sum_{k>=0} (-1)^k/(2^k * k!) = Sum_{k>=0} (-1)^k/A000165(k). - _Amiram Eldar_, Aug 15 2020
%F From _Peter Bala_, Jan 16 2022; (Start)
%F Equals 16*Sum_{n >= 0} (-1)^n*n^2/((4*n^2 - 1)*(4*n^2 - 9)*(2^n)*n!).
%F Equals 8*Sum_{n >= 0} (-1)^n/(p(n)*p(n+1)*(2^n)*n!), where p(n) = 4*n^2 + 8*n + 1.
%F Equals 48*Sum_{n >= 0} (-1)^n/(q(n)*q(n+1)*(2^n)*n!), where q(n) = 8*n^3 + 36*n^2 + 34*n + 1. (End)
%e 0.6065306597126334...
%t RealDigits[E^-(1/2),10,120][[1]] (* _Harvey P. Dale_, Jul 23 2012 *)
%o (PARI) exp(-.5) \\ _Charles R Greathouse IV_, Oct 02 2022
%Y Cf. A000165, A001113, A019774, A068985.
%K cons,nonn
%O 0,1
%A _Mohammad K. Azarian_, Apr 22 2004
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