%I #2 Oct 02 2013 16:01:16
%S 2,3,4,8,13,42,64,166,573,1711
%N Numbers n such that (n+2)*n!*Sum((-1)^k/k!),k=0..n+2 is prime.
%C No further terms up to n=20000. The sequence a[n]=(n+2)*n!*Sum((-1)^k/k!),k=0..n+2 is A000255.
%F n is an index of the sequence a[n]=(n+2)*n!*Sum((-1)^k/k!),k=0..n+2 such that a[n] is prime.
%e For n=3, a[3]=11 which is prime.
%o (PARI) z_even=1;z_odd=1;
%o for(n=1,20000,
%o if(n%2==1,
%o z_odd=(n+2)*(n-1)*z_odd+1; if((ispseudoprime(z_odd)),print(n="n)),
%o z_even=(n+2)*(n-1)*z_even-1; if((ispseudoprime(z_odd)),print(n="n))););
%Y Cf. A000255 (corresponding sequence).
%K nonn
%O 1,1
%A _Mike Oakes_, Oct 12 2009