%I
%S 0,3,4,5,7,10,12,20,37,52,73,149,304,540,2135,7112,7436,9357
%N Numbers n such that !n + 7 is prime.
%C At present the terms >= 2135 are only probable primes.
%C Expected to be finite, similar to Živković (1999).
%H M. Živković, <a href="https://doi.org/10.1090/S0025571899009904">The number of primes Sum_{i=1..n} (1)^(ni)*i! is finite</a>, Math. Comp. 68 (1999), no. 225, 403409.
%e 4 is a term, because 0! + 1! + 2! + 3! + 7 = 17 is prime.
%t Do[ If[ PrimeQ[ Sum[ k!, {k, 0, n  1} ] + 7 ], Print[ n ] ], {n, 1, 600} ]
%o (PARI) s=0; for(n=0,600,if(ispseudoprime(s + 7),print1(n,", ")); s+=n!)
%Y Cf. A001272, A063833, A100614.
%K nonn,hard,more
%O 1,2
%A _Serge Batalov_, Jul 14 2017
