%I
%S 1,4,5,6,13,14,20,66,91,124,212,282,460
%N !n  3 is prime.
%C There are no further terms, because for n >= 467, 467  !n  3.  _Serge Batalov_, Jul 14 2017
%t Do[ If[ PrimeQ[ Sum[ k!, {k, 0, n  1} ]  3 ], Print[ n ] ], {n, 1, 800} ]
%t Position[Accumulate[Range[0,500]!],_?(PrimeQ[#3]&)]//Flatten (* _Harvey P. Dale_, Sep 20 2019 *)
%Y Cf. A063508.
%K nonn,fini,full
%O 1,2
%A _Robert G. Wilson v_, Aug 21 2001
