A319224 - OEIS

%I #51 May 12 2019 03:43:05

%S 7,11,19,61,2557

%N Integers q for which f(q) = ((((q - 2)! - 1) / q) - 1) / (q + 1) is a prime number.

%C For q < 7, f(q) is not an integer.

%C f(q) for q = 2557 is a PRP7592.

%C According to Wilson's theorem, f(q) can be an integer only if q is prime.

%t a[q_]:=If[PrimeQ[((((q - 2)! - 1) / q) - 1) / (q + 1)], q]; DeleteCases[Array[a, 100], Null] (* _Stefano Spezia_, Nov 04 2018 *)

%o (PARI) forprime(q=7, 2557, my(p = ((((q - 2)! - 1) / q) - 1) / (q + 1)); if(ispseudoprime(p), print1(q, ", ")))

%Y Cf. A193447, A319304.

%K nonn,hard,more

%O 1,1

%A _Rashid Naimi_, Sep 13 2018