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A271376 Integers n such that n!/(n-2) + 1 is prime.

%I A271376 #25 Sep 08 2022 08:46:16
%S A271376 3,4,5,6,7,10,12,13,21,24,37,64,68,136,169,216,276,435,617,753,1722,
%T A271376 1775,2762,3974,5006,5931,7480,11442,11896,13200,13534,23240,27971,
%U A271376 31867
%N A271376 Integers n such that n!/(n-2) + 1 is prime.
%C A271376 Corresponding primes are 7, 13, 41, 181, 1009, 453601, ...
%e A271376 3 is a term because 2*3 + 1 = 7 is prime.
%e A271376 4 is a term because 1*3*4 + 1 = 13 is prime.
%e A271376 5 is a term because 1*2*4*5 + 1 = 41 is prime.
%e A271376 6 is a term because 1*2*3*5*6 + 1 = 181 is prime.
%e A271376 7 is a term because 1*2*3*4*6*7 + 1 = 1009 is prime.
%t A271376 Select[Range[3, 2000], PrimeQ[( #! / (# - 2) + 1)] &] (* _Vincenzo Librandi_, Apr 07 2016 *)
%o A271376 (PARI) lista(nn) = for(n=3, nn, if(ispseudoprime(n!/(n-2)+1), print1(n, ", ")));
%o A271376 (PFGW) ABC2 $a!/($a-2) + 1
%o A271376 a: from 3 to 100000
%o A271376 (Magma) [n: n in [3..500] | IsPrime(Factorial(n)  div (n-2) + 1)]; // _Vincenzo Librandi_, Apr 07 2016
%Y A271376 Cf. A002981, A052747.
%K A271376 nonn
%O A271376 1,1
%A A271376 _Altug Alkan_, Apr 05 2016
%E A271376 a(23) from _Charles R Greathouse IV_, Apr 05 2016
%E A271376 a(24)-a(27) from _Charles R Greathouse IV_, Apr 06 2016
%E A271376 a(28)-a(32) from _Charles R Greathouse IV_, Apr 18 2016
%E A271376 a(33) from _Charles R Greathouse IV_, Apr 30 2016
%E A271376 a(34) from _Charles R Greathouse IV_, May 09 2016