A271376 - OEIS

%I #25 Sep 08 2022 08:46:16

%S 3,4,5,6,7,10,12,13,21,24,37,64,68,136,169,216,276,435,617,753,1722,

%T 1775,2762,3974,5006,5931,7480,11442,11896,13200,13534,23240,27971,

%U 31867

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

%C Corresponding primes are 7, 13, 41, 181, 1009, 453601, ...

%e 3 is a term because 2*3 + 1 = 7 is prime.

%e 4 is a term because 1*3*4 + 1 = 13 is prime.

%e 5 is a term because 1*2*4*5 + 1 = 41 is prime.

%e 6 is a term because 1*2*3*5*6 + 1 = 181 is prime.

%e 7 is a term because 1*2*3*4*6*7 + 1 = 1009 is prime.

%t Select[Range[3, 2000], PrimeQ[( #! / (# - 2) + 1)] &] (* _Vincenzo Librandi_, Apr 07 2016 *)

%o (PARI) lista(nn) = for(n=3, nn, if(ispseudoprime(n!/(n-2)+1), print1(n, ", ")));

%o (PFGW) ABC2 $a!/($a-2) + 1

%o a: from 3 to 100000

%o (Magma) [n: n in [3..500] | IsPrime(Factorial(n)  div (n-2) + 1)]; // _Vincenzo Librandi_, Apr 07 2016

%Y Cf. A002981, A052747.

%K nonn

%O 1,1

%A _Altug Alkan_, Apr 05 2016

%E a(23) from _Charles R Greathouse IV_, Apr 05 2016

%E a(24)-a(27) from _Charles R Greathouse IV_, Apr 06 2016

%E a(28)-a(32) from _Charles R Greathouse IV_, Apr 18 2016

%E a(33) from _Charles R Greathouse IV_, Apr 30 2016

%E a(34) from _Charles R Greathouse IV_, May 09 2016