cp's OEIS Frontend

A291322 Numbers k such that k!/(k-2) - 1 is prime.

%I A291322 #25 Jan 01 2025 09:54:36
%S A291322 3,4,6,8,9,10,18,21,23,26,46,70,83,156,553,591,741,790,1430,2139,5509,
%T A291322 11429,11881,14343
%N A291322 Numbers k such that k!/(k-2) - 1 is prime.
%C A291322 Corresponding primes are 5, 11, 179, 6719, 51839, 453599, ...
%C A291322 Initial terms common with A271376 (that generate twin primes): 3, 4, 6, 10, 21.
%C A291322 Union of this sequence and A271376 is the sequence {3, 4, 5, 6, 7, 8, 9, 10, 12, 13, ...}.
%e A291322 3 is a term because 2*3 - 1 = 5 is prime.
%e A291322 4 is a term because 1*3*4 - 1 = 11 is prime.
%e A291322 6 is a term because 1*2*3*5*6 - 1 = 179 is prime.
%t A291322 Select[Range[3, 6000], PrimeQ[( #! / (# - 2) - 1)] &]
%o A291322 (PARI) lista(nn) = for(n=3, nn, if(ispseudoprime(n!/(n-2)-1), print1(n, ", ")));
%o A291322 (PFGW) ABC2 $a!/($a-2) - 1
%o A291322 a: from 3 to 6000
%o A291322 (Magma) [n: n in [3..1000] | IsPrime(Factorial(n)  div (n-2) - 1)];
%Y A291322 Cf. A002982, A052747, A271376.
%K A291322 nonn,more
%O A291322 1,1
%A A291322 _Amiram Eldar_ and _Altug Alkan_, Aug 22 2017
%E A291322 a(22)-a(23) from _Giovanni Resta_, Aug 23 2017
%E A291322 a(24) from _Michael S. Branicky_, Dec 31 2024