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

3, 4, 6, 8, 9, 10, 18, 21, 23, 26, 46, 70, 83, 156, 553, 591, 741, 790, 1430, 2139, 5509, 11429, 11881, 14343

Offset: 1

Author

Amiram Eldar and Altug Alkan, Aug 22 2017

Keywords

• nonn
• more

Comments

Corresponding primes are 5, 11, 179, 6719, 51839, 453599, ...

Initial terms common with A271376 (that generate twin primes): 3, 4, 6, 10, 21.

Union of this sequence and A271376 is the sequence {3, 4, 5, 6, 7, 8, 9, 10, 12, 13, ...}.

Examples

			3 is a term because 2*3 - 1 = 5 is prime.
4 is a term because 1*3*4 - 1 = 11 is prime.
6 is a term because 1*2*3*5*6 - 1 = 179 is prime.
		

Crossrefs

Cf. A002982, A052747, A271376.

Programs

Magma

[n: n in [3..1000] | IsPrime(Factorial(n)  div (n-2) - 1)];

Mathematica

Select[Range[3, 6000], PrimeQ[( #! / (# - 2) - 1)] &]

PARI

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

PFGW

ABC2 $a!/($a-2) - 1
a: from 3 to 6000

Extensions

a(22)-a(23) from Giovanni Resta, Aug 23 2017

a(24) from Michael S. Branicky, Dec 31 2024