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

Offset

1,1

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, ...}.

Links

Table of n, a(n) for n=1..23.

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A002982, A052747, A271376.

Sequence in context: A025063 A050849 A039008 * A322741 A161579 A276214

Adjacent sequences: A291319 A291320 A291321 * A291323 A291324 A291325

Keyword

nonn,more

Author

Amiram Eldar and Altug Alkan, Aug 22 2017

Extensions

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

Status

approved