A049420 Composite numbers k such that k!/k# + 1 is prime, where k# = primorial numbers A034386.

4, 8, 14, 20, 26, 34, 56, 104, 153, 182, 194, 217, 230, 280, 462, 529, 1445, 2515, 3692, 6187, 6851, 13917, 17258, 48934, 83515, 96835

Offset: 1

Author

Paul Jobling (paul.jobling(AT)whitecross.com)

Keywords

• nonn
• more

Comments

Note that k!/k# is known as k compositorial.

Subset of A140294. Prime numbers are excluded since k!/k# = (k-1)!/(k-1)# when k is prime. - Giovanni Resta, Mar 28 2013

a(23) > 14000. - Giovanni Resta, Apr 02 2013

a(25) > 50000. - Roger Karpin, Jul 07 2015

The prime associated with a(26) was discovered by Serge Batalov in 2015. All k up to 10^5 were resolved by PrimeGrid administrator "Stream" (Roman Trunov) who found a(25) and the position of a(26). - Jeppe Stig Nielsen, Jul 13 2025

Links

• Chris Caldwell, Compositorial

Crossrefs

Cf. A034386, A140293, A140294, A140315, A049421, A053982.

Programs

Mathematica

Primorial[n_] := Product[Prime[i], {i, 1, PrimePi[n]}];
Select[Range[2,
1000], ! PrimeQ[#] && PrimeQ[(#! / Primorial[#]) + 1] &] (* Robert Price, Oct 11 2019 *)

Extensions

a(20) from Giovanni Resta, Mar 28 2013

a(21)-a(22) from Giovanni Resta, Apr 02 2013

a(23) from Roger Karpin, Nov 28 2014

a(24) from Roger Karpin, Jul 07 2015

a(25)-a(26) communicated by Jeppe Stig Nielsen, Jul 13 2025