cp's OEIS Frontend

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

%I A049420 #42 Jul 13 2025 16:28:48
%S A049420 4,8,14,20,26,34,56,104,153,182,194,217,230,280,462,529,1445,2515,
%T A049420 3692,6187,6851,13917,17258,48934,83515,96835
%N A049420 Composite numbers k such that k!/k# + 1 is prime, where k# = primorial numbers A034386.
%C A049420 Note that k!/k# is known as k compositorial.
%C A049420 Subset of A140294. Prime numbers are excluded since k!/k# = (k-1)!/(k-1)# when k is prime. - _Giovanni Resta_, Mar 28 2013
%C A049420 a(23) > 14000. - _Giovanni Resta_, Apr 02 2013
%C A049420 a(25) > 50000. - _Roger Karpin_, Jul 07 2015
%C A049420 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
%H A049420 Chris Caldwell, <a href="https://t5k.org/glossary/page.php?sort=Compositorial">Compositorial</a>
%t A049420 Primorial[n_] := Product[Prime[i], {i, 1, PrimePi[n]}];
%t A049420 Select[Range[2,
%t A049420 1000], ! PrimeQ[#] && PrimeQ[(#! / Primorial[#]) + 1] &] (* _Robert Price_, Oct 11 2019 *)
%Y A049420 Cf. A034386, A140293, A140294, A140315, A049421, A053982.
%K A049420 nonn,more
%O A049420 1,1
%A A049420 Paul Jobling (paul.jobling(AT)whitecross.com)
%E A049420 a(20) from _Giovanni Resta_, Mar 28 2013
%E A049420 a(21)-a(22) from _Giovanni Resta_, Apr 02 2013
%E A049420 a(23) from _Roger Karpin_, Nov 28 2014
%E A049420 a(24) from _Roger Karpin_, Jul 07 2015
%E A049420 a(25)-a(26) communicated by _Jeppe Stig Nielsen_, Jul 13 2025