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A049420
Composite numbers k such that k!/k# + 1 is prime, where k# = primorial numbers A034386.
6
4, 8, 14, 20, 26, 34, 56, 104, 153, 182, 194, 217, 230, 280, 462, 529, 1445, 2515, 3692, 6187, 6851, 13917, 17258, 48934
OFFSET
1,1
COMMENTS
Note that k!/k# is known as n 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
MATHEMATICA
Primorial[n_] := Product[Prime[i], {i, 1, PrimePi[n]}];
Select[Range[2,
1000], ! PrimeQ[#] && PrimeQ[(#! / Primorial[#]) + 1] &] (* Robert Price, Oct 11 2019 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Paul Jobling (paul.jobling(AT)whitecross.com)
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
STATUS
approved