A140293 Numbers k such that k!/k#-1 is prime, where k# is the primorial function (A034386).

4, 5, 6, 7, 8, 16, 17, 21, 34, 39, 45, 50, 72, 73, 76, 133, 164, 202, 216, 221, 280, 281, 496, 605, 2532, 2967, 3337, 8711, 10977, 13724, 15250, 18160, 20943, 33684, 41400

Offset

1,1

Comments

a(31) > 14000. - Giovanni Resta, Apr 02 2013

a(36) > 50000. - Roger Karpin, Jul 07 2015

If k is a prime and k is a member, then k-1 is also a member, and k!/k# - 1 is the same as (k-1)!/(k-1)# - 1. See A049421. - Jeppe Stig Nielsen, Aug 12 2024

Links

Table of n, a(n) for n=1..35.

Chris Caldwell, Compositorial

Chris Caldwell, Compositorial list search

Formula

n such that n!/n# - 1 is prime, where n# is the primorial function n# = product(i = 1 .. pi(n), prime(i)), where pi(n) is the prime counting function.

Example

7!/7# = 5040/210 = 24. 24 - 1 = 23, which is prime.

Mathematica

Select[Range[16], PrimeQ[#!/(Times@@Prime[Range[PrimePi[#]]]) - 1] &] (* Alonso del Arte, Nov 28 2014 *)

Prog

(PARI) g(n) = for(x=4, n, y=x!/primorial(x)-1; z=nextprime(y+1); if(ispseudoprime(y), print1(x", ")))

Crossrefs

Cf. A140294, A140315, A049420, A049421, A049614, A057017.

Sequence in context: A071623 A274552 A280682 * A075341 A309358 A143789

Adjacent sequences: A140290 A140291 A140292 * A140294 A140295 A140296

Keyword

nonn,more

Author

Cino Hilliard, May 25 2008

Extensions

a(18)-a(27) from Giovanni Resta, Mar 28 2013

a(28)-a(30) from Giovanni Resta, Apr 02 2013

a(31) from Roger Karpin, Nov 28 2014

a(32)-a(33) from Daniel Heuer, ca Aug 2000

a(34)-a(35) from Serge Batalov, Feb 09 2015

Status

approved