A140293 Numbers n such that n!/n#-1 is prime.

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

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.

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