A057017 -id:A057017 - cp's OEIS frontend

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

Cino Hilliard, May 25 2008

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

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

Chris Caldwell, Compositorial
Chris Caldwell, Compositorial list search

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

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

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

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.

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

A049421 Composite numbers k such that k!/k# - 1 is prime, where k# = primorial numbers A034386.

Original entry on oeis.org

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

Offset: 1

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

k!/k# is known as n compositorial.
Subset of A140293. Prime numbers are excluded since k!/k# = (k-1)!/(k-1)# when k is prime. - Giovanni Resta, Mar 28 2013
a(31) > 50000. - Roger Karpin, Jul 08 2015

Chris Caldwell, Compositorial

Cf. A034386, A140293, A140294, A140315, A049420, A057017.

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

More terms from Robert G. Wilson v, Jun 21 2001
a(23)-a(25) from Giovanni Resta, Apr 02 2013
a(26) from Roger Karpin, Nov 29 2014
a(27)-a(28) from Daniel Heuer, ca Aug 2000
a(29)-a(30) from Serge Batalov, Feb 09 2015

A053982 Numbers k such that 1 + product of first k composite numbers is prime.

Original entry on oeis.org

1, 3, 7, 11, 16, 22, 39, 76, 116, 139, 149, 169, 179, 220, 372, 429, 1216, 2146, 3176, 5382, 5969, 12271, 15271, 43903

Offset: 1

G. L. Honaker, Jr., Apr 02 2000

Cf. A002808, A000040, A049420, A049650, A057017, A140294.

Composite[n_Integer] := (k = n + PrimePi[n] + 1; While[k - PrimePi[k] - 1 != n, k++ ]; k); Do[ If[ PrimeQ[ Product[ Composite[k], {k, 1, n} ] + 1], Print[ n ] ], {n, 1, 430} ]
Position[FoldList[Times,Select[Range[1500],CompositeQ]],?(PrimeQ[#+1]&)]//Flatten (* _Harvey P. Dale, Dec 20 2022 *)

lista(kmax) = {my(m = 1, k = 0); forcomposite(c = 1, , k++; if(k > kmax, break); m *= c; if(isprime(m+1), print1(k, ", ")));} \\ Amiram Eldar, Jun 03 2024

More terms from Jeppe Stig Nielsen, Apr 16 2000 (terms from 76 on correspond to probable primes)
a(16)-a(17) from Robert G. Wilson v, Apr 20 2001
Edited by T. D. Noe, Oct 30 2008
a(18)-a(19) from Amiram Eldar, Jun 03 2024
a(20)-a(21) from Michael S. Branicky, Jun 04 2024
More terms via A049420 from Jeppe Stig Nielsen, Aug 12 2024

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A049421 Composite numbers k such that k!/k# - 1 is prime, where k# = primorial numbers A034386.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions

A053982 Numbers k such that 1 + product of first k composite numbers is prime.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

PARI

Extensions