A089085 Numbers k such that (k! + 3)/3 is prime.

3, 5, 6, 8, 11, 17, 23, 36, 77, 93, 94, 109, 304, 497, 1330, 1996, 3027, 3053, 4529, 5841, 20556, 26558, 28167

Offset: 1

Author

Cino Hilliard, Dec 05 2003

Keywords

• nonn

Comments

a(21) > 20000. The PFGW program has been used to certify all the terms up to a(20), using the "N-1" deterministic test. - Giovanni Resta, Mar 31 2014

Crossrefs

Cf. A089131.

Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199-A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).

Programs

Magma

[n: n in [0..500] | IsPrime((Factorial(n)+3) div 3)]; // Vincenzo Librandi, Dec 12 2011

Mathematica

Select[Range[0, 1400], PrimeQ[(#!+3)/3] &] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)

PARI

is(n)=ispseudoprime(n!\3+1) \\ Charles R Greathouse IV, Mar 21 2013

Extensions

More terms from Don Reble, Dec 06 2003

1330 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008

Typo in Mma program corrected by Vincenzo Librandi, Dec 12 2011

a(16)-a(20) from Giovanni Resta, Mar 31 2014

a(21)-a(23) from Serge Batalov, Feb 17 2015