%I #31 Sep 08 2022 08:45:12

%S 3,5,6,8,11,17,23,36,77,93,94,109,304,497,1330,1996,3027,3053,4529,

%T 5841,20556,26558,28167

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

%C 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

%t Select[Range[0, 1400], PrimeQ[(#!+3)/3] &] (* _Vladimir Joseph Stephan Orlovsky_, Apr 29 2008 *)

%o (Magma) [n: n in [0..500] | IsPrime((Factorial(n)+3) div 3)]; // _Vincenzo Librandi_, Dec 12 2011

%o (PARI) is(n)=ispseudoprime(n!\3+1) \\ _Charles R Greathouse IV_, Mar 21 2013

%Y Cf. A089131.

%Y 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).

%K nonn

%O 1,1

%A _Cino Hilliard_, Dec 05 2003

%E More terms from _Don Reble_, Dec 06 2003

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

%E Typo in Mma program corrected by _Vincenzo Librandi_, Dec 12 2011

%E a(16)-a(20) from _Giovanni Resta_, Mar 31 2014

%E a(21)-a(23) from _Serge Batalov_, Feb 17 2015