A139199 - OEIS

%I #13 Sep 25 2016 12:33:49

%S 4,5,6,7,8,10,15,18,23,157,165,183,184,362,611,908,2940,6875,9446,

%T 16041

%N Numbers k such that (k!-4)/4 is prime.

%C Numbers k such that (k!-m)/m is prime:

%C for m=1 see A002982

%C for m=2 prime or pseudoprime see A082671

%C for m=3 see A139056

%C for m=4 see A139199

%C for m=5 see A139200

%C for m=6 see A139201

%C for m=7 see A139202

%C for m=8 see A139203

%C for m=9 see A139204

%C for m=10 see A139205

%C a(17) > 2000 - _Ray G. Opao_, Sep 30 2008

%C a(21) > 25000 - _Robert Price_, Sep 25 2016

%t a = {}; Do[If[PrimeQ[(n! - 4)/4], Print[a]; AppendTo[a, n]], {n, 1, 184}]; a (*Artur Jasinski*)

%o (PARI) is(n)=n>3 && isprime(n!/4-1) \\ _Charles R Greathouse IV_, Apr 29 2015

%Y Cf. A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197, A139198.

%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 hard,more,nonn

%O 1,1

%A _Artur Jasinski_, Apr 11 2008

%E a(15)-a(16) from _Ray G. Opao_, Sep 30 2008

%E a(17) from _Serge Batalov_, Feb 18 2015

%E a(18)-a(20) from _Robert Price_, Sep 25 2016