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Numbers k such that (k!-6)/6 is prime.
3

%I #12 Feb 06 2019 00:32:03

%S 4,5,7,8,11,14,16,17,18,20,43,50,55,59,171,461,859,2830,3818,5421,

%T 5593,10118,10880,24350

%N Numbers k such that (k!-6)/6 is prime.

%C a(25) > 25000. - _Robert Price_, Dec 15 2016

%p a:=proc(n) if isprime((1/6)*factorial(n)-1)=true then n else end if end proc: seq(a(n),n=4..500); # _Emeric Deutsch_, Apr 29 2008

%t a = {}; Do[If[PrimeQ[(n! - 6)/6], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a (* _Artur Jasinski_ *)

%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 nonn

%O 1,1

%A _Artur Jasinski_, Apr 11 2008

%E 2 more terms from _Emeric Deutsch_, Apr 29 2008

%E More terms from _Serge Batalov_, Feb 18 2015

%E a(22)-a(24) from _Robert Price_, Dec 15 2016