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Numbers k such that (k!-9)/9 is prime.
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%I #21 Mar 29 2017 19:46:20

%S 6,15,17,18,21,27,29,30,37,47,50,64,125,251,602,611,1184,1468,5570,

%T 10679,15798,21237

%N Numbers k such that (k!-9)/9 is prime.

%C a(20) > 10000. The PFGW program has been used to certify all the terms up to a(19), using a deterministic test which exploits the factorization of a(n) + 1. - _Giovanni Resta_, Mar 28 2014

%C a(23) > 25000. - _Robert Price_, Mar 29 2017

%t a = {}; Do[If[PrimeQ[(n! - 9)/9], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a

%o (PARI) for(n=1,1000,if(floor(n!/9-1)==n!/9-1,if(ispseudoprime(n!/9-1),print(n)))) \\ _Derek Orr_, Mar 28 2014

%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(14)-a(16) from _Derek Orr_, Mar 28 2014

%E a(17)-a(19) from _Giovanni Resta_, Mar 28 2014

%E a(20)-a(22) from _Robert Price_, Mar 29 2017