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%I #45 Apr 03 2023 10:36:11
%S 4,6,12,16,29,34,43,111,137,181,528,2685,39477,43697
%N Numbers k for which (k!-3)/3 is prime.
%C Corresponding primes (k!-3)/3 are in A139057.
%C a(13) > 10000. The PFGW program has been used to certify all the terms up to a(12), using a deterministic test which exploits the factorization of a(n) + 1. - _Giovanni Resta_, Mar 28 2014
%C 98166 is a member of the sequence but its index is not yet determined. The interval where sieving and tests were not run is [60000,90000]. - _Serge Batalov_, Feb 24 2015
%H C. Caldwell. The Prime database entry for <a href="https://t5k.org/primes/page.php?id=119403">the prime generated by a(i)=98166</a>.
%t a = {}; Do[If[PrimeQ[(-3 + n!)/3], AppendTo[a, n]], {n, 1, 1000}]; a
%o (PARI) for(n=1,1000,if(floor(n!/3-1)==n!/3-1,if(ispseudoprime(n!/3-1),print(n)))) \\ _Derek Orr_, Mar 28 2014
%Y Cf. A007749, A117141.
%Y Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199-A139205.
%Y Cf. n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071.
%Y Cf. m*n!-1 is a prime: A076133, A076134, A099350, A099351, A180627-A180631.
%Y Cf. m*n!+1 is a prime: A051915, A076679-A076683, A178488, A180626, A126896.
%K nonn,more
%O 1,1
%A _Artur Jasinski_, Apr 07 2008
%E Definition corrected by _Derek Orr_, Mar 28 2014
%E a(8)-a(11) from _Derek Orr_, Mar 28 2014
%E a(12) from _Giovanni Resta_, Mar 28 2014
%E a(13)-a(14) from _Serge Batalov_, Feb 24 2015
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