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A204664 Numbers n such that n!8-2 is prime.

%I A204664 #26 Apr 03 2023 10:36:12
%S A204664 4,5,7,9,11,15,17,25,27,33,47,59,63,77,87,89,93,95,107,119,127,133,
%T A204664 139,193,201,217,269,291,369,373,435,445,669,803,831,859,907,1271,
%U A204664 1705,1743,1849,3087,3189,3497,4221,4475,5119,6013,8023,9237,12755,16501,16747,17021,17309,20671,21539,28377,33625,35645,36831,54663,56223,65299,66159,68121,69339,70579,73511,77745,94601
%N A204664 Numbers n such that n!8-2 is prime.
%C A204664 n!8 = A114800(n).
%C A204664 See also links in A156165.
%C A204664 For odd k, n!k +- 2 is even for all n > k and thus cannot be prime.
%C A204664 a(62) > 50000. - _Robert Price_, Aug 27 2012
%C A204664 The first 10 associated primes: 2, 3, 5, 7, 31, 103, 151, 3823, 16927, 126223. - _Robert Price_, Mar 10 2017
%C A204664 a(72) > 10^5. - _Robert Price_, Apr 24 2017
%H A204664 C. Caldwell and H. Dubner (Eds): <a href="https://t5k.org/lists/top_ten/">The top ten prime numbers: from the unpublished collections of R. Ondrejka</a> (May 2001), Table 21 F, p. 75
%H A204664 Ken Davis, <a href="http://mfprimes.free-dc.org">Status of Search for Multifactorial Primes</a>.
%t A204664 MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
%t A204664 Select[Range[4, 50000], PrimeQ[MultiFactorial[#, 8] - 2] &] (* _Robert Price_, Mar 10 2017 *)
%o A204664 (PARI) for(n=0,9999,isprime(prod(i=0,(n-2)\8,n-8*i)-2)& print1(n","))
%Y A204664 Cf. A204657, A204658, A204659, A204660, A204661, A204662, A204663, A156165, A156167, A085150, A085148, A085146, A037083, A080778, A002981.
%K A204664 nonn,hard
%O A204664 1,1
%A A204664 _M. F. Hasler_, Jan 17 2012
%E A204664 a(46)-a(61) from _Robert Price_, Aug 27 2012
%E A204664 a(62)-a(71) from _Robert Price_, Apr 24 2017