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A156165 Numbers k such that k![7]+1 is prime (n![7] = A114799(n) = septuple factorial).

%I A156165 #23 Apr 03 2023 10:36:11
%S A156165 0,1,2,4,6,9,10,12,13,24,25,26,29,31,35,36,47,49,57,58,64,71,73,75,78,
%T A156165 80,97,123,125,129,131,135,147,150,159,183,201,250,251,255,298,336,
%U A156165 337,458,467,556,570,657,743,801,908,925,1003,1209,1473,1524,1716,1881,1926
%N A156165 Numbers k such that k![7]+1 is prime (n![7] = A114799(n) = septuple factorial).
%C A156165 a(103) > 50000. - _Robert Price_, Sep 03 2012
%H A156165 Robert Price, <a href="/A156165/b156165.txt">Table of n, a(n) for n = 1..102</a>
%H A156165 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The top ten prime numbers: from the unpublished collections of R. Ondrejka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 A156165 Ken Davis, <a href="http://mfprimes.free-dc.org">Status of Search for Multifactorial Primes</a>.
%H A156165 Ken Davis, <a href="http://mfprimes.free-dc.org/mfdata/f07p.html">Results for n!7+1.</a>
%t A156165 mf[n_, k_] := Product[n - i k, {i, 0, Quotient[n - 2, k]}];
%t A156165 Reap[For[k = 0, k <= 2000, k++, If[PrimeQ[mf[k, 7] + 1], Sow[k]]]][[2, 1]] (* _Jean-François Alcover_, Feb 26 2019 *)
%t A156165 Select[Range[0,2000],PrimeQ[Times@@Range[#,1,-7]+1]&] (* _Harvey P. Dale_, Aug 21 2021 *)
%o A156165 (PARI) mf(n,k=7)=prod(i=0,(n-2)\k,n-i*k)
%o A156165 for( n=0,9999, ispseudoprime(mf(n)+1) & print1(n","))
%Y A156165 Cf. A156167, A085150, A085148, A085146, A037083, A080778, A002981.
%K A156165 nonn
%O A156165 1,3
%A A156165 _M. F. Hasler_, Feb 10 2009