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%I #14 Aug 10 2017 03:31:16
%S 11,17,41,1277,21557,26681,28277,113147,128981,421697,665111,844427,
%T 1164587,1615631,2073347,2798921,2846771,3053747,3992201,4889237,
%U 5071667,5093507,5344247,5706641,6184637,6383051,8396777
%N Primes p such that the polynomial x^2 + x + p generates only primes for x = 1..6.
%C All terms = {11,17} mod 30. - _Zak Seidov_, May 08 2011
%H Zak Seidov, <a href="/A144051/b144051.txt">Table of n, a(n) for n = 1..1000</a>
%H H. J. Weber, <a href="http://arxiv.org/abs/1103.0447">Regularities of Twin, Triplet and Multiplet Prime Numbers</a>, arXiv:1103.0447 [math.NT], 2011-2012.
%e a(3) = 41 because 0^2 + 0 + 41 = 41; 1^2 + 1 + 41 = 43; 2^2 + 2 + 41 = 47; 3^2 + 3 + 41 = 53; 4^2 + 4 + 41 = 61; 5^2 + 5 + 41 = 71; 6^2 + 6 + 41 = 83, all primes.
%t lst={}; Do[p1=Prime[n]; If[PrimeQ[p2=p1+2] && PrimeQ[p3=p1+6] && PrimeQ[p4=p1+12] && PrimeQ[p5=p1+20] && PrimeQ[p6=p1+30] && PrimeQ[p7=p1+42], AppendTo[lst,p1]], {n,10^5}]; lst
%t okQ[n_] := And @@ PrimeQ[Table[i^2 + i + n, {i, 0, 6}]]; Select[Range[10000], okQ] (* _T. D. Noe_, Mar 03 2011 *)
%Y Cf. A187057, A187058.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Sep 08 2008
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