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A144051
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Primes p such that the polynomial x^2 + x + p generates only primes for x = 1..6.
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3
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11, 17, 41, 1277, 21557, 26681, 28277, 113147, 128981, 421697, 665111, 844427, 1164587, 1615631, 2073347, 2798921, 2846771, 3053747, 3992201, 4889237, 5071667, 5093507, 5344247, 5706641, 6184637, 6383051, 8396777
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| All terms = {11,17} mod 30. - Zak Seidov, May 08 2011
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LINKS
| Zak Seidov, Table of n, a(n) for n = 1..1000
H. J. Weber, Regularities of Twin, Triplet and Multiplet Prime Numbers, arXiv:1103.0447, Mar 2, 2011.
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EXAMPLE
| 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.
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MATHEMATICA
| 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
okQ[n_] := And @@ PrimeQ[Table[i^2 + i + n, {i, 0, 6}]]; Select[Range[10000], okQ] (* T. D. Noe, Mar 03 2011 *)
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CROSSREFS
| Cf. A187057, A187058.
Sequence in context: A090609 A187057 A187058 * A187060 A190800 A191456
Adjacent sequences: A144048 A144049 A144050 * A144052 A144053 A144054
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KEYWORD
| nonn
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AUTHOR
| Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 08 2008
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