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Search: id:A106859
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| A106859 |
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Primes of the form 2x^2+xy+2y^2, with x and y any integer. |
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3
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| 2, 3, 5, 17, 23, 47, 53, 83, 107, 113, 137, 167, 173, 197, 227, 233, 257, 263, 293, 317, 347, 353, 383, 443, 467, 503, 557, 563, 587, 593, 617, 647, 653, 677, 683, 743, 773, 797, 827, 857, 863, 887, 947, 953, 977, 983, 1013, 1097, 1103, 1163, 1187, 1193
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Discriminant=-15. See A106856 for more information.
If p is a prime >=17 in this sequence then k==0 (mod 4) for all k satisfying "B(2k)(p^k-1) is an integer" where B are the Bernoulli numbers. - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 14 2005
Equals {2, 3, 5 and primes congruent to 17, 23 (mod 30)}; see A039949 and A132235. Except for 2, the same as primes of the form 3x^2 + 5y^2, which has discriminant -60. - T. D. Noe (noe(AT)sspectra.com), May 02 2008
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MATHEMATICA
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f[x_, y_]:=2*x^2+x*y+2*y^2; lst={}; Do[Do[p=f[x, y]; If[PrimeQ[p], AppendTo[lst, p]], {y, -5!, 6!}], {x, -5!, 6!}]; Take[Union[lst], 5! ] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jul 04 2009]
Union[QuadPrimes[2, 1, 2, 10000], QuadPrimes[2, -1, 2, 10000]] (* see A106856 *)
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CROSSREFS
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Cf. A139827, A039949, A132235.
Sequence in context: A049577 A121558 A089442 this_sequence A055472 A077499 A127061
Adjacent sequences: A106856 A106857 A106858 this_sequence A106860 A106861 A106862
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KEYWORD
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nonn,easy
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), May 09 2005
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