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Search: id:A107003
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| A107003 |
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Primes of the form 5x^2+2xy+5y^2, with x and y any integer. |
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+0
5
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| 5, 29, 53, 101, 149, 173, 197, 269, 293, 317, 389, 461, 509, 557, 653, 677, 701, 773, 797, 821, 941, 1013, 1061, 1109, 1181, 1229, 1277, 1301, 1373, 1493, 1613, 1637, 1709, 1733, 1877, 1901, 1949, 1973, 1997, 2069, 2141, 2213, 2237, 2309, 2333
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Discriminant=-96. See A106856 for more information.
Primes = 5, 29, 53, or 77 (mod 96).
Also primes of the forms 5x^2+4xy+20y^2 and 5x^2+2xy+29y^2. See A140633. - T. D. Noe (noe(AT)sspectra.com), May 19 2008
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FORMULA
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Appears to be primes of the form 5+24k. - T. D. Noe, Apr 24 2008
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MATHEMATICA
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Clear[f, lst, p, x, y]; f[x_, y_]:=5*x^2+2*x*y+5*y^2; lst={}; Do[Do[p=f[x, y]; If[PrimeQ[p]&&p<9174, AppendTo[lst, p]], {y, -4!, 6!}], {x, -4!, 6!}]; Take[Union[lst], 140] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 04 2009]
Union[QuadPrimes[5, 2, 5, 10000], QuadPrimes[5, -2, 5, 10000]] (* see A106856 *)
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CROSSREFS
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Sequence in context: A081116 A146829 A141374 this_sequence A147153 A115706 A031394
Adjacent sequences: A107000 A107001 A107002 this_sequence A107004 A107005 A107006
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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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