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Search: id:A107006
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| A107006 |
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Primes of the form 4x^2-4xy+7y^2, with x and y nonnegative. |
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+0
14
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| 7, 31, 79, 103, 127, 151, 199, 223, 271, 367, 439, 463, 487, 607, 631, 727, 751, 823, 919, 967, 991, 1039, 1063, 1087, 1231, 1279, 1303, 1327, 1399, 1423, 1447, 1471, 1543, 1567, 1663, 1759, 1783, 1831, 1879, 1951, 1999, 2143, 2239, 2287, 2311
(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.
Also, primes of the form 24n+7. - Artur Jasinski (grafix(AT)csl.pl), Nov 25 2007 [See the Reble link]
Also primes of the forms 4x^2+4xy+7y^2, 7x^2+6xy+15y^2, 7x^2+2xy+7y^2 and 7x^2+4xy+28y^2. See A140633. - T. D. Noe (noe(AT)sspectra.com), May 19 2008
Contribution from Tito Piezas III (tpiezas(AT)gmail.com), Jan 01 2009: (Start)
Also, primes of form u^2+6v^2 with odd v while sequence A107008 is even v. This can be seen by expressing its form as (2x-y)^2+6y^2 (where y can only be odd) while the latter is x^2+6(2y)^2. Additionally, this sequence is 7 mod 24 while the second is 1 mod 24 and together, they are the primes of form x^2+6y^2 (A033199) which are either {1,7} mod 24.
(End)
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LINKS
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Don Reble, Notes on this sequence
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MATHEMATICA
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a = {}; Do[If[PrimeQ[24n + 7], AppendTo[a, 24n + 7]], {n, 0, 100}]; a - Artur Jasinski (grafix(AT)csl.pl), Nov 25 2007
QuadPrimes[4, -4, 7, 10000] (* see A106856 *)
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CROSSREFS
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Cf. A124477.
Sequence in context: A090684 A033199 A003550 this_sequence A107005 A164621 A118934
Adjacent sequences: A107003 A107004 A107005 this_sequence A107007 A107008 A107009
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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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