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Search: id:A141175
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| A141175 |
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Primes of the form -x^2+4*x*y+4*y^2 (as well as of the form 7*x^2+12*x*y+4*y^2). |
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+0
8
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| 7, 23, 31, 47, 71, 79, 103, 127, 151, 167, 191, 199, 223, 239, 263, 271, 311, 359, 367, 383, 431, 439, 463, 479, 487, 503, 599, 607, 631, 647, 719, 727, 743, 751, 823, 839, 863, 887, 911, 919, 967, 983, 991
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Discriminant = 32. Class = 2. Binary quadratic forms a*x^2+b*x*y+c*y^2 have discriminant d=b^2-4ac and gcd(a,b,c)=1
Values of the quadratic form are {0,4,7} mod 8, so this is a subset of A007522. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 30 2008
Is this the same sequence as A007522?
Contribution from Tito Piezas III (tpiezas(AT)gmail.com), Dec 28 2008: (Start)
As this is a subset of A141131, this is also a subset of the primes of form x^2-2y^2. (End)
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REFERENCES
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Borevich and Shafaewich, Number Theory.
D. B. Zagier, Zetafunktionen und quadratische Koerper.
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EXAMPLE
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a(2)=23 because we can write 23=-1^2+4*1*2+4*2^2 (or 23=7*1^2+12*1*1+4*1^2)
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CROSSREFS
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Cf. A141174 (d=32), A007522 (Primes of form 8n+7.) A038872 (d=5). A141131 (d=8). A141122, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65).
Sequence in context: A004628 A089199 A014663 this_sequence A007522 A157811 A098029
Adjacent sequences: A141172 A141173 A141174 this_sequence A141176 A141177 A141178
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KEYWORD
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nonn,more
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AUTHOR
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Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (oscfalgan(AT)yahoo.es), Jun 12 2008
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