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Search: id:A141172
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| A141172 |
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Primes of the form 2*x^2+2*x*y-3*y^2 (as well as of the form 2*x^2+6*x*y+y^2). |
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7
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| 2, 29, 37, 53, 109, 113, 137, 149, 193, 197, 233, 277, 281, 317, 337, 373, 389, 401, 421, 449, 457, 541, 557, 569, 613, 617, 641, 653, 673, 701, 709, 757, 809, 821, 877, 953, 977
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OFFSET
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1,1
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COMMENT
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Discriminant = 28. 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
Contribution from Tito Piezas III (tpiezas(AT)gmail.com), Dec 28 2008: (Start)
Also, primes of form u^2-7v^2. The transformation {u,v}={3x+y,x} yields the second quadratic form given in the title. (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)=29 because we can write 29=2*4^2+2*4*3-3*3^2 (or
29=2*1^2+6*1*3+3^2)
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CROSSREFS
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Cf. A141173 (d=28) A038872 (d=5). A141131 (d=8). A141122, A141123 (d=12). A038883 (d=13). A038889 (d=17): A141111, A141112 (d=65).
Sequence in context: A041969 A019392 A060503 this_sequence A139833 A059700 A078329
Adjacent sequences: A141169 A141170 A141171 this_sequence A141173 A141174 A141175
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KEYWORD
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nonn
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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 (marcanmar(AT)alum.us.es), Jun 12 2008
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