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A141190
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Primes of the form 2*x^2+4*x*y-5*y^2 (as well as of the form 2*x^2+8*x*y+y^2).
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7
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2, 11, 43, 67, 107, 113, 137, 163, 179, 193, 211, 233, 281, 331, 337, 347, 379, 401, 443, 449, 457, 491, 499, 547, 569, 571, 617, 641, 659, 673, 683, 739, 809, 827, 883, 907, 947, 953, 977, 1009, 1019, 1033, 1051, 1129, 1163, 1171, 1187, 1201, 1283, 1289
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OFFSET
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1,1
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COMMENTS
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Discriminant = 56. Class = 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac.
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REFERENCES
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Z. I. Borevich and I. R. Shafarevich, Number Theory.
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LINKS
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EXAMPLE
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a(3) = 43 is in the sequence because we can write 43 = 2*4^2 + 4*4*1 - 5*1^2, or 43 = 2*3^2 + 8*3*1 + 1^2.
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MATHEMATICA
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xy[{x_, y_}]:={2 x^2 + 4 x y - 5 y^2, 2 y^2 + 4 x y - 5 x^2}; Union[Select[Flatten[xy/@Subsets[Range[50], {2}]], #>0&&PrimeQ[#]&]] (* Vincenzo Librandi, Jun 09 2014 *)
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CROSSREFS
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For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.
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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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STATUS
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approved
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