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A141375
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Primes of the form x^2 + 8*x*y - 8*y^2 (as well as of the form x^2 + 10*x*y + y^2).
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4
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73, 97, 193, 241, 313, 337, 409, 433, 457, 577, 601, 673, 769, 937, 1009, 1033, 1129, 1153, 1201, 1249, 1297, 1321, 1489, 1609, 1657, 1753, 1777, 1801, 1873, 1993, 2017, 2089, 2113, 2137, 2161, 2281, 2377, 2473, 2521, 2593, 2617, 2689, 2713, 2833, 2857
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OFFSET
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1,1
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COMMENTS
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Discriminant = +96.
x^2 + 8*x*y - 8*y^2 = (x+4*y)^2 - 24*y^2, and x^2 + 10*x*y + y^2 = (x+5*y)^2 - 24*y^2, so this sequence is also primes of the form x^2 - 24*y^2. - Michael Somos, Jun 05 2013
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REFERENCES
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Z. I. Borevich and I. R. Shafarevich. Number Theory. Academic Press. 1966.
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LINKS
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EXAMPLE
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a(1) = 73 because we can write 73 = 5^2 + 8*5*2 - 8*2^2 (or 73 = 2^2 + 10*2*3 + 3^2).
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MATHEMATICA
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Union[Select[Flatten[Table[x^2 + 8*x*y - 8*y^2, {x, 40}, {y, 40}]], # > 0 && PrimeQ[#] &]] (* T. D. Noe, Jun 12 2013 *)
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CROSSREFS
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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 (oscfalgan(AT)yahoo.es), Jun 28 2008
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EXTENSIONS
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STATUS
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approved
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