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A142956
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Primes of the form -3*x^2 + 4*x*y + 5*y^2 (as well as of the form 6*x^2 + 10*x*y + y^2).
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1
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5, 17, 61, 73, 101, 137, 149, 157, 197, 229, 233, 277, 313, 349, 353, 389, 397, 457, 461, 541, 557, 577, 593, 613, 617, 653, 701, 709, 733, 757, 761, 769, 809, 821, 853, 881, 929, 937, 997, 1013, 1033, 1049, 1061, 1069, 1109, 1201, 1213, 1217, 1277, 1289
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OFFSET
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1,1
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COMMENTS
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Discriminant = 76. 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. Academic Press, NY, 1966.
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LINKS
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EXAMPLE
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a(2) = 17 because we can write 17 = -3*3^2 + 4*3*2 + 5*2^2 (or 17 = 6*1^2 + 10*1*1 + 1^2).
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MATHEMATICA
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Reap[For[p = 2, p < 2000, p = NextPrime[p], If[FindInstance[p == -3*x^2 + 4*x*y + 5*y^2, {x, y}, Integers, 1] =!= {}, Print[p]; Sow[p]]]][[2, 1]] (* Jean-François Alcover, Oct 25 2016 *)
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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 (laucabfer(AT)alum.us.es), Jul 14 2008
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EXTENSIONS
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STATUS
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approved
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