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A141336
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Primes of the form 2*x^2+6*x*y-7*y^2 (as well as of the form 2*x^2+10*x*y+y^2).
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2
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2, 13, 29, 41, 73, 101, 173, 193, 197, 233, 257, 269, 277, 317, 349, 353, 397, 409, 449, 461, 509, 541, 577, 593, 601, 653, 673, 761, 809, 821, 829, 853, 857, 877, 929, 997, 1013, 1021, 1061, 1093, 1097, 1117, 1129, 1153, 1181, 1237, 1277, 1289, 1297, 1301
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OFFSET
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1,1
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COMMENTS
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Discriminant = 92. 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.
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REFERENCES
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Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, NY, 1966.
D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.
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LINKS
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EXAMPLE
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a(2)=13 because we can write 13=2*2^2+6*2*1-7*1^2 (or 13=2*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 == 2*x^2 + 6*x*y - 7*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 (oscfalgan(AT)yahoo.es), Jun 25 2008
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EXTENSIONS
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STATUS
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approved
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