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A141181
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Primes of the form 2*x^2+3*x*y-4*y^2 (as well as of the form 2*x^2+7*x*y+y^2).
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5
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2, 5, 23, 31, 37, 41, 43, 59, 61, 73, 83, 103, 107, 113, 127, 131, 139, 163, 173, 197, 223, 241, 251, 269, 271, 277, 283, 307, 337, 349, 353, 359, 367, 373, 379, 389, 401, 409, 419, 431, 433, 443, 449, 461, 467, 487, 491, 523, 541, 569, 599, 607, 613, 617, 619
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OFFSET
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1,1
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COMMENTS
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Discriminant = 41. Class = 1. 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(3) = 23 because we can write 23 = 2*3^2+3*3*1-4*1^2 (or 23 = 2*2^2+7*2*1+1^2).
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MATHEMATICA
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Reap[For[p = 2, p < 1000, p = NextPrime[p], If[FindInstance[p == 2*x^2 + 3*x*y - 4*y^2, {x, y}, Integers, 1] =!= {}, Print[p]; Sow[p]]]][[2, 1]] (* Jean-François Alcover, Oct 25 2016 *)
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PROG
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(PARI) select(p->isprime(p)&&qfbsolve(Qfb(1, 7, 2), p), [1..1500]) \\ This is to provide a generic characteristic function ("is_A141181") as 1st arg of select(), there are other ways to produce the sequence more efficiently. - M. F. Hasler, Jan 15 2016
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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,changed
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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 12 2008
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STATUS
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approved
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