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A141182
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Primes of the form x^2+6*x*y-2*y^2 (as well as of the form 5*x^2+8*x*y+y^2).
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7
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5, 37, 53, 89, 97, 113, 137, 157, 181, 229, 257, 269, 313, 317, 353, 389, 397, 401, 421, 433, 449, 509, 521, 577, 617, 641, 653, 661, 709, 757, 773, 797, 829, 881, 929, 977, 1013, 1021, 1049, 1061, 1093, 1109, 1153, 1181, 1193, 1213, 1237, 1277, 1301, 1321, 1373
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OFFSET
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1,1
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COMMENTS
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Discriminant = 44. Class = 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac.
Also, primes of the form u^2 - 11v^2. The transformation {u, v} = {x+3y, y} yields the form in the title. - Tito Piezas III, Dec 28 2008
Also primes p == 1 (mod 4) and == 1, 3, 4, 5 or 9 (mod 11). - Juan Arias-de-Reyna, Mar 20 2011.
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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)=53 because we can write 53=5^2+6*5*1-2*1^2 (or 53=5*1^2+8*1*4+4^2)
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MATHEMATICA
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Select[Prime[Range[250]], MatchQ[Mod[#, 44], Alternatives[1, 5, 9, 25, 37]] &] (* Jean-François Alcover, Oct 28 2016 *)
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PROG
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(PARI) isA141182(p) = p%4==1 & issquare(Mod(p, 11)) \\ M. F. Hasler, Mar 20 2011
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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 (lourdescm84(AT)hotmail.com), Jun 12 2008
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STATUS
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approved
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