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 A141182 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). 7
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. REFERENCES Z. I. Borevich and I. R. Shafarevich, Number Theory. LINKS Juan Arias-de-Reyna, Table of n, a(n) for n = 1..10000 N. J. A. Sloane et al., Binary Quadratic Forms and OEIS: Index to related sequences, programs, references. OEIS wiki, June 2014. D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981. EXAMPLE 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) MATHEMATICA Select[Prime[Range[250]], MatchQ[Mod[#, 44], Alternatives[1, 5, 9, 25, 37]] &] (* Jean-François Alcover, Oct 28 2016 *) PROG (PARI) isA141182(p) = p%4==1 & issquare(Mod(p, 11)) \\ M. F. Hasler, Mar 20 2011 CROSSREFS Cf. A141183 (d=44), A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17): A141111, A141112 (d=65). Cf. also A243166. For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link. Sequence in context: A144960 A173826 A071680 * A127589 A244374 A238477 Adjacent sequences: A141179 A141180 A141181 * A141183 A141184 A141185 KEYWORD nonn AUTHOR 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 STATUS approved

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Last modified December 7 11:41 EST 2023. Contains 367656 sequences. (Running on oeis4.)