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 A141772 Primes of the form 3*x^2 + 5*x*y - 5*y^2 (as well as of the form 7*x^2 + 13*x*y + 3*y^2). 2
 3, 5, 7, 17, 23, 37, 73, 97, 107, 113, 163, 167, 173, 193, 197, 227, 233, 277, 283, 313, 317, 337, 347, 367, 397, 487, 503, 547, 607, 617, 643, 653, 673, 677, 683, 743, 787, 823, 827, 853, 857, 877, 887, 907, 947, 983, 997, 1013, 1093, 1117, 1153, 1163, 1187 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Discriminant = 85. Class = 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac. REFERENCES Z. I. Borevich and I. R. Shafarevich, Number Theory. LINKS Table of n, a(n) for n=1..53. 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(1) = 3 because we can write 3 = 3*1^2 + 5*1*0 - 5*0^2 (or 3 = 7*0^2 + 13*0*1 + 3*1^2). CROSSREFS Cf. A141773 (d=85). See also A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141158 (d=20). A141159, A141160 (d=21). A141170, A141171 (d=24). A141172, A141173 (d=28). A141174, A141175 (d=32). A141176, A141177 (d=33). A141178 (d=37). A141179, A141180 (d=40). A141181 (d=41). A141182, A141183 (d=44). A033212, A141785 (d=45). A068228, A141187 (d=48). A141188 (d=52). A141189 (d=53). A141190, A141191 (d=56). A141192, A141193 (d=57). A107152, A141302, A141303, A141304 (d=60). A141215 (d=61). A141111, A141112 (d=65). A141750 (d=73). A141161, A141163 (d=148). A141165, A141166 (d=229). A141167, A141168 (d=257). Sequence in context: A331894 A357234 A086086 * A220454 A257592 A032496 Adjacent sequences: A141769 A141770 A141771 * A141773 A141774 A141775 KEYWORD nonn AUTHOR Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (sergarmor(AT)yahoo.es), Jul 04 2008 EXTENSIONS More terms from Colin Barker, Apr 04 2015 Typo in crossrefs fixed by Colin Barker, Apr 05 2015 STATUS approved

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Last modified December 5 03:48 EST 2023. Contains 367567 sequences. (Running on oeis4.)