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A142956
Primes of the form -3*x^2 + 4*x*y + 5*y^2 (as well as of the form 6*x^2 + 10*x*y + y^2).
1
5, 17, 61, 73, 101, 137, 149, 157, 197, 229, 233, 277, 313, 349, 353, 389, 397, 457, 461, 541, 557, 577, 593, 613, 617, 653, 701, 709, 733, 757, 761, 769, 809, 821, 853, 881, 929, 937, 997, 1013, 1033, 1049, 1061, 1069, 1109, 1201, 1213, 1217, 1277, 1289
OFFSET
1,1
COMMENTS
Discriminant = 76. 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. Academic Press, NY, 1966.
LINKS
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(2) = 17 because we can write 17 = -3*3^2 + 4*3*2 + 5*2^2 (or 17 = 6*1^2 + 10*1*1 + 1^2).
MATHEMATICA
Reap[For[p = 2, p < 2000, p = NextPrime[p], If[FindInstance[p == -3*x^2 + 4*x*y + 5*y^2, {x, y}, Integers, 1] =!= {}, Print[p]; Sow[p]]]][[2, 1]] (* Jean-François Alcover, Oct 25 2016 *)
CROSSREFS
Cf. A142955 (d=76). A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65).
Sequence in context: A149661 A146130 A026619 * A273422 A192146 A273607
KEYWORD
nonn
AUTHOR
Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (laucabfer(AT)alum.us.es), Jul 14 2008
EXTENSIONS
More terms from Colin Barker, Apr 05 2015
Edited by M. F. Hasler, Feb 18 2022
STATUS
approved