A141192 Primes of the form 3*x^2+3*x*y-4*y^2 (as well as of the form 8*x^2+11*x*y+2*y^2).

2, 3, 29, 41, 53, 59, 71, 89, 107, 113, 167, 173, 179, 227, 257, 269, 281, 293, 317, 383, 401, 431, 449, 509, 521, 563, 569, 599, 641, 659, 677, 683, 743, 773, 797, 827, 839, 857, 863, 887, 911, 941, 953, 971, 977, 983, 1019, 1091, 1097, 1181, 1193, 1229, 1283, 1307, 1319

Offset

1,1

Comments

Discriminant = 57. Class = 2. Binary quadratic forms a*x^2+b*x*y+c*y^2 have discriminant d=b^2-4ac and gcd(a,b,c)=1

p = 3 and primes p = 2 mod 3 such that 57 is a square mod p. - 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)

D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.

Example

a(6)=59 because we can write 59=3*7^2+3*7*8-4*8^2 (or 59=8*1^2+11*1*3+2*3^2)

Mathematica

Select[Prime[Range[250]], # == 3 || MatchQ[Mod[#, 57], Alternatives[2, 8, 14, 29, 32, 41, 50, 53, 56]]&] (* Jean-François Alcover, Oct 28 2016 *)

Crossrefs

Cf. A141193 (d=57). A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65).

Primes in A243192.

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: A042335 A218995 A284649 * A215135 A059453 A235481

Adjacent sequences: A141189 A141190 A141191 * A141193 A141194 A141195

Keyword

nonn

Author

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

Status

approved