cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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).

Original entry on oeis.org

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

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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

Keywords

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

Examples

			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)

References

  • Z. I. Borevich and I. R. Shafarevich, Number Theory.

Links

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.

Programs

  • 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 *)
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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