A106864 Primes of the form 2x^2+2xy+3y^2 with x and y nonnegative.

2, 3, 7, 43, 47, 83, 103, 107, 163, 167, 223, 263, 283, 347, 367, 383, 443, 467, 487, 503, 523, 547, 607, 643, 683, 743, 787, 823, 827, 863, 883, 887, 947, 967, 983, 1063, 1087, 1123, 1223, 1303, 1307, 1367, 1423, 1427, 1447, 1483, 1487, 1523, 1583

Offset: 1

Author

T. D. Noe, May 09 2005

Keywords

• nonn
• easy

Comments

See A106865 for all primes represented by this form.

Discriminant=-20.

Union of {2} and primes == 3 or 7 mod 20. - N. J. A. Sloane, Sep 04 2012

References

• David A. Cox, Primes of the Form x^2 + n y^2, Wiley, 1989. See Eq. (2.22), p. 33. - N. J. A. Sloane, Sep 04 2012

Links

• Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Cf. A106865.

Programs

Mathematica

QuadPrimes2[2, 2, 3, 10000] (* see A106856 *)