A140620 Primes of the form 23x^2+4xy+68y^2.

23, 263, 503, 647, 887, 1223, 1583, 1823, 1847, 2063, 2207, 2447, 2687, 2903, 3407, 3527, 3623, 3767, 4007, 4463, 4703, 4943, 4967, 5087, 5303, 5807, 5903, 5927, 6263, 6863, 7127, 7487, 7583, 7823, 8087, 8423, 8447, 9623, 9767, 10007, 10247

Offset: 1

Author

T. D. Noe, May 19 2008

Keywords

• nonn
• easy

Comments

Discriminant=-6240. Also primes of the form 23x^2+18xy+207y^2.

In base 12, the sequence is 1E, 19E, 35E, 45E, 61E, 85E, XEE, 107E, 109E, 123E, 133E, 14EE, 167E, 181E, 1E7E, 205E, 211E, 221E, 239E, 26EE, 287E, 2X3E, 2X5E, 2E3E, 309E, 343E, 34EE, 351E, 375E, 3E7E, 415E, 43EE, 447E, 463E, 481E, 4X5E, 4X7E, 569E, 579E, 595E, 5E1E, where X is 10 and E is 11. Moreover, the discriminant is -3740. - Walter Kehowski, Jun 01 2008

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. A140633.

Programs

Mathematica

Union[QuadPrimes2[23, 4, 68, 10000], QuadPrimes2[23, -4, 68, 10000]] (* see A106856 *)