A140615 Primes of the form 13x^2+6xy+21y^2.

13, 61, 109, 277, 349, 373, 541, 613, 733, 853, 877, 997, 1069, 1117, 1381, 1429, 1597, 1669, 1693, 1789, 1861, 1933, 2053, 2221, 2389, 2437, 2749, 2917, 3109, 3181, 3229, 3253, 3373, 3517, 3541, 3637, 3709, 4021, 4549, 4597, 4813, 4861

Offset: 1

Author

T. D. Noe, May 19 2008

Keywords

• nonn
• easy

Comments

Discriminant=-1056. Also primes of the form 13x^2+2xy+61y^2.

In base 12, the sequence is 11, 51, 91, 1E1, 251, 271, 391, 431, 511, 5E1, 611, 6E1, 751, 791, 971, 9E1, E11, E71, E91, 1051, 10E1, 1151, 1231, 1351, 1471, 14E1, 1711, 1831, 1971, 1X11, 1X51, 1X71, 1E51, 2051, 2071, 2131, 2191, 23E1, 2771, 27E1, 2951, 2991, where X is 10 and E is 11. Moreover, the discriminant is -740. - Walter Kehowski, May 31 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[13, 6, 21, 10000], QuadPrimes2[13, -6, 21, 10000]] (* see A106856 *)