A107201 Primes of the form 8x^2 + 11y^2.

11, 19, 43, 83, 107, 131, 139, 211, 227, 283, 307, 347, 491, 523, 547, 563, 571, 659, 739, 787, 811, 827, 1019, 1051, 1091, 1163, 1187, 1283, 1427, 1451, 1459, 1531, 1579, 1619, 1627, 1667, 1723, 1811, 1867, 1931, 1979, 1987, 2131, 2243, 2251

Offset: 1

Author

T. D. Noe, May 13 2005

Keywords

• nonn
• easy

Comments

Discriminant = -352. See A107132 for more information.

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. A139827.

Programs

Magma

[11] cat[ p: p in PrimesUpTo(4000) | p mod 88 in {19, 35, 43, 51, 83}]; // Vincenzo Librandi, Jul 28 2012

Mathematica

QuadPrimes2[8, 0, 11, 10000] (* see A106856 *)

PARI

list(lim)=my(v=List([11]), s=[19, 35, 43, 51, 83]); forprime(p=19, lim, if(setsearch(s, p%88), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 10 2017

Formula

Except for 11, the primes are congruent to {19, 35, 43, 51, 83} (mod 88). - T. D. Noe, May 02 2008