A139843 Primes of the form 6x^2 + 17y^2.

17, 23, 41, 71, 113, 167, 233, 311, 401, 431, 449, 479, 503, 521, 617, 641, 719, 743, 809, 839, 857, 881, 887, 911, 929, 983, 1031, 1049, 1151, 1193, 1217, 1289, 1319, 1367, 1433, 1439, 1553, 1559, 1601, 1697, 1847, 2063, 2081, 2111, 2153, 2207

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant = -408. See A139827 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)

Programs

Magma

[ p: p in PrimesUpTo(3000) | p mod 408 in {17, 23, 41, 65, 71, 95, 113, 143, 167, 209, 215, 233, 311, 329, 335, 377, 401}]; // Vincenzo Librandi, Jul 29 2012

Mathematica

QuadPrimes2[6, 0, 17, 10000] (* see A106856 *)

PARI

list(lim)=my(v=List([17]), s=[23, 41, 65, 71, 95, 113, 143, 167, 209, 215, 233, 311, 329, 335, 377, 401]); forprime(p=23, lim, if(setsearch(s, p%408), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 10 2017

Formula

The primes are congruent to {17, 23, 41, 65, 71, 95, 113, 143, 167, 209, 215, 233, 311, 329, 335, 377, 401} (mod 408).