A107166 Primes of the form 2x^2 + 29y^2.

2, 29, 31, 37, 47, 61, 79, 101, 127, 157, 191, 229, 263, 269, 271, 293, 311, 317, 359, 367, 389, 421, 461, 479, 503, 541, 599, 607, 653, 677, 727, 733, 743, 751, 757, 773, 797, 823, 829, 839, 853, 887, 911, 967, 983, 997, 1013, 1061, 1063, 1087, 1117

Offset: 1

Author

T. D. Noe, May 13 2005

Keywords

• nonn
• easy

Comments

Discriminant = -232. 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

[ p: p in PrimesUpTo(2000) | p mod 232 in {2, 15, 21, 29, 31, 37, 39, 47, 55, 61, 69, 77, 79, 85, 95, 101, 119, 127, 133, 135, 143, 157, 159, 189, 191, 205, 213, 215, 221, 229} ]; // Vincenzo Librandi, Jul 25 2012

Mathematica

QuadPrimes2[2, 0, 29, 10000] (* see A106856 *)

PARI

list(lim)=my(v=List([2]), s=[15, 21, 29, 31, 37, 39, 47, 55, 61, 69, 77, 79, 85, 95, 101, 119, 127, 133, 135, 143, 157, 159, 189, 191, 205, 213, 215, 221, 229]); forprime(p=29, lim, if(setsearch(s, p%232), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 10 2017

Formula

The primes are congruent to {2, 15, 21, 29, 31, 37, 39, 47, 55, 61, 69, 77, 79, 85, 95, 101, 119, 127, 133, 135, 143, 157, 159, 189, 191, 205, 213, 215, 221, 229} (mod 232). - T. D. Noe, May 02 2008