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

1,1

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)

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

Mathematica

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

Prog

(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
(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

Crossrefs

Cf. A139827.

Sequence in context: A140152 A089536 A019379 * A041969 A295386 A019392

Adjacent sequences: A107163 A107164 A107165 * A107167 A107168 A107169

Keyword

nonn,easy

Author

T. D. Noe, May 13 2005

Status

approved