A107138 Primes of the form 3x^2 + 11y^2.

3, 11, 23, 47, 59, 71, 179, 191, 251, 311, 383, 419, 443, 467, 587, 599, 647, 683, 719, 839, 863, 911, 947, 971, 983, 1103, 1259, 1307, 1367, 1439, 1499, 1511, 1523, 1571, 1607, 1787, 1871, 1907, 2003, 2027, 2039, 2099, 2267, 2399, 2423, 2447, 2531

Offset

1,1

Comments

Discriminant = -132. 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 {3, 11, 23, 47, 59, 71, 119} (mod 132). - T. D. Noe, May 02 2008

Mathematica

QuadPrimes2[3, 0, 11, 10000] (* see A106856 *)

Prog

(Magma) [ p: p in PrimesUpTo(3000) | p mod 132 in {3, 11, 23, 47, 59, 71, 119} ]; // Vincenzo Librandi, Jul 24 2012
(PARI) list(lim)=my(v=List([3]), s=[11, 23, 47, 59, 71, 119]); forprime(p=11, lim, if(setsearch(s, p%132), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 09 2017

Crossrefs

Cf. A139827.

Sequence in context: A294368 A296556 A141187 * A145473 A335677 A248348

Adjacent sequences: A107135 A107136 A107137 * A107139 A107140 A107141

Keyword

nonn,easy

Author

T. D. Noe, May 13 2005

Status

approved