A107147 Primes of the form 3x^2 + 14y^2.

3, 17, 41, 59, 83, 89, 131, 227, 251, 257, 353, 419, 467, 521, 563, 587, 593, 761, 857, 881, 929, 971, 1049, 1091, 1097, 1193, 1217, 1259, 1307, 1361, 1427, 1433, 1553, 1571, 1601, 1697, 1721, 1811, 1889, 1907, 1931, 1979, 2099, 2243, 2267, 2273

Offset

1,1

Comments

Discriminant = -168. 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, 17, 41, 59, 83, 89, 131} (mod 168). - T. D. Noe, May 02 2008

Mathematica

QuadPrimes2[3, 0, 14, 10000] (* see A106856 *)

Prog

(Magma) [ p: p in PrimesUpTo(3000) | p mod 168 in {3, 17, 41, 59, 83, 89, 131} ]; // Vincenzo Librandi, Jul 24 2012
(PARI) list(lim)=my(v=List([3]), s=[17, 41, 59, 83, 89, 131]); forprime(p=17, lim, if(setsearch(s, p%168), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 09 2017

Crossrefs

Cf. A139827.

Sequence in context: A196781 A298232 A340463 * A049078 A209544 A146821

Adjacent sequences: A107144 A107145 A107146 * A107148 A107149 A107150

Keyword

nonn,easy

Author

T. D. Noe, May 13 2005

Status

approved