A107167 Primes of the form 5x^2 + 12y^2.

5, 17, 53, 113, 137, 173, 197, 233, 257, 293, 317, 353, 557, 593, 617, 653, 677, 773, 797, 857, 953, 977, 1013, 1097, 1193, 1217, 1277, 1373, 1433, 1493, 1553, 1613, 1637, 1697, 1733, 1877, 1913, 1973, 1997, 2153, 2213, 2237, 2273, 2297, 2333

Offset

1,1

Comments

Discriminant = -240. 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

Except for 5, the primes are congruent to {17, 53} (mod 60). - T. D. Noe, May 02 2008

Mathematica

QuadPrimes2[5, 0, 12, 10000] (* see A106856 *)

Prog

(Magma) [5] cat [p: p in PrimesUpTo(3000) | p mod 60 in [17, 53]]; // Vincenzo Librandi, Jul 25 2012
(PARI) list(lim)=my(v=List([5]), t); forprime(p=17, lim, t=p%60; if(t==17||t==53, listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 10 2017

Crossrefs

Cf. A139827.

Sequence in context: A037544 A090575 A191139 * A201478 A176470 A240693

Adjacent sequences: A107164 A107165 A107166 * A107168 A107169 A107170

Keyword

nonn,easy

Author

T. D. Noe, May 13 2005

Status

approved