A107199 Primes of the form 5x^2 + 17y^2.

5, 17, 37, 73, 97, 113, 173, 193, 197, 233, 277, 313, 317, 337, 397, 617, 653, 673, 677, 853, 857, 877, 997, 1013, 1093, 1117, 1153, 1193, 1213, 1217, 1297, 1433, 1493, 1553, 1637, 1693, 1697, 1873, 1877, 1933, 2017, 2113, 2137, 2153, 2213

Offset

1,1

Comments

Discriminant = -340. 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 {5, 17, 37, 57, 73, 97, 113, 133, 173, 177, 193, 197, 233, 277, 313, 317, 333, 337} (mod 340). - T. D. Noe, May 02 2008

Mathematica

QuadPrimes2[5, 0, 17, 10000] (* see A106856 *)

Prog

(Magma) [ p: p in PrimesUpTo(4000) | p mod 340 in {5, 17, 37, 57, 73, 97, 113, 133, 173, 177, 193, 197, 233, 277, 313, 317, 333, 337}]; // Vincenzo Librandi, Jul 28 2012
(PARI) list(lim)=my(v=List([5]), s=[17, 37, 57, 73, 97, 113, 133, 173, 177, 193, 197, 233, 277, 313, 317, 333, 337]); forprime(p=17, lim, if(setsearch(s, p%340), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 10 2017

Crossrefs

Cf. A139827.

Sequence in context: A146781 A338277 A348228 * A048209 A181423 A146874

Adjacent sequences: A107196 A107197 A107198 * A107200 A107201 A107202

Keyword

nonn,easy

Author

T. D. Noe, May 13 2005

Status

approved