A139849 Primes of the form 10x^2 + 10xy + 13y^2.

13, 73, 97, 157, 313, 397, 433, 577, 733, 853, 937, 997, 1153, 1237, 1657, 1693, 1753, 1777, 1993, 2113, 2593, 2617, 2677, 2833, 2917, 2953, 3037, 3253, 3373, 3433, 3457, 3517, 3673, 3793, 3853, 3877, 4093, 4177, 4273, 4297, 4357, 4513

Offset

1,1

Comments

Discriminant = -420. See A139827 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 {13, 73, 97, 157, 313, 397} (mod 420).

Mathematica

QuadPrimes2[10, -10, 13, 10000] (* see A106856 *)

Prog

(Magma) [ p: p in PrimesUpTo(6000) | p mod 420 in {13, 73, 97, 157, 313, 397}]; // Vincenzo Librandi, Jul 29 2012
(PARI) list(lim)=my(v=List(), s=[13, 73, 97, 157, 313, 397]); forprime(p=13, lim, if(setsearch(s, p%420), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 10 2017

Crossrefs

Sequence in context: A300028 A322478 A107141 * A139911 A097460 A336796

Adjacent sequences: A139846 A139847 A139848 * A139850 A139851 A139852

Keyword

nonn,easy

Author

T. D. Noe, May 02 2008

Extensions

Corrected and extended b-file - Ray Chandler, Jul 29 2014

Status

approved