A107188 - OEIS

%I #20 Sep 08 2022 08:45:18

%S 13,19,37,67,109,163,229,307,331,349,379,397,421,499,541,613,619,643,

%T 661,691,709,733,739,787,811,853,877,1021,1051,1123,1237,1549,1579,

%U 1597,1627,1669,1723,1747,1789,1861,1867,1987,2179,2203,2221,2251

%N Primes of the form 6x^2 + 13y^2.

%C Discriminant = -312. See A107132 for more information.

%H Vincenzo Librandi and Ray Chandler, <a href="/A107188/b107188.txt">Table of n, a(n) for n = 1..10000</a> [First 1000 terms from Vincenzo Librandi]

%H N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)

%F The primes are congruent to {13, 19, 37, 67, 85, 109, 115, 163, 187, 229, 253, 301, 307} (mod 312). - _T. D. Noe_, May 02 2008

%t QuadPrimes2[6, 0, 13, 10000] (* see A106856 *)

%o (Magma) [ p: p in PrimesUpTo(3000) | p mod 312 in {13, 19, 37, 67, 85, 109, 115, 163, 187, 229, 253, 301, 307} ]; // _Vincenzo Librandi_, Jul 26 2012

%o (PARI) list(lim)=my(v=List([13]), s=[19, 37, 67, 85, 109, 115, 163, 187, 229, 253, 301, 307]); forprime(p=19, lim, if(setsearch(s, p%312), listput(v, p))); Vec(v) \\ _Charles R Greathouse IV_, Feb 10 2017

%Y Cf. A139827.

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 13 2005