A107189 - OEIS

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

%S 3,29,53,101,107,131,173,179,251,269,347,389,419,443,467,491,563,653,

%T 659,677,701,797,971,1013,1091,1109,1187,1277,1283,1301,1427,1499,

%U 1613,1637,1667,1733,1811,1901,1907,1949,1973,1979,2003,2027,2141

%N Primes of the form 3x^2 + 26y^2.

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

%H Vincenzo Librandi and Ray Chandler, <a href="/A107189/b107189.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 {3, 29, 35, 53, 77, 101, 107, 131, 155, 173, 179, 251, 269} (mod 312). - _T. D. Noe_, May 02 2008

%t QuadPrimes2[3, 0, 26, 10000] (* see A106856 *)

%o (Magma) [ p: p in PrimesUpTo(3000) | p mod 312 in {3, 29, 35, 53, 77, 101, 107, 131, 155, 173, 179, 251, 269} ]; // _Vincenzo Librandi_, Jul 28 2012

%o (PARI) list(lim)=my(v=List([3]), s=[29, 35, 53, 77, 101, 107, 131, 155, 173, 179, 251, 269]); forprime(p=29, 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