A107144 - OEIS

%I #23 Sep 08 2022 08:45:18

%S 5,13,37,53,157,173,197,277,293,317,373,397,557,613,653,677,733,757,

%T 773,797,853,877,997,1013,1093,1117,1213,1237,1277,1373,1453,1493,

%U 1597,1613,1637,1693,1733,1877,1933,1973,1997,2053,2213,2237,2293

%N Primes of the form 5x^2 + 8y^2.

%C Discriminant = -160. See A107132 for more information.

%C Except for 5, also primes of the form 13x^2 + 8xy + 32y^2. See A140633. - _T. D. Noe_, May 19 2008

%H Vincenzo Librandi and Ray Chandler, <a href="/A107144/b107144.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 Except for 5, the primes are congruent to {13, 37} (mod 40). - _T. D. Noe_, May 02 2008

%t QuadPrimes2[5, 0, 8, 10000] (* see A106856 *)

%o (Magma) [5] cat [ p: p in PrimesUpTo(3000) | p mod 40 in {13, 37} ]; // _Vincenzo Librandi_, Jul 24 2012

%o (PARI) list(lim)=my(v=List([5]),t); forprime(p=13,lim, t=p%40; if(t==13||t==37, listput(v,p))); Vec(v) \\ _Charles R Greathouse IV_, Feb 09 2017

%Y Cf. A139827.

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 13 2005