A107179 - OEIS

%I #21 Sep 08 2022 08:45:18

%S 5,19,59,61,101,131,139,181,229,251,269,349,419,461,509,619,661,691,

%T 811,829,859,941,971,1021,1069,1091,1109,1181,1259,1291,1301,1459,

%U 1531,1571,1669,1699,1741,1811,1861,1931,1949,1979,2029,2099,2131

%N Primes of the form 5x^2 + 14y^2.

%C Discriminant = -280. See A107132 for more information.

%H Vincenzo Librandi and Ray Chandler, <a href="/A107179/b107179.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 {5, 19, 59, 61, 69, 101, 131, 139, 171, 181, 229, 251, 269} (mod 280). - _T. D. Noe_, May 02 2008

%t QuadPrimes2[5, 0, 14, 10000] (* see A106856 *)

%o (Magma) [ p: p in PrimesUpTo(3000) | p mod 280 in {5, 19, 59, 61, 69, 101, 131, 139, 171, 181, 229, 251, 269} ]; // _Vincenzo Librandi_, Jul 26 2012

%o (PARI) list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\5), w=5*x^2; for(y=0, sqrtint((lim-w)\14), if(isprime(t=w+14*y^2), listput(v,t)))); Set(v) \\ _Charles R Greathouse IV_, Feb 10 2017

%Y Cf. A139827.

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 13 2005