A139830 - OEIS

%I #17 Sep 08 2022 08:45:33

%S 7,23,47,103,127,167,223,263,367,383,463,487,503,607,647,727,743,823,

%T 863,887,967,983,1063,1087,1103,1223,1303,1327,1367,1423,1447,1487,

%U 1543,1567,1583,1607,1663,1783,1823,1847,2063,2087,2143,2207,2287

%N Primes of the form 7x^2+6xy+7y^2.

%C Discriminant=-160. See A139827 for more information.

%C Also primes of the forms 7x^2+2xy+23y^2 and 7x^2+4xy+12y^2. See A140633. - _T. D. Noe_, May 19 2008

%H Vincenzo Librandi and Ray Chandler, <a href="/A139830/b139830.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 {7, 23} (mod 40).

%t Union[QuadPrimes2[7, 6, 7, 10000], QuadPrimes2[7, -6, 7, 10000]] (* see A106856 *)

%o (Magma) [ p: p in PrimesUpTo(3000) | p mod 40 in {7, 23}]; // _Vincenzo Librandi_, Jul 29 2012

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 02 2008