A139829 - OEIS

%I #20 Sep 08 2022 08:45:33

%S 11,19,59,131,139,179,211,251,331,379,419,491,499,571,619,659,691,739,

%T 811,859,971,1019,1051,1091,1171,1259,1291,1451,1459,1499,1531,1571,

%U 1579,1619,1699,1811,1931,1979,2011,2099,2131,2179,2251,2339,2371

%N Primes of the form 4x^2+4xy+11y^2.

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

%C Also, primes of form u^2+10v^2 with odd v, while A107145 has even v. One can transform its form as (2x+y)^2+10y^2 (where y can only be odd) and the latter is x^2+10(2y)^2. This sequence has primes {11,19} mod 20 while the second has {1,9} mod 20 and together they are the primes x^2+10y^2 (A033201) which are {1,9,11,20} mod 20. [From _Tito Piezas III_, Jan 01 2009]

%H Vincenzo Librandi and Ray Chandler, <a href="/A139829/b139829.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 {11, 19} (mod 40).

%t QuadPrimes2[4, -4, 11, 10000] (* see A106856 *)

%o (Magma) [ p: p in PrimesUpTo(3000) | p mod 40 in {11, 19}]; // _Vincenzo Librandi_, Jul 29 2012

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 02 2008