%I #30 Aug 13 2016 00:29:03
%S 5,11,31,89,179,181,191,331,401,419,421,449,521,599,619,641,709,719,
%T 829,859,911,971,991,1021,1039,1109,1259,1291,1301,1489,1511,1549,
%U 1621,1709,1831,1871,1879,2011,2039,2099,2161,2179,2281,2311,2381
%N Primes of the form 4x^2+3xy+4y^2, with x and y any integer.
%C Discriminant=-55.
%C Primes p such that x^4 - 2x^3 + x - 1 has no integer roots modulo p^2. According to the Bunyakovsky conjecture, there are infinitely many such primes. - _Griffin N. Macris_, Jul 21 2016
%H Vincenzo Librandi and Ray Chandler, <a href="/A106908/b106908.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)
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Bunyakovsky_conjecture">Bunyakovsky conjecture</a>
%e 89 is in the sequence since it is prime and with x=5 and y=-1, 4x^2 + 3xy + 4y^2 = 4*5^2 + 3*5*(-1) + 4*(-1)^2 = 100 - 15 + 4 = 89. - _Michael B. Porter_, Jul 22 2016
%p N:= 10000: # to get all terms <= N
%p S:= {}:
%p for y from 0 to floor(sqrt(16*N/55)) do
%p s:= floor(sqrt(16*N-55*y^2));
%p S:= S union select(isprime, {seq(4*x^2 + 3*x*y + 4*y^2,
%p x = ceil((-s-3*y)/8) .. floor((s-3*y)/8))})
%p od:
%p sort(convert(S,list)); # _Robert Israel_, Jul 21 2016
%t Union[QuadPrimes2[4, 3, 4, 10000], QuadPrimes2[4, -3, 4, 10000]] (* see A106856 *)
%K nonn,easy
%O 1,1
%A _T. D. Noe_, May 09 2005