cp's OEIS Frontend

A243701 Primes represented by the indefinite quadratic form x^2 + 13xy - 9y^2.

%I A243701 #21 May 04 2024 10:29:54
%S A243701 5,59,131,139,241,269,271,359,409,541,569,599,661,701,761,859,881,911,
%T A243701 941,1021,1091,1109,1291,1399,1439,1481,1549,1559,1579,1609,1619,1931,
%U A243701 1999,2011,2029,2089,2099,2111,2141,2251,2399,2459,2521,2711,2729,2731,2749
%N A243701 Primes represented by the indefinite quadratic form x^2 + 13xy - 9y^2.
%C A243701 Discriminant 205.
%C A243701 Comment from _Noam D. Elkies_, Jun 14 2014 (See the MathOverflow #171807 link): These are exactly the primes p such that the polynomial x^8+15x^6+48x^4+15x^2+1 factors into linear factors mod p.
%C A243701 4*a(n) has the form z^2 - 205*y^2, where z = 2*x+13*y. - _Bruno Berselli_, Jun 20 2014
%H A243701 Will Jagy et al.,<a href="http://mathoverflow.net/questions/171807/positive-primes-represented-by-indefinite-binary-quadratic-form">Positive primes represented by indefinite binary quadratic form"</a>, MathOverflow # 171807, 2014.
%H A243701 Will Jagy et al., <a href="http://mathoverflow.net/questions/171846/positive-primes-represented-by-an-indefinite-binary-form-reducing-poly-degree-f">Positive Primes represented by an indefinite binary form, reducing poly degree from 8 to 4</a>, MathOverflow # 171846, 2014.
%H A243701 Peter Luschny, <a href="https://github.com/PeterLuschny/BinaryQuadraticForms">Binary Quadratic Forms</a>, GitHub 2024.
%H A243701 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)
%o A243701 (PARI)
%o A243701 fc(a,b,c,M) = {
%o A243701   my(t1=List(),t2);
%o A243701   forprime(p=2,prime(M),
%o A243701     t2 = qfbsolve(Qfb(a,b,c),p);
%o A243701     if(t2 != 0, listput(t1,p))
%o A243701   );
%o A243701   Vec(t1)
%o A243701 };
%o A243701 fc(1,13,-9,600)
%o A243701 (SageMath)
%o A243701 load('https://raw.githubusercontent.com/PeterLuschny/BinaryQuadraticForms/main/BinaryQF.sage')
%o A243701 Q = binaryQF([1, 13, -9])
%o A243701 print(Q.represented_positives(2750, 'prime'))  # _Peter Luschny_, May 04 2024
%Y A243701 This sequence (primes), A243702 (all), A372518 (primitively).
%K A243701 nonn
%O A243701 1,1
%A A243701 _N. J. A. Sloane_, Jun 17 2014