OFFSET
1,1
COMMENTS
Discriminant 205.
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.
4*a(n) has the form z^2 - 205*y^2, where z = 2*x+13*y. - Bruno Berselli, Jun 20 2014
LINKS
Will Jagy et al.,Positive primes represented by indefinite binary quadratic form", MathOverflow # 171807, 2014.
Will Jagy et al., Positive Primes represented by an indefinite binary form, reducing poly degree from 8 to 4, MathOverflow # 171846, 2014.
Peter Luschny, Binary Quadratic Forms, GitHub 2024.
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)
PROG
(PARI)
fc(a, b, c, M) = {
my(t1=List(), t2);
forprime(p=2, prime(M),
t2 = qfbsolve(Qfb(a, b, c), p);
if(t2 != 0, listput(t1, p))
);
Vec(t1)
};
fc(1, 13, -9, 600)
(SageMath)
load('https://raw.githubusercontent.com/PeterLuschny/BinaryQuadraticForms/main/BinaryQF.sage')
Q = binaryQF([1, 13, -9])
print(Q.represented_positives(2750, 'prime')) # Peter Luschny, May 04 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 17 2014
STATUS
approved