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 A243701 Primes represented by the indefinite quadratic form x^2 + 13xy - 9y^2. 2
 5, 59, 131, 139, 241, 269, 271, 359, 409, 541, 569, 599, 661, 701, 761, 859, 881, 911, 941, 1021, 1091, 1109, 1291, 1399, 1439, 1481, 1549, 1559, 1579, 1609, 1619, 1931, 1999, 2011, 2029, 2089, 2099, 2111, 2141, 2251, 2399, 2459, 2521, 2711, 2729, 2731, 2749 (list; graph; refs; listen; history; text; internal format)
 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 Table of n, a(n) for n=1..47. 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 This sequence (primes), A243702 (all), A372518 (primitively). Sequence in context: A015994 A222563 A141951 * A179028 A179029 A049079 Adjacent sequences: A243698 A243699 A243700 * A243702 A243703 A243704 KEYWORD nonn AUTHOR N. J. A. Sloane, Jun 17 2014 STATUS approved

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Last modified July 23 16:47 EDT 2024. Contains 374552 sequences. (Running on oeis4.)