OFFSET
1,1
COMMENTS
After 3, the prime terms appear to be the primes in A275878 (namely, 7, 61, 331, 547, 1951, ...)
LINKS
Joseph-Alfred Serret, Section 512, Cours d'algèbre supérieure, Gauthier-Villars.
EXAMPLE
For the first entry of Q=3, we have the polynomial x^3 - 3x + 1. Its roots, expressed as continued fractions, all have a common tail of 3, 2, 3, 1, 1, 6, 11, ... The next examples are Q=7 with the polynomial x^3 - 7x + 7, then Q=9 with the polynomial x^3 - 9x + 9, and Q=21 with the polynomials x^3 - 21x + 35 and x^3 - 21x + 37. Note that for the Q=7 example, we get the common tail of 2, 3, 1, 6, 10, 5, ... which is contained in A039921.
MATHEMATICA
SetOfQRs = {};
M = 1000;
Do[
If[Divisible[3 (a^2 - a + 1), c^2] &&
Divisible[(2 a - 1) (a^2 - a + 1), c^3] &&
3 (a^2 - a + 1)/c^2 <= M,
SetOfQRs =
Union[SetOfQRs, { { (3 (a^2 - a + 1))/
c^2, ((2 a - 1) (a^2 - a + 1))/c^3}} ]],
{c, 1, M/3 + 1, 2}, {a, 1, Sqrt[M c^2/3 + 3/4] + 1/2}];
Print[SetOfQRs // MatrixForm];
CROSSREFS
KEYWORD
nonn
AUTHOR
Greg Dresden, Jun 25 2018
EXTENSIONS
More terms from Robert G. Wilson v, Jul 02 2018
STATUS
approved