OFFSET
0,2
COMMENTS
Given the elliptic curve E : y^2 = x^3 - 11*x + 890 and the points P = (-1, 30) and Q = (7, 34) on E, a(n) is the denominator of the x-coordinate of n*P + Q on E, thus all terms a(n) of the sequence are squares. - Robin Visser, Oct 22 2023
LINKS
Robin Visser, Table of n, a(n) for n = 0..33
Matteo Verzobio, Primitive divisors of sequences associated to elliptic curves with complex multiplication, Res. Number Theory, (2021) 7:37.
EXAMPLE
For n = 1, the x-coordinate of 1*(-1, 30) + (7, 34) on E is -23/4, thus a(1) = 4. For n = 2, the x-coordinate of 2*(-1, 30) + (7, 34) on E is 55567/361, thus a(2) = 361. For n = 3, the x-coordinate of 3*(-1, 30) + (7, 34) on E is 185560858/48874081, thus a(3) = 48874081. - Robin Visser, Oct 22 2023
PROG
(Sage)
def a(n):
E = EllipticCurve([-11, 890])
return (n*E(-1, 30)+E(7, 34))[0].denominator() # Robin Visser, Oct 22 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 12 2023
EXTENSIONS
More terms from Robin Visser, Oct 22 2023
STATUS
approved