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A366469
Generators for a sequence of integral ideals associated with the points (-1, 30) and (7, 34) on the elliptic curve y^2 = x^3 -11*x + 890.
1
1, 4, 361, 48874081, 152243048819761, 95671484892005699044, 75338048604225337985930032294201, 11816627194609303949196967959213617578989121, 2867439869288362426831400403507241305570146883380880481
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
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
Cf. A000290.
Sequence in context: A334359 A203034 A215827 * A051955 A177114 A109760
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 12 2023
EXTENSIONS
More terms from Robin Visser, Oct 22 2023
STATUS
approved