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A350625
a(n) = denominator of the Y-coordinate of n*P where P is the generator [0,0] for rational points on the curve y^2 + y = x^3 + x^2.
4
1, 1, 1, 1, 8, 27, 1, 343, 1331, 8000, 6859, 658503, 6967871, 7645373, 1054977832, 19270387241, 549554511871, 199279038321, 537149706740569, 17795935051712000, 238963978065144151, 27915217583090079761, 3036108535167687186689, 338086202776927409397159
OFFSET
1,5
COMMENTS
We can take P = P[1] = [x_1, y_1] = [0,0]. Then P[n] = P[1]+P[n-1] = [x_n, y_n] for n >= 2. Sequence gives denominators of the y_n.
REFERENCES
D. Husemoller, Elliptic Curves, Springer, 1987, p. 28.
A. W. Knapp, Elliptic Curves, Princeton, 1992, p. 64.
PROG
(PARI) See A350622.
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Jan 27 2022
STATUS
approved