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.

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.

Links

Table of n, a(n) for n=1..24.

Prog

(PARI) See A350622.

Crossrefs

Cf. A028940-A028943, A350622-A350624.

Sequence in context: A119522 A070494 A334659 * A070493 A257853 A070492

Adjacent sequences: A350622 A350623 A350624 * A350626 A350627 A350628

Keyword

nonn,frac

Author

N. J. A. Sloane, Jan 27 2022

Status

approved