A350623 a(n) = denominator of the X-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, 4, 9, 1, 49, 121, 400, 361, 7569, 36481, 38809, 1036324, 7187761, 67092481, 34117281, 6607901521, 68162766400, 385083543601, 9202249657441, 209674135856641, 4853089476046161, 7099336433764, 2600282294202480889, 60193393235277536641, 1371165544633857017809

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 x_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..28.

Prog

(PARI) See A350622.

Crossrefs

Cf. A028940-A028943, A350622-A350625.

Sequence in context: A129861 A055491 A032523 * A032760 A129970 A006830

Adjacent sequences: A350620 A350621 A350622 * A350624 A350625 A350626

Keyword

nonn,frac

Author

N. J. A. Sloane, Jan 27 2022

Status

approved