A028944 Numerator of x-coordinate of (2n+1)*P where P is the generator for rational points on the curve y^2 + y = x^3 - x.

0, -1, 1, -5, -20, 116, -3741, 8385, -239785, -59997896, 1849037896, -270896443865, -16683000076735, 2786836257692691, -3148929681285740316, 342115756927607927420, -280251129922563291422645, -804287518035141565236193151

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..105

B. Mazur, Arithmetic on curves, Bull. Amer. Math. Soc. 14 (1986), 207-259; see p. 225.

Formula

P = (0, 0), 2P = (1, 0); if kP = (a, b) then (k+1)P = (a' = (b^2 - a^3)/a^2, b' = -1 -b*a'/a).

a(n) = A028940(2n+1). - Seiichi Manyama, Nov 20 2016

Example

7P = (-5/9, 8/27).

Crossrefs

Cf. A028940, A028945.

Sequence in context: A207972 A117736 A258665 * A332710 A352743 A054720

Adjacent sequences: A028941 A028942 A028943 * A028945 A028946 A028947

Keyword

sign,frac

Author

N. J. A. Sloane

Status

approved