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A350624 a(n) = numerator 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

%I #11 Jun 27 2022 23:11:51

%S 0,-1,-2,3,1,-28,-99,20,-931,-10527,76400,71117,-7705242,-97805561,

%T 317884519,-6053168484,-584285903929,17516504939480,21171512841831,

%U -20045208029885441,-987005650468865600,26826505806361752519,-24519007717765931978,-338107738763085297600203,37652404140584119758794769,262883121764561512399492,-470660250581978416129759599211,-103603683448954712692908522816060,17053994466435658069907361489699701

%N a(n) = numerator 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.

%C 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 numerators of the y_n.

%D D. Husemoller, Elliptic Curves, Springer, 1987, p. 28.

%D A. W. Knapp, Elliptic Curves, Princeton, 1992, p. 64.

%o (PARI) See A350622.

%Y Cf. A028940-A028943, A350622-A350625.

%K sign,frac

%O 1,3

%A _N. J. A. Sloane_, Jan 27 2022

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Last modified July 2 21:16 EDT 2024. Contains 373960 sequences. (Running on oeis4.)