login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

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

%I #14 Jul 08 2022 08:13:30

%S 1,1,1,1,8,27,1,343,1331,8000,6859,658503,6967871,7645373,1054977832,

%T 19270387241,549554511871,199279038321,537149706740569,

%U 17795935051712000,238963978065144151,27915217583090079761,3036108535167687186689,338086202776927409397159

%N 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.

%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 denominators 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-A350624.

%K nonn,frac

%O 1,5

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