This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A028942 #39 Jul 08 2025 18:57:08 %S A028942 0,0,1,3,5,-14,-8,69,435,2065,3612,-28888,43355,2616119,28076979, %T A028942 -332513754,-331948240,8280062505,641260644409,18784454671297, %U A028942 318128427505160,-10663732503571536,-66316334575107447,8938035295591025771 %N A028942 Negative of numerator of y coordinate of n*P where P is the generator [0,0] for rational points on curve y^2+y = x^3-x. %C A028942 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 negated numerators of the y_n. - _N. J. A. Sloane_, Jan 27 2022 %C A028942 a(n) = A278314(n) up to sign. - _Michael Somos_, Nov 19 2016 %D A028942 A. W. Knapp, Elliptic Curves, Princeton 1992, p. 77. %H A028942 Seiichi Manyama, <a href="/A028942/b028942.txt">Table of n, a(n) for n = 1..173</a> %H A028942 B. Mazur, <a href="https://doi.org/10.1090/S0273-0979-1986-15430-3">Arithmetic on curves</a>, Bull. Amer. Math. Soc. 14 (1986), 207-259; see p. 225. %F A028942 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). %e A028942 3P = (-1, -1), %e A028942 4P = (2, -3), %e A028942 5P = (1/4, -5/8), %e A028942 6P = (6, 14). %o A028942 (PARI) - see A028940. %Y A028942 Cf. A028940, A028941, A028943, A278314. %K A028942 sign,frac %O A028942 1,4 %A A028942 _N. J. A. Sloane_