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Negative of numerator of y-coordinate of (2n)*P where P is generator for rational points on curve y^2 + y = x^3 - x.
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%I #22 Nov 20 2016 04:00:17

%S 0,3,-14,69,2065,-28888,2616119,-332513754,8280062505,18784454671297,

%T -10663732503571536,8938035295591025771,31636113722016288336230,

%U -41974401721854929811774227,754388827236735824355996347601

%N Negative of numerator of y-coordinate of (2n)*P where P is generator for rational points on curve y^2 + y = x^3 - x.

%H Seiichi Manyama, <a href="/A028938/b028938.txt">Table of n, a(n) for n = 1..86</a>

%H 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 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).

%F a(n) = A028942(2n). - _Seiichi Manyama_, Nov 19 2016

%e 4P = (2, -3).

%Y Cf. A028936, A028937, A028939 (denominator), A028942.

%K sign,frac

%O 1,2

%A _N. J. A. Sloane_