%I #30 Jun 27 2022 01:51:53

%S 1,1,1,1,4,1,9,25,49,16,529,841,3481,16641,98596,4225,2337841,

%T 13608721,67387681,264517696,6941055969,12925188721,384768368209,

%U 5677664356225,61935294530404,49020596163841,16063784753682169

%N Denominator of X-coordinate of n*P where P is the generator [0,0] for rational points on curve y^2+y = x^3-x.

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

%C Squares of terms in A006769 (or A006720).

%D G. Everest, A. J. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences: Examples and Applications, AMS Monographs, 2003

%D A. W. Knapp, Elliptic Curves, Princeton 1992, p. 77.

%H Seiichi Manyama, <a href="/A028941/b028941.txt">Table of n, a(n) for n = 1..212</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 This sequence satisfies the quadratic recurrence relation a(n)a(n-6)=-a(n-1)a(n-5)+2a(n-2)a(n-4)+2a(n-3)^2 which is a generalized Somos-6 relation. - Graham Everest (g.everest(AT)uea.ac.uk), Dec 16 2002

%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).

%o (PARI) - see A028940.

%Y Cf. A028940, A028942, A028943.

%K nonn,frac

%O 1,5

%A _N. J. A. Sloane_