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A350623
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a(n) = denominator of the X-coordinate of n*P where P is the generator [0,0] for rational points on the curve y^2 + y = x^3 + x^2.
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1
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1, 1, 1, 1, 4, 9, 1, 49, 121, 400, 361, 7569, 36481, 38809, 1036324, 7187761, 67092481, 34117281, 6607901521, 68162766400, 385083543601, 9202249657441, 209674135856641, 4853089476046161, 7099336433764, 2600282294202480889, 60193393235277536641, 1371165544633857017809
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OFFSET
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1,5
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COMMENTS
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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.
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REFERENCES
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D. Husemoller, Elliptic Curves, Springer, 1987, p. 28.
A. W. Knapp, Elliptic Curves, Princeton, 1992, p. 64.
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LINKS
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Table of n, a(n) for n=1..28.
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PROG
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(PARI) See A350622.
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CROSSREFS
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Cf. A028940-A028943, A350622-A350625.
Sequence in context: A129861 A055491 A032523 * A032760 A129970 A006830
Adjacent sequences: A350620 A350621 A350622 * A350624 A350625 A350626
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KEYWORD
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nonn,frac
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AUTHOR
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N. J. A. Sloane, Jan 27 2022
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STATUS
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approved
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