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A258928 a(n) = number of integral points on the elliptic curve y^2 = x^3 - (n^2)*x + 1, considering only nonnegative values of y. 0
3, 6, 11, 9, 15, 13, 14, 17, 26, 12, 12, 11, 12, 19, 20, 11, 19, 36, 12, 17, 16, 11, 19, 16, 15, 27, 17, 17, 18, 16, 12, 15, 17, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

For n>3, the number of integral points on y = x^3 - (n^2)*x + 1 is at least 11. These 11 points correspond to the solutions x = {-1, 0, n, -n, n + 2, -n + 2, n^2 - 1, n^2 - 2n + 2, n^2 + 2n + 2, n^4 + 2n, n^4 - 2n}.

LINKS

Table of n, a(n) for n=0..33.

EXAMPLE

a(0) = 3 because the integer points on y^2 = x^3 + 1 are (-1, 0), (0, 1), and (2, 3).

CROSSREFS

Cf. A081119, A081120, A259191.

Sequence in context: A093903 A117128 A006509 * A144562 A102889 A183543

Adjacent sequences:  A258925 A258926 A258927 * A258929 A258930 A258931

KEYWORD

nonn,more

AUTHOR

Morris Neene, Jun 14 2015

STATUS

approved

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Last modified February 23 18:13 EST 2019. Contains 320437 sequences. (Running on oeis4.)