

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
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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



