A095979 Height of n-th rational point on y^2=x^3 + 17.

2, 1, 4, 2, 4, 106, 2228, 76271, 9776276, 3497742218, 1160536538401, 1610419388060961, 43923749623043363812, 102656671584861356692801, 18531846858359807878734515284, 370183335711420357564604634095918, 125067940343620957546805016634617881761, 14803896396546295880463242120819717253248409

Offset

1,1

Comments

The height of a rational point (A/B,C/D) is max{|A|,|B|}.

References

J. H. Silverman, A Friendly Introduction to Number Theory, pp. 337, Prentice Hall NJ, 2001.

Links

Table of n, a(n) for n=1..18.

Mathematica

next[{x1_, y1_}, {x2_, y2_}] :=
 With[{y = With[{m = (y2 - y1)/(x2 - x1)}, m x + (y1 - m x1)]},
  With[{c =
     Coefficient[
      PolynomialQuotient[y^2 - (x^3 + 17), (x - x1) (x - x2), x], x,
      0]}, {x, -y} /. x -> c]];
With[{P1 = {-2, 3}, P2 = {-1, 4}},
 Map[Max@NumeratorDenominator@Abs@First@# &,
Join[{P1}, NestList[next[P1, #] &, P2, 18]]]] (* Oliver Seipel, Sep 26 2025 *)

Crossrefs

Sequence in context: A216568 A219432 A120988 * A377781 A276133 A307602

Adjacent sequences: A095976 A095977 A095978 * A095980 A095981 A095982

Keyword

nonn

Author

Lekraj Beedassy, Jul 16 2004

Extensions

More terms from Oliver Seipel, Sep 26 2025

Status

approved