A134106 Complete list of solutions to y^2 = x^3 - 207; sequence gives y values.

3, 39, 75, 172, 5511, 6022, 223063347

Offset

1,1

Comments

For corresponding x values see A134107.

Links

Table of n, a(n) for n=1..7.

Example

a(1)^2 = 3^2 = 9 = A134107(1)^3 - 207 = 216 - 207.
a(2)^2 = 39^2 = 1521 = A134107(2)^3 - 207 = 1728 - 207.
a(3)^2 = 75^2 = 5625 = A134107(3)^3 - 207 = 5832 - 207.
a(4)^2 = 172^2 = 29584 = A134107(4)^3 - 207 = 29791 - 207.
a(5)^2 = 5511^2 = 30371121 = A134107(5)^3 - 207 = 30371328 - 207.
a(6)^2 = 6022^2 = 36264484 = A134107(6)^3 - 207 = 36264691 - 207.
a(7)^2 = 223063347^2 = 49757256774842409 = A134107(7)^3 - 207 = 49757256774842616 - 207.

Prog

(Magma) Sort([ Abs(p[2]) : p in IntegralPoints(EllipticCurve([0, -207])) ]); /* adapted from A029727 */
(Sage) [x[1] for x in EllipticCurve([0, -207]).integral_points()] # Charles R Greathouse IV, Aug 09 2024

Crossrefs

Cf. A134107, A134102, A134104, A029727, A134043, A134073.

Sequence in context: A163789 A183182 A277713 * A153875 A082954 A209366

Adjacent sequences: A134103 A134104 A134105 * A134107 A134108 A134109

Keyword

nonn,fini,full,changed

Author

Klaus Brockhaus, Oct 08 2007

Status

approved