A134102 Complete list of solutions to y^2 = x^3 + 225; sequence gives y values.

3, 10, 15, 17, 21, 35, 60, 165, 465, 2415, 6159, 6576, 611085363

Offset

1,1

Comments

For corresponding x values see A134103.

Links

Table of n, a(n) for n=1..13.

Example

a(1)^2 = 3^2 = 9 = A134103(1)^3 + 225 = -216 + 225.
a(2)^2 = 10^2 = 100 = A134103(2)^3 + 225 = -125 + 225.
a(3)^2 = 15^2 = 225 = A134103(3)^3 + 225 = 0 + 225.
a(4)^2 = 17^2 = 289 = A134103(4)^3 + 225 = 64 + 225.
a(5)^2 = 21^2 = 441 = A134103(5)^3 + 225 = 216 + 225.
a(6)^2 = 35^2 = 1225 = A134103(6)^3 + 225 = 1000 + 225.
a(7)^2 = 60^2 = 3600 = A134103(7)^3 + 225 = 3375 + 225.
a(8)^2 = 165^2 = 27225 = A134103(8)^3 + 225 = 27000 + 225.
a(9)^2 = 465^2 = 216225 = A134103(9)^3 + 225 = 216000 + 225.
a(10)^2 = 2415^2 = 5832225 = A134103(10)^3 + 225 = 5832000 + 225.
a(11)^2 = 6159^2 = 37933281 = A134103(11)^3 + 225 = 37933056 + 225.
a(12)^2 = 6576^2 = 43243776 = A134103(12)^3 + 225 = 43243551 + 225.
a(13)^2 = 611085363^2 = 373425320872841769 = A134103(13)^3 + 225 = 373425320872841544 + 225.

Mathematica

Select[Table[Sqrt[x^3+225], {x, -6, 721000}], IntegerQ] (* Harvey P. Dale, Dec 25 2022 *)

Prog

(Magma) { x : x in Sort([ Abs(p[2]) : p in IntegralPoints(EllipticCurve([0, 225])) ]) }; /* adapted from A029727 */

Crossrefs

Cf. A134103, A134104, A134106, A029727, A134043, A134073.

Sequence in context: A048852 A226101 A141463 * A173600 A328987 A108770

Adjacent sequences: A134099 A134100 A134101 * A134103 A134104 A134105

Keyword

nonn,fini,full

Author

Klaus Brockhaus, Oct 08 2007

Status

approved