A134043 Complete list of solutions to y^2 = x^3 + 113; sequence gives y values.

7, 11, 25, 38, 133, 8669

Offset: 1

Author

Artur Jasinski, Oct 03 2007

Keywords

• nonn
• fini
• full

Comments

For corresponding x values see A134043.

Examples

			a(1)^2 = 7^2 = 49 = A134042(1)^3 + 113 = -64 + 113.
a(2)^2 = 11^2 = 121 = A134042(2)^3 + 113 = 8 + 113.
a(3)^2 = 25^2 = 625 = A134042(3)^3 + 113 = 512 + 113.
a(4)^2 = 38^2 = 1444 = A134042(4)^3 + 113 = 1331+ 113.
a(5)^2 = 133^2 = 17689 = A134042(5)^3 + 113 = 17576 + 113.
a(6)^2 = 8669^2 = 75151561 = A134042(6)^3 + 113 = 75151448 + 113.
		

Crossrefs

Cf. A134042, A029727, A080761.

Programs

Magma

Sort([ Abs(p[2]) : p in IntegralPoints(EllipticCurve([0, 113])) ]); /* adapted from A029727 */

Mathematica

(Program does not produce first two terms) a = {}; Do[k = n^2 - (Floor[n^(2/3)])^3; If[(k > 112) && (k < 113), AppendTo[a, n]], {n, 1, 100000}]; a

Extensions

Edited and corrected by Klaus Brockhaus, Oct 04 2007