A365811 Numbers k >= 0 such that Mordell's equation y^2 = k^3 + x*(x + 1)/2 has an integral solution for a pair (x >= 0, y >= 0).

0, 1, 2, 4, 9, 11, 12, 14, 16, 25, 26, 35, 36, 38, 40, 45, 49, 57, 62, 64, 69, 71, 74, 81, 84, 85, 88, 95, 96, 97, 100, 107, 109, 117, 120, 121, 122, 134, 136, 144, 145, 146, 155, 156, 157, 169, 170, 172, 179, 180, 191, 196, 201, 213, 217, 225, 230, 240, 242, 244

Offset: 1

Author

Ctibor O. Zizka, Sep 19 2023

Keywords

• nonn

Comments

If there is a solution, then y >= k^(3/2). For k = r^2, the least solution is (x = 0, y = r^3).

Examples

			k = 4 is a term: 8^2 = 4^3.
k = 11 is a term: 39^2 = 11^3 + 19*20/2.
		

Crossrefs

Cf. A000217, A000290, A000578, A054504.

Programs

PARI

isOK(k) = { []<>bnfisintnorm(bnfinit(x^2-2),16*k^3-2)} \\ Thomas Scheuerle, Sep 19 2023