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

1,3

Comments

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

Links

Table of n, a(n) for n=1..60.

Example

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

Prog

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

Crossrefs

Cf. A000217, A000290, A000578, A054504.

Sequence in context: A372915 A096692 A203847 * A172147 A266726 A030194

Adjacent sequences: A365808 A365809 A365810 * A365812 A365813 A365814

Keyword

nonn

Author

Ctibor O. Zizka, Sep 19 2023

Status

approved