A326757 a(n) is the X-coordinate of the n-th nonattacking queen placed by a greedy algorithm on N^3 (see Comments for details).

0, 0, 2, 1, 1, 0, 4, 0, 4, 2, 1, 3, 0, 5, 0, 6, 2, 1, 3, 4, 7, 3, 5, 0, 6, 2, 1, 3, 1, 3, 7, 6, 9, 1, 5, 6, 4, 1, 3, 2, 9, 2, 1, 8, 11, 3, 1, 4, 13, 12, 8, 0, 4, 2, 7, 9, 1, 14, 2, 6, 8, 4, 0, 3, 12, 8, 10, 2, 4, 12, 5, 18, 3, 7, 0, 9, 4, 2, 10, 8, 3, 5, 7, 0

Offset: 0

Author

Rémy Sigrist and N. J. A. Sloane, Jul 23 2019

Keywords

• nonn

Comments

We consider an infinite chessboard on N^3 (the first octant of Z^3) traversed by increasing x+y+z and then increasing x+y and then increasing x and place nonattacking queens as soon as possible; these queens can attack along the 13 axes of rotation of a cube.

This sequence is a 3-dimensional variant of A275901.

Examples

			The traversal of N^3 starts:
  X  Y  Z
  -  -  -
  0  0  0
  0  0  1
  0  1  0
  1  0  0
  0  0  2
  0  1  1
  1  0  1
  0  2  0
  1  1  0
  2  0  0
  0  0  3
  0  1  2
  1  0  2
  ...
The first queen is placed at position (0, 0, 0) and attacks every position (m*i, m*j, m*k) with max(i, j, k) = 1 and m > 0.
The second queen is placed at position (0, 1, 2).
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Rémy Sigrist, PARI program for A326757
• Rémy Sigrist, Interactive scatterplot of the first 25000 queens

Crossrefs

See A326758 and A326759 for the Y- and Z- coordinates, respectively.

Cf. A275901.

Programs

PARI

See Links section.