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

0,3

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.

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

Example

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).

Prog

(PARI) See Links section.

Crossrefs

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

Cf. A275901.

Sequence in context: A305736 A324642 A371740 * A147787 A247288 A135221

Adjacent sequences: A326754 A326755 A326756 * A326758 A326759 A326760

Keyword

nonn

Author

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

Status

approved