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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).
5
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.
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
KEYWORD
nonn
AUTHOR
STATUS
approved