

A326757


a(n) is the Xcoordinate of the nth 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
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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 3dimensional 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: A325734 A305736 A324642 * 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



