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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 (list; graph; refs; listen; history; text; internal format)
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: 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

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Last modified October 19 12:21 EDT 2021. Contains 348088 sequences. (Running on oeis4.)