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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).

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%I A326757 #16 Jan 08 2022 12:28:53
%S A326757 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,
%T A326757 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,
%U A326757 10,2,4,12,5,18,3,7,0,9,4,2,10,8,3,5,7,0
%N 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).
%C A326757 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.
%C A326757 This sequence is a 3-dimensional variant of A275901.
%H A326757 Rémy Sigrist, <a href="/A326757/b326757.txt">Table of n, a(n) for n = 0..10000</a>
%H A326757 Rémy Sigrist, <a href="/A326757/a326757.gp.txt">PARI program for A326757</a>
%H A326757 Rémy Sigrist, <a href="https://practical-ardinghelli-959d8f.netlify.app/a326757">Interactive scatterplot of the first 25000 queens</a>
%e A326757 The traversal of N^3 starts:
%e A326757   X  Y  Z
%e A326757   -  -  -
%e A326757   0  0  0
%e A326757   0  0  1
%e A326757   0  1  0
%e A326757   1  0  0
%e A326757   0  0  2
%e A326757   0  1  1
%e A326757   1  0  1
%e A326757   0  2  0
%e A326757   1  1  0
%e A326757   2  0  0
%e A326757   0  0  3
%e A326757   0  1  2
%e A326757   1  0  2
%e A326757   ...
%e A326757 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.
%e A326757 The second queen is placed at position (0, 1, 2).
%o A326757 (PARI) See Links section.
%Y A326757 See A326758 and A326759 for the Y- and Z- coordinates, respectively.
%Y A326757 Cf. A275901.
%K A326757 nonn
%O A326757 0,3
%A A326757 _Rémy Sigrist_ and _N. J. A. Sloane_, Jul 23 2019