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A274641
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Counterclockwise square spiral constructed by greedy algorithm, so that each row, column, and diagonal contains distinct numbers. Start with 0 (so in this version a(n) = A274640(n) - 1).
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32
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0, 1, 2, 3, 1, 2, 3, 4, 5, 0, 3, 5, 1, 0, 5, 4, 2, 0, 4, 1, 5, 0, 1, 3, 4, 2, 6, 7, 4, 3, 8, 6, 7, 2, 9, 10, 3, 6, 7, 5, 2, 8, 4, 6, 7, 8, 9, 10, 11, 5, 7, 8, 10, 9, 11, 12, 6, 5, 9, 8, 11, 12, 13, 14, 7, 1, 8, 11, 6, 9, 10, 12, 13, 9, 8, 5, 12, 4, 2, 14, 15, 6, 0, 9, 12, 11, 13, 10, 14, 2, 7, 4, 0, 11, 10, 13, 6, 3, 1, 15, 8, 16, 0, 7, 10
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refs;
listen;
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OFFSET
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0,3
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COMMENTS
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See A274640 for further information.
Presumably every row, column, and diagonal is a permutation of the natural numbers, but is there a proof? - N. J. A. Sloane, Jul 10 2016
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 0..20000 [Based on Alois Heinz's b-file for A274640]
F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: non-attacking queens on infinite chess boards, Electronic J. Combin., 27:1 (2020), #P1.52.
Rémy Sigrist, Colored representation of the spiral for -500 <= x, y <= 500
N. J. A. Sloane, Confessions of a Sequence Addict (AofA2017), slides of invited talk given at AofA 2017, Jun 19 2017, Princeton. Mentions this sequence.
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EXAMPLE
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From Jon E. Schoenfield, Dec 26 2016: (Start)
The spiral begins:
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8--15---1---3---6--13--10--11---0---4---7
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16 7--14--13--12--11---8---9---5---6 2
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0 1 3--10---9---2---7---6---8 12 14
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7 8 6 2---4---5---0---1 3 11 10
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10 11 7 0 1---3---2 5 4 9 13
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14 6 5 4 2 0---1 3 7 10 11
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13 9 2 1 3---4---5---0 6 8 12
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6 10 8 5---0---1---3---4---2 7 9
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3 12 4---6---7---8---9--10--11---5 0
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11 13---9---8---5--12---4---2--14--15---6
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9--14---0--11--15---7--13--12--10--17--16
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(End)
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CROSSREFS
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Cf. A274640 (if start with 1 at center), A324481 (position of first n).
For the eight spokes see A324774-A324781.
Sequence in context: A033924 A276328 A276332 * A003315 A194107 A071797
Adjacent sequences: A274638 A274639 A274640 * A274642 A274643 A274644
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Jul 09 2016, based on the entry A274640 from Zak Seidov and Kerry Mitchell, Jun 30 2016
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STATUS
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approved
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