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A327131
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Cells visited by knight moves on a spirally numbered infinite hexagonal board, moving to the lowest unvisited cell at each step.
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4
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1, 20, 6, 9, 4, 8, 5, 10, 13, 2, 14, 7, 11, 22, 3, 15, 12, 23, 26, 29, 16, 19, 34, 54, 17, 31, 50, 47, 24, 21, 18, 32, 35, 55, 30, 27, 45, 68, 25, 42, 39, 36, 33, 53, 78, 48, 51, 76, 106, 49, 73, 28, 46, 43, 40, 37, 58, 84, 87, 60, 63, 41, 69, 72, 101, 67, 44
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refs;
listen;
history;
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OFFSET
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1,2
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COMMENTS
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The infinite hexagonal board is numbered spirally as:
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17--18--19...
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16 6---7---8
/ / \
15 5 1---2 9
\ \ / /
14 4---3 10
\ /
13--12--11
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In Glinski's hexagonal chess, a knight (N) can move to these (o) cells:
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. . . . .
. . o o . .
. o . . . o .
. o . . . . o .
. . . . N . . . .
. o . . . . o .
. o . . . o .
. . o o . .
. . . . .
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This sequence is finite and ends at a(83966) = 72085 when the knight is "trapped".
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LINKS
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Scott R. Shannon, Image showing the 83965 steps of the knight's path. The green central dot is the starting square and the red dot, located on the edge at the 7:30 clock position, the final square. Blue dots show the twelve occupied squares surrounding the final square. The lowest unvisited square, 71301, is the yellow dot on the edge at the 9:00 clock position.
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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