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A326413
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Successive squares visited by a knight on the single-digit square spiral, with ties resolved towards the left.
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12
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0, 0, 1, 0, 1, 0, 1, 1, 2, 2, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 2, 2, 1, 1, 0, 2, 3, 2, 2, 1, 3, 1, 1, 1, 1, 1, 2, 2, 3, 2, 3, 1, 4, 3, 5, 6, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0
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OFFSET
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1,9
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COMMENTS
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Take the standard counterclockwise square spiral starting at 0, as in A304586, but only write one digit at a time in the cells of the spiral: 0,1,2,3,4,5,6,7,8,9,1,0,1,1,1,2,...
Place a chess knight at cell 0. Move it to the lowest-numbered cell it can attack, and if there is a tie, move it to the cell closest (in Euclidean distance) to the start, and if there is still a tie, move to the left(*).
No cell can be visited more than once.
Inspired by the Trapped Knight video and A316667.
Just as for A316667, the sequence is finite. After a while, the knight has no unvisited squares it can reach, and the sequence ends with a(1217) = 4.
(*)Moving to the left means choose the point with the lowest x-coordinate. This leads to an unambiguous choice of tied squares only for the 'move left' case.
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LINKS
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EXAMPLE
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The digit-square spiral is
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2---2---2---1---2---0---2 2
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3 1---2---1---1---1 9 3
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2 3 4---3---2 0 1 1
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4 1 5 0---1 1 8 3
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2 4 6---7---8---9 1 0
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5 1---5---1---6---1---7 3
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2---6---2---7---2---8---2---9
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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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EXTENSIONS
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STATUS
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approved
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