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A306527
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Squares visited by a knight moving on an open-rectangle-numbered board and moving to the lowest available unvisited square at each step.
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1
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1, 8, 11, 2, 5, 10, 7, 4, 9, 16, 3, 6, 13, 22, 35, 18, 21, 12, 15, 26, 23, 14, 25, 38, 55, 20, 17, 32, 47, 70, 31, 34, 49, 30, 19, 36, 53, 50, 69, 46, 93, 48, 29, 68, 95, 72, 33, 54, 37, 24, 27, 42, 39, 56, 77, 52, 71, 74, 97, 100, 51, 76, 101
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listen;
history;
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OFFSET
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1,2
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COMMENTS
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The half-infinite board is numbered from square 1 as follows:
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| | | | | | | |
--+-------+-------+-------+-------+-------+-------+-------+--
| | | | | | | |
| 25 . . .24 . . .23 . . .22 . . .21 . . .20 . . .19 |
| . | | | | | | . |
--+---.---+-------+-------+-------+-------+-------+---.---+--
| . | | | | | | . |
| 26 | 13 . . .12 . . .11 . . .10 . . . 9 | 18 |
| . | . | | | | . | . |
--+---.---+---.---+-------+-------+-------+---.---+---.---+--
| . | . | | | | . | . |
| 27 | 14 | 5 . . . 4 . . . 3 | 8 | 17 |
| . | . | . | | . | . | . |
--+---.---+---.---+---.---+-------+---.---+---.---+---.---+--
| . | . | . | | . | . | . |
| 28 | 15 | 6 | 1 | 2 | 7 | 16 |
| | | | | | | |
--+-------+-------+-------+-------+-------+-------+-------+--
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The knight begins at square 1. This is a finite sequence: after 326 steps square 562 is reached after which all squares within one knight move have been visited.
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LINKS
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Scott R. Shannon, Image showing the knight path. The green dot is the starting square 1, the red dot is the end square 562. 4 Blue dots have been added around the final square to show all available positions have been visited.
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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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