STATUS
reviewed
approved
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Squares visited by a chess king on a square-spiral numbered board and stepping to the lowest unvisited adjacent square, where each step is not in the same direction as the previous step.
(history; published version)
(history; published version)
STATUS
proposed
reviewed
STATUS
editing
proposed
COMMENTS
This sequences gives the numbers of the squares visited by a chess king moving on a square-spiral numbered board where the king starts on the 1 numbered square and at each step, which is not in the same direction as its previous step, moves to an adjacent unvisited square, out of the eight adjacent neighboring squares, which contains the lowest spiral number number.
STATUS
approved
editing
STATUS
reviewed
approved
STATUS
proposed
reviewed
STATUS
editing
proposed
EXAMPLE
a(1) = 1, the starting square of the king.
a(2) = 2. The eight adjacent unvisited squares around a(1) are numbered 2,3,4,5,6,7,8,9. Of these 2 is the lowest.
a(5) = 6. The five adjacent unvisited squares around a(4) = 4 are numbered 5,6,14,15,16. Of these 5 is the lowest but that would require a step directly left from 4, which is the same step as a(3) = 3 to a(4) = 4, so is not allowed. The next lowest available square is 6.
EXAMPLE
The board is numbered with the square spiral:
.
17--16--15--14--13 .
| | .
18 5---4---3 12 29
| | | | |
19 6 1---2 11 28
| | | |
20 7---8---9--10 27
| |
21--22--23--24--25--26
.
STATUS
proposed
editing
STATUS
editing
proposed