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A332837
Squares visited by a knight moving on a double spiral numbered board and moving to the lowest available unvisited square at each step.
2
1, 10, 5, 2, 8, 7, 4, 3, 9, 6, 12, 18, 33, 39, 20, 11, 32, 19, 13, 22, 28, 15, 21, 38, 61, 30, 17, 42, 25, 31, 16, 43, 24, 51, 76, 26, 45, 70, 37, 14, 29, 23, 40, 34, 57, 86, 49, 55, 84, 78, 53, 47, 72, 107, 41, 35, 56, 27, 44, 71, 36, 59, 88, 127, 80, 115
OFFSET
1,2
COMMENTS
This sequence uses a double spiral of numbers to enumerate the squares on the board. The knight starts on the square with number 1. At each step the knight goes to an unvisited square with the smallest number.
The sequence is finite. After 2958 steps the square with number 2796 is visited, after which all neighboring squares have been visited.
The lowest unvisited square during the walk is square number 2011.
LINKS
Scott R. Shannon, Image showing the 2958 steps of the knights' path. The green dot is the starting square and the red dot the final square. Blue dots show the eight occupied squares surrounding the final square. The lowest unvisited square is the yellow dot.
EXAMPLE
The squares are numbered using the double spiral numbering shown below:
.
--48--46--44--42--40--38--36
|
27--25--23--21--19--17 34
| | |
29 10---8---6---4 15 32
| | | | |
31 12 3---1---2 13 30
| | | | |
33 14 5---7---9--11 28
| | |
35 16--18--20--22--24--26
|
37--39--41--43--45--47--49--
CROSSREFS
Cf. A220098, A316667, A329022, A332980 (quadruple spiral).
Sequence in context: A357423 A320938 A117256 * A050020 A050136 A053050
KEYWORD
nonn,walk,fini,full
AUTHOR
Scott R. Shannon, Feb 26 2020
STATUS
approved