A332980 Squares visited by a knight moving on a quadruple spiral numbered board and moving to the lowest available unvisited square at each step.

1, 10, 7, 2, 8, 3, 9, 4, 6, 5, 15, 12, 38, 11, 14, 21, 32, 20, 17, 28, 39, 13, 16, 19, 30, 18, 33, 44, 56, 37, 22, 34, 23, 35, 24, 36, 25, 52, 71, 29, 40, 59, 47, 66, 31, 42, 54, 77, 89, 27, 62, 43, 55, 74, 86, 117, 70, 51, 94, 67, 48, 60, 41, 26, 65, 92, 49

Offset

1,2

Comments

This sequence uses a quadruple 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 1837 steps the square with number 1748 is visited, after which all neighboring squares have been visited.

The lowest unvisited square during the walk is square number 1211.

Links

Scott R. Shannon, Table of n, a(n) for n = 1..1838

Scott R. Shannon, Image showing the 1837 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 quadruple spiral numbering shown below:
                             |
  --49--45--41--37--33--29  48
                         |   |
    26--22--18--14--10  25  44
     |               |   |   |
    30  11---7---3   6  21  40
     |   |       |   |   |   |
    34  15   4-- 1---2  17  36
     |   |   |   |       |   |
    38  19   8   5---9--13  32
     |   |   |               |
    42  23  12--16--20--24--28
     |   |
    46  27--31--35--39--43--47--
     |

Crossrefs

Cf. A220098, A316667, A329022, A332837 (double spiral).

Sequence in context: A358394 A248153 A079166 * A246662 A246651 A089245

Adjacent sequences: A332977 A332978 A332979 * A332981 A332982 A332983

Keyword

nonn,walk,fini,full

Author

Scott R. Shannon, Mar 04 2020

Status

approved