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

Author

Scott R. Shannon, Mar 04 2020

Keywords

• nonn
• walk
• fini
• full

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.

Examples

			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--
     |
		

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.

Crossrefs

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