A332837 Squares visited by a knight moving on a double spiral numbered board and moving to the lowest available unvisited square at each step.

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

Author

Scott R. Shannon, Feb 26 2020

Keywords

• nonn
• walk
• fini
• full

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.

Examples

			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--
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..2959
• 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.

Crossrefs

Cf. A220098, A316667, A329022, A332980 (quadruple spiral).