Integer Sequence A309382

26 Jul 2019 by Mason Manetta

Link to Publication

https://oeis.org/A309382

A309382

Successive squares visited by a knight without the (-2,-1) and (-2,1) moves on a spirally numbered board moving to the lowest available unvisited square at each step.

Sequence

1, 10, 3, 8, 5, 2, 13, 28, 25, 50, 27, 12, 9, 4, 7, 18, 15, 6, 17, 34, 59, 
14, 11, 24, 49, 52, 29, 32, 55, 58, 89, 54, 31, 88, 53, 26, 79, 120, 83, 
122, 173, 126, 87, 56, 91, 130, 177, 232, 295, 228, 225, 290, 227, 172, 125, 
82, 51, 80, 121, 124, 85, 128, 175...

Comments

Board is numbered with the following square spiral:

  17--16--15--14--13
   |               |
  18   5---4---3  12   .
   |   |       |   |
  19   6   1---2  11   .
   |   |           |
  20   7---8---9--10   .
   |
  21--22--23--24--25--26

Move clarification: starting at 1 the knight can move to 16, 14, 12, 10, 24, and 22 but not 18 or 20.

The sequence is finite: at step 90, square 30 is visited after which there are no free squares to move to and the sequence ends.

Math