A361377 Squares visited by a knight moving on a spirally numbered board always to the lowest unvisited coprime square.

1, 10, 3, 8, 5, 2, 7, 4, 9, 22, 19, 16, 33, 58, 13, 28, 25, 46, 21, 40, 17, 6, 23, 20, 39, 70, 43, 76, 47, 26, 11, 14, 29, 32, 15, 62, 37, 18, 35, 38, 63, 34, 59, 30, 53, 12, 31, 54, 85, 124, 51, 80, 83, 52, 49, 24, 77, 48, 119, 50, 27, 86, 55, 128, 89, 92

Offset: 1

Author

Jodi Spitz, Mar 09 2023

Keywords

• nonn
• fini
• full

Comments

Many of these sequences (see cross-references) are finite. I've worked this out by hand, but I suspect this sequence is also finite.

The sequence is finite with 156 terms. - Rémy Sigrist, Mar 12 2023

Examples

			The spiral board begins:
   .---.---.--33--32--31
                       |
  17--16--15--14--13  30
   |               |   |
  18   5---4---3  12  29
   |   |       |   |   |
  19   6   1---2  11  28
   |   |           |   |
  20   7---8---9--10  27
   |                   |
  21--22--23--24--25--26
a(9) = 9 and a(10) = 22. For a knight on square 9, the smallest unused square which is both coprime to and a knight's move away from 9 is 22.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..156
• Rémy Sigrist, PARI program

Crossrefs

Cf. A316667, A326922, A328929, A328928.

Programs

PARI

See Links section.

Extensions

Data corrected by Rémy Sigrist, Mar 12 2023