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

1,2

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

Links

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

Rémy Sigrist, PARI program

Example

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.

Prog

(PARI) See Links section.

Crossrefs

Cf. A316667, A326922, A328929, A328928.

Sequence in context: A330008 A335844 A110409 * A309382 A064211 A050133

Adjacent sequences: A361374 A361375 A361376 * A361378 A361379 A361380

Keyword

nonn,fini,full

Author

Jodi Spitz, Mar 09 2023

Extensions

Data corrected by Rémy Sigrist, Mar 12 2023

Status

approved