A361377 - OEIS

%I #25 Mar 19 2023 21:15:45

%S 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,

%T 43,76,47,26,11,14,29,32,15,62,37,18,35,38,63,34,59,30,53,12,31,54,85,

%U 124,51,80,83,52,49,24,77,48,119,50,27,86,55,128,89,92

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

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

%C The sequence is finite with 156 terms. - _Rémy Sigrist_, Mar 12 2023

%H Rémy Sigrist, <a href="/A361377/b361377.txt">Table of n, a(n) for n = 1..156</a>

%H Rémy Sigrist, <a href="/A361377/a361377.gp.txt">PARI program</a>

%e The spiral board begins:

%e    .---.---.--33--32--31

%e                        |

%e   17--16--15--14--13  30

%e    |               |   |

%e   18   5---4---3  12  29

%e    |   |       |   |   |

%e   19   6   1---2  11  28

%e    |   |           |   |

%e   20   7---8---9--10  27

%e    |                   |

%e   21--22--23--24--25--26

%e 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.

%o (PARI) See Links section.

%Y Cf. A316667, A326922, A328929, A328928.

%K nonn,fini,full

%O 1,2

%A _Jodi Spitz_, Mar 09 2023

%E Data corrected by _Rémy Sigrist_, Mar 12 2023