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

%I A361377 #25 Mar 19 2023 21:15:45
%S A361377 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 A361377 43,76,47,26,11,14,29,32,15,62,37,18,35,38,63,34,59,30,53,12,31,54,85,
%U A361377 124,51,80,83,52,49,24,77,48,119,50,27,86,55,128,89,92
%N A361377 Squares visited by a knight moving on a spirally numbered board always to the lowest unvisited coprime square.
%C A361377 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 A361377 The sequence is finite with 156 terms. - _Rémy Sigrist_, Mar 12 2023
%H A361377 Rémy Sigrist, <a href="/A361377/b361377.txt">Table of n, a(n) for n = 1..156</a>
%H A361377 Rémy Sigrist, <a href="/A361377/a361377.gp.txt">PARI program</a>
%e A361377 The spiral board begins:
%e A361377    .---.---.--33--32--31
%e A361377                        |
%e A361377   17--16--15--14--13  30
%e A361377    |               |   |
%e A361377   18   5---4---3  12  29
%e A361377    |   |       |   |   |
%e A361377   19   6   1---2  11  28
%e A361377    |   |           |   |
%e A361377   20   7---8---9--10  27
%e A361377    |                   |
%e A361377   21--22--23--24--25--26
%e A361377 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 A361377 (PARI) See Links section.
%Y A361377 Cf. A316667, A326922, A328929, A328928.
%K A361377 nonn,fini,full
%O A361377 1,2
%A A361377 _Jodi Spitz_, Mar 09 2023
%E A361377 Data corrected by _Rémy Sigrist_, Mar 12 2023