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A362027 Squares visited by a knight moving on a square-spiral numbered board where the knight moves to a previously unvisited square with a number as close as possible to the number of the current square. If two such squares exist the smaller numbered square is chosen.

%I A362027 #18 Apr 16 2023 20:25:56
%S A362027 1,10,3,6,9,12,15,18,7,4,11,8,5,2,13,28,25,46,21,40,17,34,59,56,29,32,
%T A362027 55,58,33,30,53,26,47,22,19,16,37,62,95,136,91,130,87,52,49,24,27,48,
%U A362027 51,80,83,120,123,84,81,118,77,44,41,68,103,100,63,66,39,36,61,94,57,88,127,174,229,170
%N A362027 Squares visited by a knight moving on a square-spiral numbered board where the knight moves to a previously unvisited square with a number as close as possible to the number of the current square. If two such squares exist the smaller numbered square is chosen.
%C A362027 This sequence is finite: after 130 squares have been visited the square with number 50 is reached after which all eight neighboring squares the knight could move to have already been visited. See the linked image. The largest visited square is a(117) = 247 while the smallest unvisited square is 20.
%H A362027 Scott R. Shannon, <a href="/A362027/b362027.txt">Table of n, a(n) for n = 1..130</a>.
%H A362027 Scott R. Shannon, <a href="/A362027/a362027.png">Image showing the 129 steps of the knight's path</a>. The first and last squares are highlighted in green and red respectively while the eight squares blocking the final square are surrounded in blue.
%e A362027 The board is numbered with the square spiral:
%e A362027 .
%e A362027   17--16--15--14--13   .
%e A362027    |               |   .
%e A362027   18   5---4---3  12   29
%e A362027    |   |       |   |   |
%e A362027   19   6   1---2  11   28
%e A362027    |   |           |   |
%e A362027   20   7---8---9--10   27
%e A362027    |                   |
%e A362027   21--22--23--24--25--26
%e A362027 .
%e A362027 a(6) = 12 as after the knight moves to the square containing 9 the available unvisited squares are 4, 12, 22, 26, 28, 46, 48. Of these 12, where |12 - 9| = 3, is the closest number to 9. This is the first term to differ from A316667.
%Y A362027 Cf. A316667, A358278, A358150, A328929, A328909, A174344, A274923.
%K A362027 nonn,fini,full
%O A362027 1,2
%A A362027 _Scott R. Shannon_, Apr 05 2023