cp's OEIS Frontend

A358278 Squares visited by a knight moving on a square-spiral numbered board where the knight moves to the smallest numbered unvisited square and where the square is on a different square ring of numbers than the current square.

%I A358278 #7 Nov 10 2022 07:40:52
%S A358278 1,10,3,16,33,4,11,8,19,38,5,14,29,2,13,28,9,12,27,24,7,18,35,60,15,6,
%T A358278 17,34,59,30,53,26,79,46,21,40,67,36,61,32,55,86,51,48,23,44,71,20,39,
%U A358278 66,99,62,37,68,41,22,43,70,105,148,65,98,139,94,31,54,85,50,25,52,49,78,45,74
%N A358278 Squares visited by a knight moving on a square-spiral numbered board where the knight moves to the smallest numbered unvisited square and where the square is on a different square ring of numbers than the current square.
%C A358278 This sequence is finite: after 1455 squares have been visited the square with number 1345 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(1374) = 1996 while the smallest unvisited square is 1024.
%H A358278 Scott R. Shannon, <a href="/A358278/a358278.png">Image showing the knight's path on the square spiral</a>. The starting 1 square is shown as a green dot while the final square numbered 1345, near the middle of the bottom edge, is shown as a red dot. Also shown as blue dots are the eight occupied squares around the final square.
%e A358278 The board is numbered using a square spiral. The square rings of numbers are shown below:
%e A358278 .
%e A358278     17--16--15--14--13   .
%e A358278      |               |   .
%e A358278     18   5---4---3  12  29
%e A358278      |   |       |   |   |
%e A358278     19   6   1   2  11  28
%e A358278      |   |       |   |   |
%e A358278     20   7---8---9  10  27
%e A358278      |               |   |
%e A358278     21--22--23--24--25  26
%e A358278                          |
%e A358278    -44--45--46--47--48--49
%e A358278 .
%e A358278 a(4) = 16 as after the knight moves to the square containing a(3) = 3 the available unvisited squares are 6, 8, 16, 28, 30, 32, 34. Of these 6 and 8 are the smallest but both of them lie on the first square ring of numbers, the same as the current number 3. Of the remaining squares the smallest unvisited square is 16. This is the first term to differ from A316667.
%Y A358278 Cf. A316667, A358150, A328929, A328909, A174344, A274923.
%K A358278 nonn,fini
%O A358278 1,2
%A A358278 _Scott R. Shannon_ and _Eric Angelini_, Nov 08 2022