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A306527 Squares visited by a knight moving on an open-rectangle-numbered board and moving to the lowest available unvisited square at each step.

%I A306527 #24 Mar 24 2022 16:32:25
%S A306527 1,8,11,2,5,10,7,4,9,16,3,6,13,22,35,18,21,12,15,26,23,14,25,38,55,20,
%T A306527 17,32,47,70,31,34,49,30,19,36,53,50,69,46,93,48,29,68,95,72,33,54,37,
%U A306527 24,27,42,39,56,77,52,71,74,97,100,51,76,101
%N A306527 Squares visited by a knight moving on an open-rectangle-numbered board and moving to the lowest available unvisited square at each step.
%C A306527 The half-infinite board is numbered from square 1 as follows:
%C A306527 .
%C A306527   |       |       |       |       |       |       |       |
%C A306527 --+-------+-------+-------+-------+-------+-------+-------+--
%C A306527   |       |       |       |       |       |       |       |
%C A306527   |  25 . . .24 . . .23 . . .22 . . .21 . . .20 . . .19   |
%C A306527   |   .   |       |       |       |       |       |   .   |
%C A306527 --+---.---+-------+-------+-------+-------+-------+---.---+--
%C A306527   |   .   |       |       |       |       |       |   .   |
%C A306527   |  26   |  13 . . .12 . . .11 . . .10 . . . 9   |  18   |
%C A306527   |   .   |   .   |       |       |       |   .   |   .   |
%C A306527 --+---.---+---.---+-------+-------+-------+---.---+---.---+--
%C A306527   |   .   |   .   |       |       |       |   .   |   .   |
%C A306527   |  27   |  14   |   5 . . . 4 . . . 3   |   8   |  17   |
%C A306527   |   .   |   .   |   .   |       |   .   |   .   |   .   |
%C A306527 --+---.---+---.---+---.---+-------+---.---+---.---+---.---+--
%C A306527   |   .   |   .   |   .   |       |   .   |   .   |   .   |
%C A306527   |  28   |  15   |   6   |   1   |   2   |   7   |  16   |
%C A306527   |       |       |       |       |       |       |       |
%C A306527 --+-------+-------+-------+-------+-------+-------+-------+--
%C A306527 .
%C A306527 The knight begins at square 1. This is a finite sequence: after 326 steps square 562 is reached after which all squares within one knight move have been visited.
%H A306527 Scott R. Shannon, <a href="/A306527/b306527.txt">Table of n, a(n) for n = 1..326</a>
%H A306527 Scott R. Shannon, <a href="/A306527/a306527.png">Image showing the knight path</a>. The green dot is the starting square 1, the red dot is the end square 562. 4 Blue dots have been added around the final square to show all available positions have been visited.
%H A306527 Scott R. Shannon, <a href="/A306527/a306527.java.txt">Simplified Java code for the sequence</a>
%H A306527 N. J. A. Sloane and Brady Haran, <a href="https://www.youtube.com/watch?v=RGQe8waGJ4w">The Trapped Knight</a>, Numberphile video (2019)
%Y A306527 Cf. A316667, A316588.
%K A306527 nonn,fini,full
%O A306527 1,2
%A A306527 _Scott R. Shannon_, Feb 21 2019