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A332837 Squares visited by a knight moving on a double spiral numbered board and moving to the lowest available unvisited square at each step.

%I A332837 #23 Jul 02 2020 08:50:00
%S A332837 1,10,5,2,8,7,4,3,9,6,12,18,33,39,20,11,32,19,13,22,28,15,21,38,61,30,
%T A332837 17,42,25,31,16,43,24,51,76,26,45,70,37,14,29,23,40,34,57,86,49,55,84,
%U A332837 78,53,47,72,107,41,35,56,27,44,71,36,59,88,127,80,115
%N A332837 Squares visited by a knight moving on a double spiral numbered board and moving to the lowest available unvisited square at each step.
%C A332837 This sequence uses a double spiral of numbers to enumerate the squares on the board. The knight starts on the square with number 1. At each step the knight goes to an unvisited square with the smallest number.
%C A332837 The sequence is finite. After 2958 steps the square with number 2796 is visited, after which all neighboring squares have been visited.
%C A332837 The lowest unvisited square during the walk is square number 2011.
%H A332837 Scott R. Shannon, <a href="/A332837/b332837.txt">Table of n, a(n) for n = 1..2959</a>
%H A332837 Scott R. Shannon, <a href="/A332837/a332837.png">Image showing the 2958 steps of the knights' path</a>. The green dot is the starting square and the red dot the final square. Blue dots show the eight occupied squares surrounding the final square. The lowest unvisited square is the yellow dot.
%e A332837 The squares are numbered using the double spiral numbering shown below:
%e A332837 .
%e A332837   --48--46--44--42--40--38--36
%e A332837                              |
%e A332837     27--25--23--21--19--17  34
%e A332837      |                   |   |
%e A332837     29  10---8---6---4  15  32
%e A332837      |   |           |   |   |
%e A332837     31  12   3---1---2  13  30
%e A332837      |   |   |           |   |
%e A332837     33  14   5---7---9--11  28
%e A332837      |   |                   |
%e A332837     35  16--18--20--22--24--26
%e A332837      |
%e A332837     37--39--41--43--45--47--49--
%Y A332837 Cf. A220098, A316667, A329022, A332980 (quadruple spiral).
%K A332837 nonn,walk,fini,full
%O A332837 1,2
%A A332837 _Scott R. Shannon_, Feb 26 2020