A395441 - OEIS

%I #7 May 18 2026 10:11:36

%S 1,10,12,14,16,18,3,9,5,19,7,6,4,2,8,24,15,11,13,21,27,32,26,28,40,48,

%T 29,47,25,17,23,52,22,46,34,20,49,41,75,59,39,78,44,42,30,36,45,71,69,

%U 33,61,74,106,38,58,94,109,67,35,55,31,70,64,60,86,54,43,97

%N Squares visited by five knights, all starting on square 1, when moving on a square-spiral numbered board and always moving to the lowest available unvisited square.

%C All five knights, numbered 1..5, start at square one, and each moves in turn to the lowest available unvisited square, starting with the lowest numbered knight.

%C The sequence is finite - knight 2 is trapped on square 2768 after visiting 570 squares, knight 3 is trapped on square 4129 after visiting 809 squares, knight 5 is trapped on square 3799 after visiting 1155 squares, knight 1 is trapped on square 5876 after visiting 1268 squares, and knight 4 is trapped on square 10535 after visiting 6209 squares, giving a total of 10007 visited squares.

%H Scott R. Shannon, <a href="/A395441/b395441.txt">Table of n, a(n) for n = 1..10007</a>

%H Scott R. Shannon, <a href="/A395441/a395441.png">Image of the knights' paths</a>. The knights' paths are colored red, yellow, green, blue and indigo, the final squares for knights 1, 2, 3 and 5 are colored yellow, and the final square for knight 4 is colored red.

%Y Cf. A338290, A395439, A395440, A395442-A395444, A316667.

%K nonn,fini,full

%O 1,2

%A _Scott R. Shannon_, Apr 23 2026