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A306197 The label of the largest square that an (m,n)-leaper (a generalization of a chess knight) reaches before it can no longer move, starting on a board with squares spirally numbered, starting at 1. Each move is to the lowest-numbered unvisited square. 0

%I #10 Sep 26 2019 11:03:13

%S 3199,9173,7416,16270,12669,4238,36667,10947,4851,15027,34407,36777,

%T 28411,29623,5832,237635,17075,14329,17064,8669,9152,191876,65307,

%U 10536,50425,7243,17187,9730,307545,45627,82813,16948,24847,66622,23741,24678,259181,147061,48250,43525,78711,19501,18600,59821,15410,334131

%N The label of the largest square that an (m,n)-leaper (a generalization of a chess knight) reaches before it can no longer move, starting on a board with squares spirally numbered, starting at 1. Each move is to the lowest-numbered unvisited square.

%C The entries are the lower triangle of an array, for (m,n)-leaper, where 1 <= n < m, ordered: (2,1), (3,1), (3,2), (4,1), (4,2), etc. Are all terms finite?

%H N. J. A. Sloane and Brady Haran, <a href="https://www.youtube.com/watch?v=RGQe8waGJ4w">The Trapped Knight</a>, Numberphile video (2019).

%e A chess knight (a (2,1)-leaper) reaches the square labeled 3199 before it reaches the square labeled 2084 and has no moves available (see A316667).

%Y Cf. A316667, A323749, A323750, A317106, A317471, A317416, A323750, A317438, A317916.

%K nonn,tabf

%O 1,1

%A _Jud McCranie_, Jan 28 2019

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