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.

3199, 9173, 7416, 16270, 12669, 4238, 36667, 10947, 4851, 15027, 34407, 36777, 28411, 29623, 5832, 237635, 17075, 14329, 17064, 8669, 9152, 191876, 65307, 10536, 50425, 7243, 17187, 9730, 307545, 45627, 82813, 16948, 24847, 66622, 23741, 24678, 259181, 147061, 48250, 43525, 78711, 19501, 18600, 59821, 15410, 334131

Offset

1,1

Comments

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?

Links

Table of n, a(n) for n=1..46.

N. J. A. Sloane and Brady Haran, The Trapped Knight, Numberphile video (2019).

Example

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).

Crossrefs

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

Sequence in context: A250386 A069401 A225056 * A211840 A235786 A235781

Adjacent sequences: A306194 A306195 A306196 * A306198 A306199 A306200

Keyword

nonn,tabf

Author

Jud McCranie, Jan 28 2019

Status

approved