

A316328


Lexicographically earliest knight's path on spiral on infinite chessboard.


16



0, 9, 2, 5, 8, 3, 6, 1, 4, 7, 10, 13, 28, 31, 14, 11, 26, 23, 44, 19, 22, 43, 40, 17, 34, 37, 18, 15, 32, 29, 52, 25, 46, 21, 42, 69, 20, 39, 16, 33, 12, 27, 24, 45, 74, 41, 68, 103, 36, 61, 94, 57, 54, 85, 50, 47, 76, 113, 72, 107, 150, 67, 102, 63, 66, 35
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OFFSET

0,2


COMMENTS

On a doublyinfinite chessboard, number all the cells in a counterclockwise spiral starting at a central cell labeled 0. Start with a knight at cell 0, and thereafter always move the knight to the smallest unvisited cell. Sequence gives succession of squares visited.
Sequence ends if knight is unable to move.
Inspired by A316588 and, like that sequence, has only finitely many terms (see A316667 for details).


LINKS

Daniël Karssen, Table of n, a(n) for n = 0..2015
Neil Sloane and Brady Haran, The Trapped Knight, Numberphile video (2019)


FORMULA

a(n) = A316667(n+1)  1.


CROSSREFS

Cf. A316588, A316667, A316338.
Sequence in context: A154838 A082831 A085551 * A323809 A275967 A155799
Adjacent sequences: A316325 A316326 A316327 * A316329 A316330 A316331


KEYWORD

nonn,fini,full,look


AUTHOR

N. J. A. Sloane, Jul 13 2018


EXTENSIONS

Terms a(17) on computed by Daniël Karssen, Jul 10 2018


STATUS

approved



