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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

On a doubly-infinite 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

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Last modified June 19 17:48 EDT 2019. Contains 324222 sequences. (Running on oeis4.)