A324606 The x-coordinates of squares visited by knight moves on a spirally numbered board and moving to the lowest available unvisited square at each step.

0, 2, 1, -1, 1, 0, -1, 1, -1, 0, 2, 1, 3, 2, 0, 2, 3, 1, -1, -2, 0, -2, -3, -2, -1, -3, -2, -1, 1, 3, 4, 3, 1, -1, -3, -4, -2, -3, -2, 0, 2, 3, 2, 0, -2, -3, -4, -5, -3, -1, 1, 3, 4, 5, 4, 2, 0, -2, -4, -5, -6, -4, -5, -3, -4, -2, -3, -4, -2, 0, 2, 4, 5, 4, 3

Offset

1,2

Links

Peter Kagey, Table of n, a(n) for n = 1..2016

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

Visualization of walk using Plot 2. - Peter Kagey, Jul 15 2019

Formula

a(n) = A174344(A316667(n)).

Crossrefs

Cf. A174344, A316667.

A324607 gives y-coordinates.

Sequence in context: A261029 A117195 A156606 * A194087 A107034 A117410

Adjacent sequences: A324603 A324604 A324605 * A324607 A324608 A324609

Keyword

sign,fini,full,walk

Author

Peter Kagey, Jun 06 2019

Status

approved