A337254 Squares visited by a rook moving on a spirally numbered board always to the lowest available unvisited square with a move length of the current square (in decimal) + 1.

1, 11, 13, 15, 17, 19, 21, 23, 25, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 227, 229, 231, 233, 235, 237, 239, 241, 243, 245, 247, 249, 251

Offset

1,2

Comments

The rook may move over squares it has already visited, only the final square after a full move must not have been visited before.

As for A316667, the rook gets trapped as well. This happens after step 185 on square 118.

Rook movement on the square spiral is also considered in A336447 and A336413.

This is a variation of generalized knights, as in A323749, where here each move is a (x,0)-leaper but as opposed to A323749 the x changes depending on the current square rather than having a fixed size for each move.

Links

Patrick Wienhöft, Table of n, a(n) for n = 1..185

Patrick Wienhöft, Python implementation (incl. graphical output).

Example

The rook starts on square a(1) = 1. Thus its available moves are of length len(1) + 1 = 2, possibly reaching squares 11, 15, 19 and 23. Since 11 is the smallest value, a(2) = 11. From there on, the next move must have length len(11) + 1 = 3, etc.

Crossrefs

Cf. A316667, A323749, A336413, A336447.

Sequence in context: A292513 A171491 A277268 * A152200 A277694 A179084

Adjacent sequences: A337251 A337252 A337253 * A337255 A337256 A337257

Keyword

nonn

Author

Patrick Wienhöft, Aug 21 2020

Status

approved