Patrick Wienhöft - cp's OEIS frontend

User: Patrick Wienhöft

Patrick Wienhöft has authored 1 sequences.

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

Patrick Wienhöft, Aug 21 2020

nonn

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.

			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.

Patrick Wienhöft, Table of n, a(n) for n = 1..185
Patrick Wienhöft, Python implementation (incl. graphical output).

Cf. A316667, A323749, A336413, A336447.

cp's OEIS Frontend

User: Patrick Wienhöft

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.

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