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

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Last modified April 1 05:25 EDT 2023. Contains 361673 sequences. (Running on oeis4.)