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%I #23 Dec 23 2020 07:52:38
%S 1,11,13,15,17,19,21,23,25,51,53,55,57,59,61,63,65,67,69,71,73,75,77,
%T 79,81,123,125,127,129,131,133,135,137,139,141,143,145,147,149,151,
%U 153,155,157,159,161,163,165,167,169,227,229,231,233,235,237,239,241,243,245,247,249,251
%N 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.
%C The rook may move over squares it has already visited, only the final square after a full move must not have been visited before.
%C As for A316667, the rook gets trapped as well. This happens after step 185 on square 118.
%C Rook movement on the square spiral is also considered in A336447 and A336413.
%C 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.
%H Patrick Wienhöft, <a href="/A337254/b337254.txt">Table of n, a(n) for n = 1..185</a>
%H Patrick Wienhöft, <a href="https://github.com/PattuX/Traveling-Chess-Piece">Python implementation (incl. graphical output)</a>.
%e 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.
%Y Cf. A316667, A323749, A336413, A336447.
%K nonn
%O 1,2
%A _Patrick Wienhöft_, Aug 21 2020