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%I A344367 #15 Jun 18 2021 14:50:37
%S A344367 1,11,10,12,13,14,15,16,17,18,19,39,38,37,36,35,34,33,32,31,30,3,23,
%T A344367 22,21,20,40,41,42,43,44,45,46,47,24,25,26,27,28,29,2,52,51,50,80,81,
%U A344367 82,83,84,85,86,87,88,89,90,91,92,93,94,59,58,57,56,55,54,53,125,124,123,122,121,120
%N A344367 Squares visited on a spirally numbered board when stepping to the closest unvisited square that contains a number that shares one or more digits with the number of the current square. If two or more such squares are the same distance away the one with the smaller number is chosen.
%H A344367 Scott R. Shannon, <a href="/A344367/a344367.png">Image of the first 1000 steps.</a>. The colors are graduated across the spectrum to show the relative step order. The lowest unvisited square, 4, is marked with a yellow dot.
%H A344367 Scott R. Shannon, <a href="/A344367/a344367_2.png">Image of the first 200000 steps</a>.
%e A344367 The board is numbered with the square spiral:
%e A344367 .
%e A344367   17--16--15--14--13   .
%e A344367    |               |   .
%e A344367   18   5---4---3  12  29
%e A344367    |   |       |   |   |
%e A344367   19   6   1---2  11  28
%e A344367    |   |           |   |
%e A344367   20   7---8---9--10  27
%e A344367    |                   |
%e A344367   21--22--23--24--25--26
%e A344367 .
%e A344367 a(2) = 11. There are three squares 2 units away from the starting square 1 that also contain the digit 1 - 11, 15, and 19. Of these 11 is the smallest so is the square stepped to.
%e A344367 a(3) = 10. Of the two adjacent squares to 11 that also contain the digit 1 the square 10 is the smallest.
%e A344367 a(4) = 12. This is the only unvisited square within 2 units of a(3) = 10 that also contains the digit 1.
%e A344367 a(12) = 39. This is the only unvisited square within sqrt(2) units of a(11) = 19 that contains either the digit 3 or 9. It is also the first square stepped to that does not share the digit 1 with the previous square.
%Y A344367 Cf. A343530, A296030, A174344, A274923, A067581, A330979, A332767.
%K A344367 nonn,base
%O A344367 1,2
%A A344367 _Scott R. Shannon_ and _Eric Angelini_, May 16 2021

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