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A335899
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Squares visited when moving on a square-spiral numbered board to an unvisited diagonally adjacent square containing the spiral number with the fewest divisors. In case of a tie it chooses the square with the lowest spiral number.
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1
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1, 3, 11, 29, 13, 31, 59, 33, 61, 97, 139, 191, 251, 193, 141, 99, 65, 37, 17, 5, 19, 7, 23, 47, 79, 49, 25, 9
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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The movement on the board in this sequence is restricted to the unvisted diagonally adjacent squares, like a chess bishop but with only one square moves.
The sequence is finite. After 27 steps the square with number 9 is visited, after which all four neighboring squares have been visited.
Due to the paths preference for squares with the fewest divisors it will move to a prime numbered square when possible, and the lowest prime if two or more unvisited primes are in neighboring squares. Of the 27 visited squares 20 contain prime numbers while only 7 contain composites. The largest visited square is a(13) = 251.
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LINKS
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Scott R. Shannon, Image showing the 27 steps of the path. A green dot marks the starting 1 square and a red dot the final square with number 9. The red dot is surrounded by four blue dots to show the occupied neighboring squares. A yellow dots marks the smallest unvisited square with number 2.
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EXAMPLE
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The board is numbered with the square spiral:
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17--16--15--14--13 .
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18 5---4---3 12 29
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19 6 1---2 11 28
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20 7---8---9--10 27
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21--22--23--24--25--26
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a(1) = 1, the starting square of the walk.
a(2) = 3. The four unvisited diagonally adjacent squares around a(1) are numbered 3,5,7,9. Of these 3,5,7 have only two divisors, and 3 is the lowest of those.
a(3) = 11. The three unvisited diagonally adjacent squares around a(2) are numbered 11,13,15. Of these 11 and 13 have only two divisors, and 11 is the lowest of those.
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CROSSREFS
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KEYWORD
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nonn,walk,fini,full
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AUTHOR
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STATUS
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approved
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