|
%I #9 Jul 25 2020 09:48:28
%S 1,3,11,29,13,31,59,33,61,97,139,191,251,193,141,99,65,37,17,5,19,7,
%T 23,47,79,49,25,9
%N 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.
%C 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.
%C The sequence is finite. After 27 steps the square with number 9 is visited, after which all four neighboring squares have been visited.
%C 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.
%H Scott R. Shannon, <a href="/A335899/a335899.png"> Image showing the 27 steps of the path</a>. 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.
%e The board is numbered with the square spiral:
%e .
%e 17--16--15--14--13 .
%e | | .
%e 18 5---4---3 12 29
%e | | | | |
%e 19 6 1---2 11 28
%e | | | |
%e 20 7---8---9--10 27
%e | |
%e 21--22--23--24--25--26
%e .
%e a(1) = 1, the starting square of the walk.
%e 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.
%e 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.
%K nonn,walk,fini,full
%O 1,2
%A _Scott R. Shannon_, Jun 29 2020
|
