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%I #9 Oct 06 2021 12:48:58
%S 1,11,55,15,21,3,9,27,30,2,6,14,16,10,4,8,12,18,20,32,34,28,22,24,26,
%T 36,33,39,42,38,40,46,44,48,45,5,25,65,13,91,7,35,49,105,51,17,153,57,
%U 19,114,50,52,54,56,66,68,62,58,29,87,84,60,63,69,23,161,77,99,93,31,124,70,72
%N The numbers visited on a square spiral when stepping to the smallest unvisited number that is not visible from and shares a divisor > 1 with the current number. Start with 1 and 11.
%C A number is not visible from the current number if, given it has coordinates (x,y) relative to the current number, the greatest common divisor of |x| and |y| is greater than 1. The sequence has a(2) = 11 as that is the smallest number not visible from a(1) = 1.
%C In the first 10000 terms the longest single step is one at n = 6888 of length sqrt(22556) units between 22203 to 7389. The maximum difference between terms in the same range is from 3469 to 58973 at n = 9709.
%H Scott R. Shannon, <a href="/A348025/a348025.gif">Image of the path for the first 10000 terms</a>. The colors are graduated across the spectrum to show the relative step order.
%e The square spiral is numbered as follows:
%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(3) = 55 as gcd(55,11) = 11 and 55 is unvisited and not visible from 11, being blocked by 29.
%e a(4) = 15 as gcd(15,55) = 5 and 15 is unvisited and not visible from 55, being blocked by 13, 14 and 30.
%e a(5) = 21 as gcd(21,15) = 3 and 21 is unvisited and not visible from 15, being blocked by 6.
%Y Cf. A348022 (visible), A331400, A335661, A063826, A332767.
%K nonn
%O 1,2
%A _Scott R. Shannon_, Sep 25 2021
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