A348025 - OEIS

%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