This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A335585 #21 Feb 05 2021 00:16:57 %S A335585 1,2,3,4,9,8,15,14,5,6,25,12,35,16,7,10,21,20,27,22,39,11,18,77,24,49, %T A335585 34,63,17,28,51,40,33,46,45,23,30,161,26,69,13,36,65,32,55,38,75,19, %U A335585 42,95,44,85,48,115,52,105,62,87,68,29,54,203,60,119,76,153,70,117,50,57,56,81,58,93 %N A335585 The numbers visited on a square spiral, with a(n) = n for 1 <= n <= 3, when stepping to an unvisited number as close as possible to the n = 1 starting position that has at least one common factor with the second last visited number but none with the last visited number. In case of a tie, choose the smallest number. %C A335585 This sequence is the square spiral version of the Yellowstone permutation A098550. The same rules for selecting the next number apply except that, instead of choosing the smallest unvisited number for a(n), the number closest to the starting n = 1 position which satisfies the selection rules is chosen. If two or more such numbers exist then the smallest is chosen. %C A335585 The first term that differs from A098550 is a(23) = 18. See the examples below. %H A335585 Scott R. Shannon, <a href="/A335585/b335585.txt">Table of n, a(n) for n = 1..10000</a> %H A335585 Scott R. Shannon, <a href="/A335585/a335585.png">Image of the first 50000 visited numbers on the square spiral</a>. The colors are graduated across the spectrum from red to violet to indicate the relative visit order of the numbers. The starting 1 position is colored white. %e A335585 The square spiral used is: %e A335585 . %e A335585 17--16--15--14--13 . %e A335585 | | . %e A335585 18 5---4---3 12 29 %e A335585 | | | | | %e A335585 19 6 1---2 11 28 %e A335585 | | | | %e A335585 20 7---8---9--10 27 %e A335585 | | %e A335585 21--22--23--24--25--26 %e A335585 . %e A335585 a(7) = 15 as a(5) = 9 = 3*3 and a(8) = 8 = 2*2*2, thus a(7) must contain 3 as a factor but not 2. The closest unvisited number to the starting 1 position that satisfies these conditions is 15. %e A335585 a(23) = 18 as a(21) = 39 = 3*13 and a(22) = 11, thus a(23) must contain 3 or 13 as a factor but not 11. The smallest unvisited number satisfying these conditions is 13, which is sqrt(8) units from 1. However 18 is unvisited and also satisfies the conditions, and is only sqrt(5) units from 1, thus a(23) = 18. This is the first term that differs from A098550. %Y A335585 Cf. A098550, A335661, A330979, A340783, A336957, A064413. %K A335585 nonn,walk %O A335585 1,2 %A A335585 _Scott R. Shannon_, Jan 26 2021