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.
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, 34, 63, 17, 28, 51, 40, 33, 46, 45, 23, 30, 161, 26, 69, 13, 36, 65, 32, 55, 38, 75, 19, 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
Offset: 1
Examples
The square spiral used is: . 17--16--15--14--13 . | | . 18 5---4---3 12 29 | | | | | 19 6 1---2 11 28 | | | | 20 7---8---9--10 27 | | 21--22--23--24--25--26 . 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. 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.
Links
- Scott R. Shannon, Table of n, a(n) for n = 1..10000
- Scott R. Shannon, Image of the first 50000 visited numbers on the square spiral. 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.
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