A361486 Lexicographically earliest sequence of positive numbers on a square spiral such that no three equal numbers are collinear.

1, 1, 1, 1, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 1, 3, 3, 1, 4, 1, 4, 3, 5, 5, 1, 4, 3, 4, 5, 4, 4, 5, 6, 6, 7, 4, 4, 5, 5, 6, 2, 4, 1, 4, 5, 1, 6, 2, 6, 4, 6, 5, 5, 7, 2, 3, 4, 6, 5, 5, 7, 2, 3, 8, 1, 4, 3, 6, 7, 5, 5, 3, 5, 7, 6, 3, 1, 1, 7, 8, 7, 7, 4, 5, 8, 5, 9, 6, 6, 8, 7, 7, 6, 8, 9, 9, 3

Offset: 1

Author

Scott R. Shannon, Mar 13 2023

Keywords

• nonn
• look

Comments

The first term a(1) = 1 lies at the (0,0) origin while all other terms lie on integer coordinates.

Examples

			a(5) = 2 as a(3) = 1 and a(4) = 1 lie on the horizontal line y = 1 relative to the starting square (assuming a counter-clockwise spiral) so a(5) cannot be 1.
a(7) = 3 as a(5) = 2 and a(6) = 2 lie on the vertical line x = -1 so a(7) cannot be 2, while a(1) = 1 and a(3) = 1 lie on the line y = x so a(7) cannot be 1.
a(21) = 4 as a(18) = 3 and a(19) = 3 lie on the line x = -2, a(6) = 2 and a(15) = 2 lie on the line y = 2*x + 2, while a(1) = 1 and a(3) = 1 lie on the line y = x, so a(21) cannot be 1, 2 or 3.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..10000
• Scott R. Shannon, Image of the first 50000 terms on the square spiral. The values are scaled across the spectrum from red to violet to show their relative size. Zoom in to see the numbers.
• Scott R. Shannon, Image highlighting the 1 valued terms in the first 50000 terms on the square spiral. Zoom in to see the numbers.

Crossrefs

Cf. A274640, A229037, A174344, A274923, A346294.