A361702 Lexicographically earliest sequence of positive numbers on a square spiral such that no four equal numbers lie on the circumference of a circle.

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

Offset

1,4

Comments

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

Links

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Scott R. Shannon, Image of the first 10000 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 10000 terms on the square spiral. Zoom in to see the numbers.

Example

a(4) = 2 as a(1) = a(2) = a(3) = 1 all lie on the circumference of a circle with radius 1/sqrt(2) centered at (1/2,1/2), assuming a counter-clockwise spiral, so a(4) cannot be 1.
a(12) = 3 as a(2) = a(3) = a(11) = 1 all lie on the circumference of a circle with radius 1/sqrt(2) centered at (3/2,1/2), so a(12) cannot be 1, while a(4) = a(8) = a(10) = 2 all lie on the circumference of a circle with radius sqrt(2) centered at (1,0), so a(12) cannot be 2.
a(22) = 4 as a(1) = a(2) = a(7) = 1 all lie on the circumference of a circle with radius sqrt(10)/2 centered at (1/2,-3/2), so a(22) cannot be 1, a(6) = a(19) = a(21) = 2 all lie on the circumference of a circle with radius sqrt(5)/2 centered at (-3/2,-1), so a(22) cannot be 2, while a(12) = a(16) = a(20) = 3 all lie on the circumference of a circle with radius sqrt(5) centered at (0,0), so a(22) cannot be 3.

Crossrefs

Cf. A361486, A274640, A229037, A174344, A274923, A346294.

Sequence in context: A269252 A291150 A292375 * A295218 A338430 A223135

Adjacent sequences: A361699 A361700 A361701 * A361703 A361704 A361705

Keyword

nonn

Author

Scott R. Shannon, Mar 21 2023

Status

approved