A337293 a(n) is the squared distance to the origin of the n-th vertex on an acute angled Babylonian spiral.

0, 1, 1, 1, 2, 2, 5, 1, 8, 8, 5, 17, 1, 26, 0, 29, 5, 25, 25, 18, 34, 5, 50, 1, 49, 17, 18, 52, 5, 85, 2, 90, 18, 61, 125, 13, 148, 10, 153, 20, 98, 125, 41, 145, 4, 148, 18, 85, 170, 18, 225, 148, 202, 173, 61, 197, 41, 226, 10, 229, 25, 117, 170, 5, 208, 80

Offset: 0

Author

John Bailey, Aug 21 2020

Keywords

• nonn

Comments

An acute angled Babylonian spiral is constructed by starting with a zero vector and progressively concatenating the next longest vector with integral endpoints on a Cartesian grid. (The squares of the lengths of these vectors are A001481.) The direction of the new vector is chosen to maximize the change in direction from the previous vector. The Babylonian spiral (A256111) minimizes this angle.

Examples

			The coordinates of the first few points are (0,0), (0,1), (1,0), (-1,0), (1,1), (-1,-1), (-1,2).
		

Links

• John Bailey, Table of n, a(n) for n = 0..10000
• John Bailey, Illustrations of 10, 100, 1000, 10000, 100000, 1500000, 10000000
• John Bailey, Python code with plots

Crossrefs

x-coordinates given in A337311. y-coordinates given in A337312.

Cf. A001481, A256111.

Programs

Python

# See Bailey link.

Formula

a(n) = A337311(n)^2 + A337312(n)^2.