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

0,5

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.

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

Formula

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

Example

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

Prog

(Python) # See Bailey link.

Crossrefs

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

Cf. A001481, A256111.

Sequence in context: A071950 A274847 A165922 * A307834 A326616 A249033

Adjacent sequences: A337290 A337291 A337292 * A337294 A337295 A337296

Keyword

nonn

Author

John Bailey, Aug 21 2020

Status

approved