OFFSET
1,5
COMMENTS
The idea underlying this sequence is to build an infinite binary tree of Gaussian integers:
- for any n > 0, f(n) has children f(2*n) and f(2*n+1),
- f(n), f(2*n) and f(2*n+1) form a right triangle,
- when u has child v and v has child w, then the angle between the vectors (u,v) and (v,w) is 45 degrees.
Among the first 2^20-1 terms, some values around the origin are missing: -2 - 3*i, -2, i, 2 - 2*i, 2, 4 + i, 5 - 2*i; will they ever appear?
Graphically, f has interesting features (see representations of f in Links section).
This sequence has similarities with A322574.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..8191
Rémy Sigrist, Representation of the first layers of the binary tree
Rémy Sigrist, Colored representation of f(n) for n = 1..2^20-1 (where the hue is function of n)
Rémy Sigrist, Colored representation of f(n) for n = 1..2^20-1 (where black pixels correspond to even n)
Rémy Sigrist, Density plot of the first 2^22-1 terms
Rémy Sigrist, PARI program for A326280
EXAMPLE
See representation of the first layers of the binary tree in links section.
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
sign,look
AUTHOR
Rémy Sigrist, Jun 22 2019
STATUS
approved