OFFSET
0,2
COMMENTS
This sequence is a permutation of the nonnegative integers with inverse A329180.
Apparently, fixed points correspond to A001196.
The sequence has fractal features; for any k >= 0, the set of points { (n, a(n)), n = 0..4^k-1 } is symmetrical relative to the line of equation y + x = 4^k - 1 (see scatterplots in Links section).
LINKS
Rémy Sigrist, Table of n, a(n) for n = 0..4095
Rémy Sigrist, PARI program for A329101
Rémy Sigrist, Scatterplot of the sequence for n = 0..4^3-1
Rémy Sigrist, Scatterplot of the sequence for n = 0..4^10-1
Rémy Sigrist, Colored scatterplot of the sequence for n = 0..4^10-1 (where the color is function of A160381(n))
EXAMPLE
The first terms, alongside the base 4 representations of n and of a(n), are:
n a(n) qua(n) qua(a(n))
-- ---- ------ ---------
0 0 0 0
1 2 1 2
2 1 2 1
3 3 3 3
4 6 10 12
5 10 11 22
6 8 12 20
7 9 13 21
8 4 20 10
9 11 21 23
10 5 22 11
11 7 23 13
12 12 30 30
13 14 31 32
14 13 32 31
15 15 33 33
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Nov 07 2019
STATUS
approved