OFFSET
0,3
COMMENTS
We ignore leading zeros (and 0 is assumed to have binary length 0).
This sequence is a permutation of the nonnegative integers with inverse A360983.
The order of appearance of two distinct integers, say x and y with x > y, depends on the parity of A360963(x, y): even implies x appears before y, odd implies x appears after y.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 0..8191
Rémy Sigrist, Scatterplot of the first 2^15 terms
Rémy Sigrist, PARI program
EXAMPLE
The first terms, alongside the binary length of their first powers, are:
n a(n) w1 w2 w3 w4 w5 w6
-- ---- -- -- -- -- -- --
0 0 0
1 1 1
2 3 2 4
3 2 2 3
4 6 3 6 8
5 7 3 6 9
6 5 3 5 7 10
7 4 3 5 7 9
8 12 4 8 11
9 15 4 8 12 16 20 24
10 14 4 8 12 16 20 23
11 13 4 8 12 15
12 10 4 7 10 14
13 9 4 7 10 13 16 20
14 8 4 7 10 13 16 19
15 11 4 7 11
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Feb 27 2023
STATUS
approved