A342102 Lexicographically latest sequence of distinct nonnegative integers such that for any n >= 0, {A000120(n), A080791(n)} = {A000120(a(n)), A080791(a(n))}.
0, 1, 2, 3, 6, 5, 4, 7, 14, 12, 10, 13, 9, 11, 8, 15, 30, 28, 26, 25, 24, 22, 21, 29, 20, 19, 18, 27, 17, 23, 16, 31, 62, 60, 58, 56, 57, 52, 50, 54, 53, 49, 44, 51, 42, 48, 46, 61, 45, 41, 38, 43, 37, 40, 39, 59, 35, 36, 34, 55, 33, 47, 32, 63, 126, 124, 122
Offset: 0
Examples
The first terms, in decimal and in binary, alongside {A000120(n), A080791(n)}, are:
n a(n) bin(n) bin(a(n)) {A000120(n), A080791(n)}
-- ---- ------ --------- ------------------------
0 0 0 0 {0}
1 1 1 1 {0, 1}
2 2 10 10 {1}
3 3 11 11 {0, 2}
4 6 100 110 {1, 2}
5 5 101 101 {1, 2}
6 4 110 100 {1, 2}
7 7 111 111 {0, 3}
8 14 1000 1110 {1, 3}
9 12 1001 1100 {2}
10 10 1010 1010 {2}
11 13 1011 1101 {1, 3}
12 9 1100 1001 {2}
13 11 1101 1011 {1, 3}
14 8 1110 1000 {1, 3}
15 15 1111 1111 {0, 4}
Links
- Rémy Sigrist, Table of n, a(n) for n = 0..8191
- Rémy Sigrist, Colored scatterplot of the first 2^20 terms (where the color is function of min(A000120(n), A080791(n)))
- Rémy Sigrist, PARI program for A342102
- Index entries for sequences related to binary expansion of n
- Index entries for sequences that are permutations of the natural numbers
Crossrefs
Programs
-
PARI
\\ See Links section.
Formula
a(2^k-1) = 2^k-1 for any k >= 0.
a(n) < 2^k for any n < 2^k.
Comments