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A302544
Lexicographically earliest sequence of distinct nonnegative numbers such that for any n >= 0, A065359(a(n)) = - A065359(n).
2
0, 2, 1, 3, 8, 10, 6, 11, 4, 9, 5, 7, 12, 14, 13, 15, 26, 34, 18, 32, 40, 42, 35, 43, 24, 38, 16, 27, 41, 46, 30, 44, 19, 33, 17, 22, 36, 47, 25, 39, 20, 28, 21, 23, 31, 45, 29, 37, 48, 50, 49, 51, 56, 58, 54, 59, 52, 57, 53, 55, 60, 62, 61, 63, 74, 106, 66
OFFSET
0,2
COMMENTS
This sequence is a self-inverse permutation of the nonnegative numbers, with fixed points A039004.
We can build an analog of this sequence for any base b > 1 by considering the alternating sum of digits in base b instead of A065359.
This sequence has similarities with A298847.
The scatter plots have an interesting, "fibrous" look. - Antti Karttunen, Jul 21 2018
EXAMPLE
The first terms, alongside the binary representations of n and of a(n), and A065359(n), are:
n a(n) bin(n) bin(a(n)) A065359(n)
-- ---- ------ --------- ----------
0 0 0 0 0
1 2 1 10 1
2 1 10 1 -1
3 3 11 11 0
4 8 100 1000 1
5 10 101 1010 2
6 6 110 110 0
7 11 111 1011 1
8 4 1000 100 -1
9 9 1001 1001 0
10 5 1010 101 -2
11 7 1011 111 -1
12 12 1100 1100 0
13 14 1101 1110 1
14 13 1110 1101 -1
15 15 1111 1111 0
16 26 10000 11010 1
17 34 10001 100010 2
18 18 10010 10010 0
19 32 10011 100000 1
20 40 10100 101000 2
PROG
(C++) See Links section.
CROSSREFS
Cf. A039004 (fixed points), A065359, A298847.
Sequence in context: A342224 A145490 A329180 * A057300 A076655 A236438
KEYWORD
nonn,look,base
AUTHOR
Rémy Sigrist, Apr 09 2018
STATUS
approved