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A332022
Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, n and a(n) have no common term in their Zeckendorf representations.
6
0, 2, 1, 5, 7, 3, 8, 4, 6, 13, 14, 15, 18, 9, 10, 11, 21, 23, 12, 24, 22, 16, 20, 17, 19, 34, 35, 36, 37, 38, 39, 40, 41, 47, 25, 26, 27, 28, 29, 30, 31, 32, 55, 57, 56, 60, 62, 33, 58, 59, 61, 63, 64, 65, 66, 42, 44, 43, 48, 49, 45, 50, 46, 51, 52, 53, 54, 89
OFFSET
0,2
COMMENTS
This sequence is a self-inverse permutation of the nonnegative integers.
Apparently, {a(0), ..., a(k)} = {0, ..., k} for infinitely many integers k.
FORMULA
A003714(n) AND A003714(a(n)) = 0 for any n >= 0 (where AND denotes the bitwise AND operator).
EXAMPLE
The first terms, alongside the Zeckendorf representation in binary of n and of a(n), are:
n a(n) z(n) z(a(n))
-- ---- ----- -------
0 0 0 0
1 2 1 10
2 1 10 1
3 5 100 1000
4 7 101 1010
5 3 1000 100
6 8 1001 10000
7 4 1010 101
8 6 10000 1001
9 13 10001 100000
10 14 10010 100001
PROG
(PARI) See Links section.
CROSSREFS
Cf. A003714, A238757 (binary analog), A332565.
Sequence in context: A369527 A370382 A059039 * A109261 A085240 A002251
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Apr 23 2020
STATUS
approved