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A370629
Lexicographically earliest sequence of distinct positive integers such that for any n > 0, the Zeckendorf expansions of n and a(n) have exactly one common term.
1
1, 2, 3, 6, 5, 4, 10, 8, 11, 7, 9, 14, 13, 12, 16, 15, 18, 17, 22, 23, 21, 19, 20, 26, 28, 24, 29, 25, 27, 35, 36, 37, 40, 34, 30, 31, 32, 39, 38, 33, 42, 41, 47, 48, 49, 52, 43, 44, 45, 58, 56, 46, 59, 57, 55, 51, 54, 50, 53, 63, 65, 64, 60, 62, 61, 68, 70
OFFSET
1,2
COMMENTS
This sequence is a self-inverse permutation of the positive integers.
Fixed points correspond to positive Fibonacci numbers.
FORMULA
A000120(A003714(n), A003714(a(n))) = 1.
EXAMPLE
The first terms, alongside the Zeckendorf expansion in binary of n and of a(n), are:
n a(n) z(n) z(a(n))
-- ---- ------ -------
1 1 1 1
2 2 10 10
3 3 100 100
4 6 101 1001
5 5 1000 1000
6 4 1001 101
7 10 1010 10010
8 8 10000 10000
9 11 10001 10100
10 7 10010 1010
11 9 10100 10001
12 14 10101 100001
PROG
(PARI) \\ See Links section.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, May 01 2024
STATUS
approved