login
A370631
Lexicographically earliest sequence of distinct positive integers such that the Zeckendorf expansions of two consecutive terms have at least one common term.
3
1, 4, 3, 11, 8, 9, 6, 5, 7, 2, 10, 12, 14, 13, 15, 16, 17, 18, 19, 20, 23, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 57, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67
OFFSET
1,2
COMMENTS
This sequence is a permutation of the positive integers with inverse A370632:
- for k >= 7, the values whose Zeckendorf expansions have largest term A000045(k) appear in a single run of consecutive values; the first value being A000045(k) + 1 or 2, the second value being A000045(k), the remaining values appearing in ascending order.
FORMULA
A000120(A003714(a(n)), A003714(a(n+1))) > 0.
EXAMPLE
The first terms, alongside the Zeckendorf expansion in binary of a(n), are:
n a(n) z(a(n))
-- ---- -------
1 1 1
2 4 101
3 3 100
4 11 10100
5 8 10000
6 9 10001
7 6 1001
8 5 1000
9 7 1010
10 2 10
11 10 10010
12 12 10101
PROG
(PARI) \\ See Links section.
CROSSREFS
Sequence in context: A353341 A375035 A346614 * A370630 A005013 A241643
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, May 01 2024
STATUS
approved