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A356331
Bit-reverse the odd part of the negaFibonacci representation of n: a(n) = A356327(A057889(A215024(n))).
3
0, 1, 2, 3, 4, 5, 6, 7, 8, 17, 10, 11, 12, 13, 14, 15, 19, 9, 18, 16, 20, 21, 51, 44, 24, 38, 26, 32, 28, 45, 46, 31, 27, 33, 34, 35, 36, 48, 25, 39, 40, 49, 53, 43, 23, 29, 30, 47, 37, 41, 50, 22, 52, 42, 54, 55, 140, 133, 58, 106, 115, 79, 62, 113, 127, 99
OFFSET
0,3
COMMENTS
This sequence is a self-inverse permutation of the nonnegative integers similar to A343150, A344682, A345201 and A356332.
FORMULA
a(a(n)) = n.
a(n) <= A000045(2*k) iff n <= A000045(2*k).
EXAMPLE
The first terms, alongside the corresponding negaFibonacci representations, are:
n a(n) nega(n) nega(a(n))
-- ---- ------- ----------
0 0 0 0
1 1 1 1
2 2 100 100
3 3 101 101
4 4 10010 10010
5 5 10000 10000
6 6 10001 10001
7 7 10100 10100
8 8 10101 10101
9 17 1001010 1010010
10 10 1001000 1001000
11 11 1001001 1001001
12 12 1000010 1000010
13 13 1000000 1000000
14 14 1000001 1000001
15 15 1000100 1000100
16 19 1000101 1010001
17 9 1010010 1001010
18 18 1010000 1010000
19 16 1010001 1000101
20 20 1010100 1010100
21 21 1010101 1010101
PROG
(PARI) See Links section.
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Aug 04 2022
STATUS
approved