A356331 Bit-reverse the odd part of the negaFibonacci representation of n: a(n) = A356327(A057889(A215024(n))).

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

Author

Rémy Sigrist, Aug 04 2022

Keywords

• nonn
• base

Comments

This sequence is a self-inverse permutation of the nonnegative integers similar to A343150, A344682, A345201 and A356332.

Examples

			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
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..6765
• Rémy Sigrist, PARI program
• Index entries for sequences related to Zeckendorf expansion of n
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000045, A057889, A215025, A343150, A344682, A345201, A356327, A356332.

Programs

PARI

See Links section.

Formula

a(a(n)) = n.

a(n) <= A000045(2*k) iff n <= A000045(2*k).