A356332 Bit-reverse the odd part of the negaFibonacci representation of -n (and negate): a(n) = -A356327(A057889(A215025(n))).

0, 1, 2, 3, 4, 10, 6, 7, 8, 9, 5, 11, 12, 31, 27, 23, 16, 17, 28, 19, 20, 21, 22, 15, 24, 30, 26, 14, 18, 29, 25, 13, 32, 33, 86, 82, 65, 71, 38, 78, 61, 57, 42, 51, 44, 45, 72, 83, 74, 62, 50, 43, 75, 53, 54, 55, 56, 41, 58, 77, 70, 40, 49, 63, 64, 36, 79, 85

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 A356331.

Examples

			The first terms, alongside the corresponding negaFibonacci representations, are:
  n   a(n)  nega(-n)  nega(-a(n))
  --  ----  --------  -----------
   0     0         0            0
   1     1        10           10
   2     2      1001         1001
   3     3      1000         1000
   4     4      1010         1010
   5    10    100101       101001
   6     6    100100       100100
   7     7    100001       100001
   8     8    100000       100000
   9     9    100010       100010
  10     5    101001       100101
  11    11    101000       101000
  12    12    101010       101010
  13    31  10010101     10101001
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10945
• 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, A356331.

Programs

PARI

See Links section.

Formula

a(a(n)) = n.

a(n) < A000045(2*k+1) iff n < A000045(2*k+1).