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

0,3

Comments

This sequence is a self-inverse permutation of the nonnegative integers similar to A343150, A344682, A345201 and A356331.

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

Formula

a(a(n)) = n.

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

Example

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A000045, A057889, A215025, A343150, A344682, A345201, A356327, A356331.

Sequence in context: A256618 A140598 A129920 * A065634 A364223 A087548

Adjacent sequences: A356329 A356330 A356331 * A356333 A356334 A356335

Keyword

nonn,base

Author

Rémy Sigrist, Aug 04 2022

Status

approved