A377980 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the binary expansions of A184616(n) and A184616(a(n)) have no common 1's.

0, 1, 2, 4, 3, 5, 7, 6, 8, 9, 10, 14, 15, 16, 11, 12, 13, 17, 18, 20, 19, 21, 27, 28, 29, 30, 31, 22, 23, 24, 25, 26, 32, 33, 34, 36, 35, 37, 39, 38, 40, 41, 42, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 65, 66, 68

Offset

0,3

Comments

A self-inverse permutation of the nonnegative integers.

Empirically, for any n >= 0, abs(a(n) - n) belongs to A001045.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Rémy Sigrist, Colored scatterplot of the sequence for n = 0..2^11 (where the color is function of a(n)-n)

Rémy Sigrist, PARI program

Index entries for sequences that are permutations of the natural numbers

Formula

a(n) <= 2^k iff n <= 2^k.

Example

The first terms, alongside the binary expansions of A184616(n) and A184616(a(n)), are:
  n   a(n)  bin(A184616(n))  bin(A184616(a(n)))
  --  ----  ---------------  ------------------
   0     0                0                   0
   1     1                0                   0
   2     2                0                   0
   3     4                1                   0
   4     3                0                   1
   5     5                0                   0
   6     7               10                   1
   7     6                1                  10
   8     8                0                   0
   9     9                0                   0
  10    10                0                   0
  11    14              101                  10
  12    15              100                   1
  13    16              100                   0
  14    11               10                 101
  15    12                1                 100
  16    13                0                 100

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A001045, A184616.

Sequence in context: A258238 A166266 A011295 * A082016 A074135 A074146

Adjacent sequences: A377977 A377978 A377979 * A377981 A377982 A377983

Keyword

nonn,base

Author

Rémy Sigrist, Dec 28 2024

Status

approved