A357616 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the number of 1's in the ternary expansion of n equals the number of 2's in the ternary expansion of a(n) and vice versa.

0, 2, 1, 6, 8, 5, 3, 7, 4, 18, 20, 11, 24, 26, 17, 15, 23, 14, 9, 19, 10, 21, 25, 16, 12, 22, 13, 54, 56, 29, 60, 62, 35, 33, 47, 32, 72, 74, 51, 78, 80, 53, 59, 71, 44, 45, 61, 34, 65, 77, 50, 38, 52, 41, 27, 55, 28, 57, 69, 42, 30, 46, 31, 63, 73, 48, 75, 79

Offset: 0

Author

Rémy Sigrist, Oct 06 2022

Keywords

• nonn
• base

Comments

This sequence is a self-inverse permutation of the nonnegative integers.

Examples

			The first terms, alongside their ternary expansions, are:
  n   a(n)  ter(n)  ter(a(n))
  --  ----  ------  ---------
   0     0       0          0
   1     2       1          2
   2     1       2          1
   3     6      10         20
   4     8      11         22
   5     5      12         12
   6     3      20         10
   7     7      21         21
   8     4      22         11
   9    18     100        200
  10    20     101        202
  11    11     102        102
  12    24     110        220
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..6560
• Rémy Sigrist, PARI program
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A004488, A005823, A005836, A039001 (fixed points), A062756, A081603, A352760.

Programs

PARI

See Links section.

Formula

A081603(a(n)) = A062756(n).

A062756(a(n)) = A081603(n).

a(n) < 3^k iff n < 3^k.

a(n) = n iff n belongs to A039001.

Empirically:

- a(n) = n/2 iff n belongs to A005823,

- a(n) = 2*n iff n belongs to A005836.