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

0,2

Comments

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

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

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.

Example

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

Prog

(PARI) See Links section.

Crossrefs

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

Sequence in context: A342369 A342842 A352760 * A048850 A004488 A224976

Adjacent sequences: A357613 A357614 A357615 * A357617 A357618 A357619

Keyword

nonn,base

Author

Rémy Sigrist, Oct 06 2022

Status

approved