A361945 If the ternary expansion of n starts with the digit 1, then replace 2's by 0's and vice versa; if the ternary expansion of n starts with the digit 2, then replace 1's by 0's and vice versa; a(0) = 0.

0, 1, 2, 5, 4, 3, 7, 6, 8, 17, 16, 15, 14, 13, 12, 11, 10, 9, 22, 21, 23, 19, 18, 20, 25, 24, 26, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 67, 66, 68, 64, 63, 65, 70, 69, 71, 58, 57, 59, 55, 54

Offset: 0

Author

Rémy Sigrist, Mar 31 2023

Keywords

• nonn
• base
• easy

Comments

Leading zeros in ternary expansions are ignored.

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

Examples

			The first terms, in decimal and in ternary, are:
  n   a(n)  ter(n)  ter(a(n))
  --  ----  ------  ---------
   0     0       0          0
   1     1       1          1
   2     2       2          2
   3     5      10         12
   4     4      11         11
   5     3      12         10
   6     7      20         21
   7     6      21         20
   8     8      22         22
   9    17     100        122
  10    16     101        121
  11    15     102        120
  12    14     110        112
  13    13     111        111
  14    12     112        110
  15    11     120        102
		

Links

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

Crossrefs

Cf. A048328 (fixed points), A122586, A171960.

Programs

PARI

a(n) = { my (d = digits(n, 3), m); if (#d==0, m = [0,1,2], d[1]==1, m = [2,1,0], m = [1,0,2]); fromdigits(apply(t -> m[1+t], d), 3); }

Formula

a(n) = n iff n belongs to A048328.

a(n) = A171960(n) when A122586(n) = 1.