A343600 For any positive number n, the ternary representation of a(n) is obtained by left-rotating the ternary representation of n until a nonzero digit appears again as the leftmost digit; a(0) = 0.

0, 1, 2, 3, 4, 7, 6, 5, 8, 9, 12, 21, 10, 13, 16, 19, 22, 25, 18, 15, 24, 11, 14, 17, 20, 23, 26, 27, 36, 63, 30, 39, 48, 57, 66, 75, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 54, 45, 72, 33, 42, 51, 60, 69, 78, 29, 32, 35, 38, 41

Offset: 0

Author

Rémy Sigrist, Apr 21 2021

Keywords

• nonn
• base
• easy

Comments

This sequence is a permutation of the nonnegative integers with inverse A343601.

Examples

			The first terms, in base 10 and in base 3, are:
  n   a(n)  ter(n)  ter(a(n))
  --  ----  ------  ---------
   0     0       0          0
   1     1       1          1
   2     2       2          2
   3     3      10         10
   4     4      11         11
   5     7      12         21
   6     6      20         20
   7     5      21         12
   8     8      22         22
   9     9     100        100
  10    12     101        110
  11    21     102        210
  12    10     110        101
  13    13     111        111
  14    16     112        121
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..6561
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A053735, A081604, A139708 (binary variant), A160384, A343601 (inverse).

Programs

PARI

a(n, base=3) = { my (d=digits(n, base)); for (k=2, #d, if (d[k], return (fromdigits(concat(d[k..#d], d[1..k-1]), base)))); n }

Formula

A053735(a(n)) = A053735(n).

A081604(a(n)) = A081604(n).

a^k(n) = n for k = A160384(n) (where a^k denotes the k-th iterate of a).