%I #10 Apr 23 2021 01:20:26

%S 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,

%T 26,27,36,63,30,39,48,57,66,75,28,31,34,37,40,43,46,49,52,55,58,61,64,

%U 67,70,73,76,79,54,45,72,33,42,51,60,69,78,29,32,35,38,41

%N 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.

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

%H Rémy Sigrist, <a href="/A343600/b343600.txt">Table of n, a(n) for n = 0..6561</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F A053735(a(n)) = A053735(n).

%F A081604(a(n)) = A081604(n).

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

%e The first terms, in base 10 and in base 3, are:

%e n a(n) ter(n) ter(a(n))

%e -- ---- ------ ---------

%e 0 0 0 0

%e 1 1 1 1

%e 2 2 2 2

%e 3 3 10 10

%e 4 4 11 11

%e 5 7 12 21

%e 6 6 20 20

%e 7 5 21 12

%e 8 8 22 22

%e 9 9 100 100

%e 10 12 101 110

%e 11 21 102 210

%e 12 10 110 101

%e 13 13 111 111

%e 14 16 112 121

%o (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 }

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

%K nonn,base,easy

%O 0,3

%A _Rémy Sigrist_, Apr 21 2021