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A343602 For any positive number n, the balanced ternary representation of a(n) is obtained by left-rotating the balanced ternary representation of n until a nonzero digit appears again as the leftmost digit; a(0) = 0.

%I A343602 #13 Apr 23 2021 01:20:35
%S A343602 0,1,-2,3,4,-11,-8,-5,-6,9,12,7,10,13,-38,-35,-32,-29,-26,-23,-20,-17,
%T A343602 -14,-33,-24,-15,-18,27,36,21,30,39,16,19,22,25,28,31,34,37,40,-119,
%U A343602 -116,-113,-110,-107,-104,-101,-98,-95,-92,-89,-86,-83,-80,-77,-74
%N A343602 For any positive number n, the balanced ternary representation of a(n) is obtained by left-rotating the balanced ternary representation of n until a nonzero digit appears again as the leftmost digit; a(0) = 0.
%C A343602 This sequence can be extended to negative indexes by setting a(-n) = -a(n) for any n > 0. We then obtain a permutation of the integers (Z) with inverse A343601 (after a similar extension to negative indexes).
%H A343602 Rémy Sigrist, <a href="/A343602/b343602.txt">Table of n, a(n) for n = 0..9841</a>
%F A343602 A065363(a(n)) = A065363(n).
%F A343602 A134021(a(n)) = A134021(n).
%F A343602 a^k(n) = n for k = A005812(n) (where a^k denotes the k-th iterate of a).
%e A343602 The first terms, in base 10 and in balanced ternary (where T denotes the digit -1), are:
%e A343602   n   a(n)  bter(n)  bter(a(n))
%e A343602   --  ----  -------  ----------
%e A343602    0     0        0           0
%e A343602    1     1        1           1
%e A343602    2    -2       1T          T1
%e A343602    3     3       10          10
%e A343602    4     4       11          11
%e A343602    5   -11      1TT         TT1
%e A343602    6    -8      1T0         T01
%e A343602    7    -5      1T1         T11
%e A343602    8    -6      10T         T10
%e A343602    9     9      100         100
%e A343602   10    12      101         110
%e A343602   11     7      11T         1T1
%e A343602   12    10      110         101
%e A343602   13    13      111         111
%e A343602   14   -38     1TTT        TTT1
%e A343602   15   -35     1TT0        TT01
%o A343602 (PARI) a(n) = { my (d = [], t); while (n, d = concat(t = centerlift(Mod(n,3)), d); n = (n-t)\3); for (k=2, #d, if (d[k], return (fromdigits(concat(d[k..#d], d[1..k-1]), 3)))); return (fromdigits(d, 3)) }
%Y A343602 Cf. A005812, A065363, A134021, A139708 (binary variant), A343600 (ternary variant), A343603 (inverse).
%K A343602 sign,base
%O A343602 0,3
%A A343602 _Rémy Sigrist_, Apr 21 2021