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A343603 For any positive number n, the balanced ternary representation of a(n) is obtained by right-rotating the balanced ternary representation of n until a nonzero digit appears again as the leftmost digit; a(0) = 0.

%I A343603 #12 Apr 23 2021 01:20:39
%S A343603 0,1,-2,3,4,-7,-8,11,-6,9,12,-5,10,13,-22,-25,32,-21,-26,33,-20,29,34,
%T A343603 -19,-24,35,-18,27,36,-17,30,37,-16,-23,38,-15,28,39,-14,31,40,-67,
%U A343603 -76,95,-66,-79,96,-65,86,97,-64,-75,98,-63,-80,99,-62,87,100,-61
%N A343603 For any positive number n, the balanced ternary representation of a(n) is obtained by right-rotating the balanced ternary representation of n until a nonzero digit appears again as the leftmost digit; a(0) = 0.
%C A343603 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 A343602 (after a similar extension to negative indexes).
%H A343603 Rémy Sigrist, <a href="/A343603/b343603.txt">Table of n, a(n) for n = 0..9841</a>
%F A343603 A065363(a(n)) = A065363(n).
%F A343603 A134021(a(n)) = A134021(n).
%F A343603 a^k(n) = n for k = A005812(n) (where a^k denotes the k-th iterate of a).
%e A343603 The first terms, in base 10 and in balanced ternary (where T denotes the digit -1), are:
%e A343603   n   a(n)  bter(n)  bter(a(n))
%e A343603   --  ----  -------  ----------
%e A343603    0     0        0           0
%e A343603    1     1        1           1
%e A343603    2    -2       1T          T1
%e A343603    3     3       10          10
%e A343603    4     4       11          11
%e A343603    5    -7      1TT         T1T
%e A343603    6    -8      1T0         T01
%e A343603    7    11      1T1         11T
%e A343603    8    -6      10T         T10
%e A343603    9     9      100         100
%e A343603   10    12      101         110
%e A343603   11    -5      11T         T11
%e A343603   12    10      110         101
%e A343603   13    13      111         111
%e A343603   14   -22     1TTT        T1TT
%e A343603   15   -25     1TT0        T01T
%o A343603 (PARI) a(n) = { my (d = [], t); while (n, d = concat(t = centerlift(Mod(n,3)), d); n = (n-t)\3); forstep (k=#d, 1, -1, if (d[k], return (fromdigits(concat(d[k..#d], d[1..k-1]), 3)))); return (fromdigits(d, 3)) }
%Y A343603 Cf. A005812, A065363, A134021, A139706 (binary variant), A343601 (ternary variant), A343602 (inverse).
%K A343603 sign,base
%O A343603 0,3
%A A343603 _Rémy Sigrist_, Apr 21 2021