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A343317 a(n) is the least k >= 0 such that A343316(n, k) = n.

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%I A343317 #8 Apr 12 2021 01:36:41
%S A343317 0,1,4,2,4,13,11,13,7,5,7,13,11,13,40,38,40,34,32,34,40,38,40,22,20,
%T A343317 22,16,14,16,22,20,22,40,38,40,34,32,34,40,38,40,121,119,121,115,113,
%U A343317 115,121,119,121,103,101,103,97,95,97,103,101,103,121,119,121
%N A343317 a(n) is the least k >= 0 such that A343316(n, k) = n.
%C A343317 To compute a(n): in the balanced ternary representation of n, replace each nonzero digit by "+1" and each nonleading zero by "-1".
%H A343317 Rémy Sigrist, <a href="/A343317/b343317.txt">Table of n, a(n) for n = 0..6561</a>
%e A343317 The first terms, alongside their balanced ternary representation (with "T" instead of digits "-1"), are:
%e A343317   n   a(n)  bter(n)  bter(a(n))
%e A343317   --  ----  -------  ----------
%e A343317    0     0        0           0
%e A343317    1     1        1           1
%e A343317    2     4       1T          11
%e A343317    3     2       10          1T
%e A343317    4     4       11          11
%e A343317    5    13      1TT         111
%e A343317    6    11      1T0         11T
%e A343317    7    13      1T1         111
%e A343317    8     7      10T         1T1
%e A343317    9     5      100         1TT
%e A343317   10     7      101         1T1
%e A343317   11    13      11T         111
%e A343317   12    11      110         11T
%e A343317   13    13      111         111
%e A343317   14    40     1TTT        1111
%e A343317   15    38     1TT0        111T
%o A343317 (PARI) a(n) = if (n==0, 0, my (d=centerlift(Mod(n, 3))); if (d, +1, -1) + 3*a((n-d)\3))
%Y A343317 Cf. A343316, A343231.
%K A343317 nonn,base
%O A343317 0,3
%A A343317 _Rémy Sigrist_, Apr 11 2021