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a(n) is the least k >= 0 such that A343316(n, k) = n.
2

%I #8 Apr 12 2021 01:36:41

%S 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 22,16,14,16,22,20,22,40,38,40,34,32,34,40,38,40,121,119,121,115,113,

%U 115,121,119,121,103,101,103,97,95,97,103,101,103,121,119,121

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

%C To compute a(n): in the balanced ternary representation of n, replace each nonzero digit by "+1" and each nonleading zero by "-1".

%H Rémy Sigrist, <a href="/A343317/b343317.txt">Table of n, a(n) for n = 0..6561</a>

%e The first terms, alongside their balanced ternary representation (with "T" instead of digits "-1"), are:

%e n a(n) bter(n) bter(a(n))

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

%e 0 0 0 0

%e 1 1 1 1

%e 2 4 1T 11

%e 3 2 10 1T

%e 4 4 11 11

%e 5 13 1TT 111

%e 6 11 1T0 11T

%e 7 13 1T1 111

%e 8 7 10T 1T1

%e 9 5 100 1TT

%e 10 7 101 1T1

%e 11 13 11T 111

%e 12 11 110 11T

%e 13 13 111 111

%e 14 40 1TTT 1111

%e 15 38 1TT0 111T

%o (PARI) a(n) = if (n==0, 0, my (d=centerlift(Mod(n, 3))); if (d, +1, -1) + 3*a((n-d)\3))

%Y Cf. A343316, A343231.

%K nonn,base

%O 0,3

%A _Rémy Sigrist_, Apr 11 2021