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For any number n with balanced ternary expansion (d_1, ..., d_k), the balanced ternary expansion of a(n), say (t_1, ..., t_k), satisfies t_m = d_1 + ... + d_m mod 3 for m = 1..k.
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%I #12 Apr 25 2021 15:12:29

%S 0,1,3,4,2,8,9,10,12,13,11,7,5,6,25,23,24,26,27,28,30,31,29,35,36,37,

%T 39,40,38,34,32,33,21,22,20,16,14,15,17,18,19,75,76,74,70,68,69,71,72,

%U 73,79,77,78,80,81,82,84,85,83,89,90,91,93,94,92,88,86,87

%N For any number n with balanced ternary expansion (d_1, ..., d_k), the balanced ternary expansion of a(n), say (t_1, ..., t_k), satisfies t_m = d_1 + ... + d_m mod 3 for m = 1..k.

%C This sequence is similar to A006068.

%C This sequence is a permutation of the nonnegative integers with inverse A341055.

%H Rémy Sigrist, <a href="/A341054/b341054.txt">Table of n, a(n) for n = 0..9841</a>

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

%e The first terms, alongside their balanced ternary expansion (with T's standing for -1's), are:

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

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

%e 0 0 0 0

%e 1 1 1 1

%e 2 3 1T 10

%e 3 4 10 11

%e 4 2 11 1T

%e 5 8 1TT 10T

%e 6 9 1T0 100

%e 7 10 1T1 101

%e 8 12 10T 110

%e 9 13 100 111

%e 10 11 101 11T

%e 11 7 11T 1T1

%e 12 5 110 1TT

%e 13 6 111 1T0

%e 14 25 1TTT 10T1

%e 15 23 1TT0 10TT

%e 16 24 1TT1 10T0

%o (PARI) a(n) = { my (d=[], s=Mod(0, 3)); while (n, my (t=centerlift(Mod(n, 3))); n=(n-t)\3; d=concat(t, d)); for (k=1, #d, d[k] = centerlift(s+=d[k])); fromdigits(d, 3) }

%Y Cf. A006068, A059095, A341055 (inverse).

%K nonn,base

%O 0,3

%A _Rémy Sigrist_, Apr 25 2021