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The positions of nonzero digits in the ternary expansions of n and a(n) are the same, and the k-th rightmost nonzero digit in a(n) equals modulo 3 the product of the k rightmost nonzero digits in n.
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%I #10 May 10 2022 02:26:32

%S 0,1,2,3,4,8,6,7,5,9,10,20,12,13,26,24,25,14,18,19,11,21,22,17,15,16,

%T 23,27,28,56,30,31,62,60,61,32,36,37,74,39,40,80,78,79,41,72,73,38,75,

%U 76,44,42,43,77,54,55,29,57,58,35,33,34,59,63,64,47,66,67

%N The positions of nonzero digits in the ternary expansions of n and a(n) are the same, and the k-th rightmost nonzero digit in a(n) equals modulo 3 the product of the k rightmost nonzero digits in n.

%C This sequence is a permutation of the nonnegative integers with inverse A353827.

%C A number is a fixed point of this sequence iff it has at most one digit 2 in its ternary expansion, that digit 2 being its leftmost nonzero digit.

%H Rémy Sigrist, <a href="/A353826/b353826.txt">Table of n, a(n) for n = 0..6561</a>

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

%F a(3*n) = 3*a(n).

%F a(3*n + 1) = 3*a(n) + 1.

%e The first terms, in decimal and in ternary, are:

%e n a(n) ter(n) ter(a(n))

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

%e 0 0 0 0

%e 1 1 1 1

%e 2 2 2 2

%e 3 3 10 10

%e 4 4 11 11

%e 5 8 12 22

%e 6 6 20 20

%e 7 7 21 21

%e 8 5 22 12

%e 9 9 100 100

%e 10 10 101 101

%e 11 20 102 202

%e 12 12 110 110

%o (PARI) a(n) = { my (d=digits(n,3), p=1); forstep (k=#d, 1, -1, if (d[k], d[k]=p*=d[k])); fromdigits(d%3,3) }

%Y See A305458, A353824, A353828, A353830 for similar sequences.

%Y Cf. A353827 (inverse).

%K nonn,base

%O 0,3

%A _Rémy Sigrist_, May 08 2022