%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