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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 leftmost nonzero digit in a(n) equals modulo 3 the product of the k leftmost nonzero digits in n.
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%I #10 May 10 2022 02:26:42

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

%T 23,27,28,29,30,31,32,33,35,34,36,37,38,39,40,41,42,44,43,45,47,46,51,

%U 53,52,48,49,50,54,56,55,60,62,61,57,58,59,72,74,73,78,80

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

%C This sequence is a permutation of the nonnegative integers with inverse A353825.

%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 rightmost nonzero digit.

%H Rémy Sigrist, <a href="/A353824/b353824.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).

%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 5 12 12

%e 6 6 20 20

%e 7 8 21 22

%e 8 7 22 21

%e 9 9 100 100

%e 10 10 101 101

%e 11 11 102 102

%e 12 12 110 110

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

%Y See A305458, A353826, A353828, A353830 for similar sequences.

%Y Cf. A353825 (inverse).

%K nonn,base

%O 0,3

%A _Rémy Sigrist_, May 08 2022