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%I #7 Jun 16 2018 13:44:14
%S 0,1,3,2,5,11,6,13,27,4,9,19,10,21,43,22,45,91,12,25,51,26,53,107,54,
%T 109,219,8,17,35,18,37,75,38,77,155,20,41,83,42,85,171,86,173,347,44,
%U 89,179,90,181,363,182,365,731,24,49,99,50,101,203,102,205,411
%N For any number n >= 0: apply the map 0 -> "0", 1 -> "01", 2 -> "011" to the ternary representation of n and interpret the result as a binary string.
%C This sequence is a ternary analog of A048678.
%C This sequence is a permutation of A003726.
%H Rémy Sigrist, <a href="/A305878/a305878.png">Colored logarithmic scatterplot of the first 3^10 terms</a> (where the color is function of A053735(n) + A081604(n))
%F a(0) = 0.
%F a(3*n) = 2*a(n).
%F a(3*n + 1) = 4*a(n) + 1.
%F a(3*n + 2) = 8*a(n) + 3.
%F A000120(a(n)) = A053735(n).
%e The first terms, alongside the ternary representation of n and the binary representation of a(n), are:
%e n a(n) tern(n) bin(a(n))
%e -- ---- ------- ---------
%e 0 0 0 0
%e 1 1 1 1
%e 2 3 2 11
%e 3 2 10 10
%e 4 5 11 101
%e 5 11 12 1011
%e 6 6 20 110
%e 7 13 21 1101
%e 8 27 22 11011
%e 9 4 100 100
%e 10 9 101 1001
%e 11 19 102 10011
%e 12 10 110 1010
%o (PARI) a(n) = if (n==0, 0, my (d=n%3); a(n\3) * 2^(d+1) + (2^d-1))
%Y Cf. A000120, A003726, A048678, A053735, A081604.
%K nonn,base
%O 0,3
%A _Rémy Sigrist_, Jun 13 2018
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