%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