A305878 - OEIS

%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