A305878 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.

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, 109, 219, 8, 17, 35, 18, 37, 75, 38, 77, 155, 20, 41, 83, 42, 85, 171, 86, 173, 347, 44, 89, 179, 90, 181, 363, 182, 365, 731, 24, 49, 99, 50, 101, 203, 102, 205, 411

Offset

0,3

Comments

This sequence is a ternary analog of A048678.

This sequence is a permutation of A003726.

Links

Table of n, a(n) for n=0..62.

Rémy Sigrist, Colored logarithmic scatterplot of the first 3^10 terms (where the color is function of A053735(n) + A081604(n))

Formula

a(0) = 0.

a(3*n) = 2*a(n).

a(3*n + 1) = 4*a(n) + 1.

a(3*n + 2) = 8*a(n) + 3.

A000120(a(n)) = A053735(n).

Example

The first terms, alongside the ternary representation of n and the binary representation of a(n), are:
  n   a(n)  tern(n)  bin(a(n))
  --  ----  -------  ---------
   0     0        0          0
   1     1        1          1
   2     3        2         11
   3     2       10         10
   4     5       11        101
   5    11       12       1011
   6     6       20        110
   7    13       21       1101
   8    27       22      11011
   9     4      100        100
  10     9      101       1001
  11    19      102      10011
  12    10      110       1010

Prog

(PARI) a(n) = if (n==0, 0, my (d=n%3); a(n\3) * 2^(d+1) + (2^d-1))

Crossrefs

Cf. A000120, A003726, A048678, A053735, A081604.

Sequence in context: A195104 A338879 A257905 * A093924 A130597 A075146

Adjacent sequences: A305875 A305876 A305877 * A305879 A305880 A305881

Keyword

nonn,base

Author

Rémy Sigrist, Jun 13 2018

Status

approved