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

Author

Rémy Sigrist, Jun 13 2018

Keywords

• nonn
• base

Comments

This sequence is a ternary analog of A048678.

This sequence is a permutation of A003726.

Examples

			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
		

Links

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

Crossrefs

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

Programs

PARI

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

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).