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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 22 12:56 EDT 2021. Contains 345380 sequences. (Running on oeis4.)