A379657 The nonadjacent form of a(n) is obtained by inserting a digit 0 before each nonzero digit in the balanced ternary expansion of n.

0, 1, 3, 2, 5, 11, 6, 13, 7, 4, 9, 19, 10, 21, 43, 22, 45, 23, 12, 25, 51, 26, 53, 27, 14, 29, 15, 8, 17, 35, 18, 37, 75, 38, 77, 39, 20, 41, 83, 42, 85, 171, 86, 173, 87, 44, 89, 179, 90, 181, 91, 46, 93, 47, 24, 49, 99, 50, 101, 203, 102, 205, 103, 52, 105

Offset

0,3

Comments

A permutation of the nonnegative integers with inverse A379658.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Joerg Arndt, Matters Computational (The Fxtbook), pages 61-62.

Wikipedia, Balanced ternary

Wikipedia, Non-adjacent form

Index entries for sequences that are permutations of the natural numbers

Formula

A334913(a(n)) = A065363(n).

Example

The first terms are:  n   a(n)  bter(n)  naf(a(n))
  --  ----  -------  ---------
   0     0        0          0
   1     1        1          1
   2     3       1T        10T
   3     2       10         10
   4     5       11        101
   5    11      1TT      10T0T
   6     6      1T0       10T0
   7    13      1T1      10T01
   8     7      10T       100T
   9     4      100        100
  10     9      101       1001
  11    19      11T      1010T
  12    10      110       1010

Prog

(PARI) a(n) = { my (v = 0, d, b = 1); while (n, d = centerlift(Mod(n, 3)); n = (n-d)/3;
 v += d * b; b *= if (d, 4, 2); ); v; }

Crossrefs

See A048680 for a similar sequence.

Cf. A065363, A334913, A379658 (inverse).

Sequence in context: A195104 A338879 A257905 * A305878 A382115 A093924

Adjacent sequences: A379654 A379655 A379656 * A379658 A379659 A379660

Keyword

nonn,base

Author

Rémy Sigrist, Dec 29 2024

Status

approved