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

Author

Rémy Sigrist, Dec 29 2024

Keywords

• nonn
• base

Comments

A permutation of the nonnegative integers with inverse A379658.

Examples

			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
		

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

Crossrefs

See A048680 for a similar sequence.

Cf. A065363, A334913, A379658 (inverse).

Programs

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; }

Formula

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