A379658 The balanced ternary expansion of a(n) is obtained by removing a digit 0 before each nonzero digit in the nonadjacent form of n.

0, 1, 3, 2, 9, 4, 6, 8, 27, 10, 12, 5, 18, 7, 24, 26, 81, 28, 30, 11, 36, 13, 15, 17, 54, 19, 21, 23, 72, 25, 78, 80, 243, 82, 84, 29, 90, 31, 33, 35, 108, 37, 39, 14, 45, 16, 51, 53, 162, 55, 57, 20, 63, 22, 69, 71, 216, 73, 75, 77, 234, 79, 240, 242, 729

Offset

0,3

Comments

A permutation of the nonnegative integers with inverse A379657.

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

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

Example

The first terms are:
  n   a(n)  naf(n)  bter(a(n))
  --  ----  ------  ----------
   0     0       0           0
   1     1       1           1
   2     3      10          10
   3     2     10T          1T
   4     9     100         100
   5     4     101          11
   6     6    10T0         1T0
   7     8    100T         10T
   8    27    1000        1000
   9    10    1001         101
  10    12    1010         110
  11     5   10T0T         1TT
  12    18   10T00        1T00

Prog

(PARI) a(n) = { my (v = 0, t = 1, d); while (n, if (n%2, n -= d = 2 - (n%4); v += d*t; t /= 3; ); n \= 2; t *= 3; ); return (v); }

Crossrefs

See A048679 for a similar sequence.

Cf. A065363, A334913, A379657 (inverse).

Sequence in context: A294370 A325984 A178774 * A320273 A379260 A266636

Adjacent sequences: A379655 A379656 A379657 * A379659 A379660 A379661

Keyword

nonn,base,new

Author

Rémy Sigrist, Dec 29 2024

Status

approved