A353828 The positions of nonzero digits in the balanced ternary expansions of n and a(n) are the same, and the k-th leftmost nonzero digit in a(n) equals the product of the k leftmost nonzero digits in n.

0, 1, 2, 3, 4, 7, 6, 5, 8, 9, 10, 11, 12, 13, 20, 21, 22, 19, 18, 17, 16, 15, 14, 25, 24, 23, 26, 27, 28, 29, 30, 31, 34, 33, 32, 35, 36, 37, 38, 39, 40, 61, 60, 59, 62, 63, 64, 65, 66, 67, 56, 57, 58, 55, 54, 53, 52, 51, 50, 47, 48, 49, 46, 45, 44, 43, 42, 41

Offset

0,3

Comments

This sequence is a permutation of the nonnegative integers with inverse A353829.

A number is a fixed point of this sequence iff it has at most one digit -1 in its balanced ternary expansion, that digit -1 being its rightmost nonzero digit.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..6561

Index entries for sequences that are permutations of the natural numbers

Formula

a(3*n) = 3*a(n).

Example

The first terms, in decimal and in balanced ternary, are:
  n   a(n)  bter(n)  bter(a(n))
  --  ----  -------  ----------
   0     0        0           0
   1     1        1           1
   2     2       1T          1T
   3     3       10          10
   4     4       11          11
   5     7      1TT         1T1
   6     6      1T0         1T0
   7     5      1T1         1TT
   8     8      10T         10T
   9     9      100         100
  10    10      101         101
  11    11      11T         11T
  12    12      110         110

Prog

(PARI) a(n) = {
    my (d=[], t, p=1);
    while (n, d=concat(t=[0, 1, -1][1+n%3], d); n=(n-t)/3);
    for (k=1, #d, if (d[k], d[k]=p*=d[k]));
    fromdigits(d, 3);
}

Crossrefs

See A305458, A353824, A353826, A353830 for similar sequences.

Cf. A353829 (inverse).

Sequence in context: A072275 A122989 A222246 * A321726 A353829 A267299

Adjacent sequences: A353825 A353826 A353827 * A353829 A353830 A353831

Keyword

nonn,base

Author

Rémy Sigrist, May 08 2022

Status

approved