A353826 The positions of nonzero digits in the ternary expansions of n and a(n) are the same, and the k-th rightmost nonzero digit in a(n) equals modulo 3 the product of the k rightmost nonzero digits in n.

0, 1, 2, 3, 4, 8, 6, 7, 5, 9, 10, 20, 12, 13, 26, 24, 25, 14, 18, 19, 11, 21, 22, 17, 15, 16, 23, 27, 28, 56, 30, 31, 62, 60, 61, 32, 36, 37, 74, 39, 40, 80, 78, 79, 41, 72, 73, 38, 75, 76, 44, 42, 43, 77, 54, 55, 29, 57, 58, 35, 33, 34, 59, 63, 64, 47, 66, 67

Offset: 0

Author

Rémy Sigrist, May 08 2022

Keywords

• nonn
• base

Comments

This sequence is a permutation of the nonnegative integers with inverse A353827.

A number is a fixed point of this sequence iff it has at most one digit 2 in its ternary expansion, that digit 2 being its leftmost nonzero digit.

Examples

			The first terms, in decimal and in ternary, are:
  n   a(n)  ter(n)  ter(a(n))
  --  ----  ------  ---------
   0     0       0          0
   1     1       1          1
   2     2       2          2
   3     3      10         10
   4     4      11         11
   5     8      12         22
   6     6      20         20
   7     7      21         21
   8     5      22         12
   9     9     100        100
  10    10     101        101
  11    20     102        202
  12    12     110        110
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..6561
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

See A305458, A353824, A353828, A353830 for similar sequences.

Cf. A353827 (inverse).

Programs

PARI

a(n) = { my (d=digits(n,3), p=1); forstep (k=#d, 1, -1, if (d[k], d[k]=p*=d[k])); fromdigits(d%3,3) }

Formula

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

a(3*n + 1) = 3*a(n) + 1.