A373712 a(n) is the least m >= 0 with the same number of ternary digits as n such that for some permutation p of 0..2, applying p to the ternary digits of n yields the ternary digits of m.

0, 1, 1, 3, 4, 3, 3, 3, 4, 9, 10, 11, 12, 13, 12, 11, 10, 9, 9, 11, 10, 11, 9, 10, 12, 12, 13, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 27, 29, 28, 33, 35, 34, 30, 32, 31, 35, 33, 34, 29, 27

Offset

0,4

Comments

Leading zeros in ternary expansions are ignored.

Empirically, A134025 corresponds to the fixed points of this sequence.

The lexicographically latest sequence b of distinct nonnegative integers such that for any n >= 0, a(n) = a(b(n)) is A371268.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..6560

Formula

a(n) <= n.

a(a(n)) = a(n).

Example

The first terms, alongside their ternary expansions, are:
  n   a(n)  ter(n)  ter(a(n))
  --  ----  ------  ---------
   0     0       0          0
   1     1       1          1
   2     1       2          1
   3     3      10         10
   4     4      11         11
   5     3      12         10
   6     3      20         10
   7     3      21         10
   8     4      22         11
   9     9     100        100
  10    10     101        101
  11    11     102        102
  12    12     110        110
  13    13     111        111
  14    12     112        110
  15    11     120        102
  16    10     121        101

Prog

(PARI) a(n, base = 3) = { my (d = digits(n, base), m = vector(base, i, -1), u = 1); for (i = 1, #d, if (m[1+d[i]] < 0, m[1+d[i]] = u; u = if (u==1, 0, u==0, 2, u+1); ); d[i] = m[1+d[i]]; ); fromdigits(d, base); }

Crossrefs

Cf. A134025, A371268, A373696 (decimal analog).

Sequence in context: A092910 A356334 A322347 * A073322 A006197 A079404

Adjacent sequences: A373709 A373710 A373711 * A373713 A373714 A373715

Keyword

nonn,base

Author

Rémy Sigrist, Aug 04 2024

Status

approved