A341054 For any number n with balanced ternary expansion (d_1, ..., d_k), the balanced ternary expansion of a(n), say (t_1, ..., t_k), satisfies t_m = d_1 + ... + d_m mod 3 for m = 1..k.

0, 1, 3, 4, 2, 8, 9, 10, 12, 13, 11, 7, 5, 6, 25, 23, 24, 26, 27, 28, 30, 31, 29, 35, 36, 37, 39, 40, 38, 34, 32, 33, 21, 22, 20, 16, 14, 15, 17, 18, 19, 75, 76, 74, 70, 68, 69, 71, 72, 73, 79, 77, 78, 80, 81, 82, 84, 85, 83, 89, 90, 91, 93, 94, 92, 88, 86, 87

Offset

0,3

Comments

This sequence is similar to A006068.

This sequence is a permutation of the nonnegative integers with inverse A341055.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..9841

Index entries for sequences that are permutations of the natural numbers

Example

The first terms, alongside their balanced ternary expansion (with T's standing for -1's), are:
  n   a(n)  bter(n)  bter(a(n))
  --  ----  -------  ----------
   0     0        0           0
   1     1        1           1
   2     3       1T          10
   3     4       10          11
   4     2       11          1T
   5     8      1TT         10T
   6     9      1T0         100
   7    10      1T1         101
   8    12      10T         110
   9    13      100         111
  10    11      101         11T
  11     7      11T         1T1
  12     5      110         1TT
  13     6      111         1T0
  14    25     1TTT        10T1
  15    23     1TT0        10TT
  16    24     1TT1        10T0

Prog

(PARI) a(n) = { my (d=[], s=Mod(0, 3)); while (n, my (t=centerlift(Mod(n, 3))); n=(n-t)\3; d=concat(t, d)); for (k=1, #d, d[k] = centerlift(s+=d[k])); fromdigits(d, 3) }

Crossrefs

Cf. A006068, A059095, A341055 (inverse).

Sequence in context: A143053 A220508 A316323 * A120239 A082362 A082364

Adjacent sequences: A341051 A341052 A341053 * A341055 A341056 A341057

Keyword

nonn,base

Author

Rémy Sigrist, Apr 25 2021

Status

approved