A343603 For any positive number n, the balanced ternary representation of a(n) is obtained by right-rotating the balanced ternary representation of n until a nonzero digit appears again as the leftmost digit; a(0) = 0.

0, 1, -2, 3, 4, -7, -8, 11, -6, 9, 12, -5, 10, 13, -22, -25, 32, -21, -26, 33, -20, 29, 34, -19, -24, 35, -18, 27, 36, -17, 30, 37, -16, -23, 38, -15, 28, 39, -14, 31, 40, -67, -76, 95, -66, -79, 96, -65, 86, 97, -64, -75, 98, -63, -80, 99, -62, 87, 100, -61

Offset: 0

Author

Rémy Sigrist, Apr 21 2021

Keywords

• sign
• base

Comments

This sequence can be extended to negative indexes by setting a(-n) = -a(n) for any n > 0. We then obtain a permutation of the integers (Z) with inverse A343602 (after a similar extension to negative indexes).

Examples

			The first terms, in base 10 and in balanced ternary (where T denotes the digit -1), are:
  n   a(n)  bter(n)  bter(a(n))
  --  ----  -------  ----------
   0     0        0           0
   1     1        1           1
   2    -2       1T          T1
   3     3       10          10
   4     4       11          11
   5    -7      1TT         T1T
   6    -8      1T0         T01
   7    11      1T1         11T
   8    -6      10T         T10
   9     9      100         100
  10    12      101         110
  11    -5      11T         T11
  12    10      110         101
  13    13      111         111
  14   -22     1TTT        T1TT
  15   -25     1TT0        T01T
		

Links

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

Crossrefs

Cf. A005812, A065363, A134021, A139706 (binary variant), A343601 (ternary variant), A343602 (inverse).

Programs

PARI

a(n) = { my (d = [], t); while (n, d = concat(t = centerlift(Mod(n,3)), d); n = (n-t)\3); forstep (k=#d, 1, -1, if (d[k], return (fromdigits(concat(d[k..#d], d[1..k-1]), 3)))); return (fromdigits(d, 3)) }

Formula

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

A134021(a(n)) = A134021(n).

a^k(n) = n for k = A005812(n) (where a^k denotes the k-th iterate of a).