A343317 a(n) is the least k >= 0 such that A343316(n, k) = n.

0, 1, 4, 2, 4, 13, 11, 13, 7, 5, 7, 13, 11, 13, 40, 38, 40, 34, 32, 34, 40, 38, 40, 22, 20, 22, 16, 14, 16, 22, 20, 22, 40, 38, 40, 34, 32, 34, 40, 38, 40, 121, 119, 121, 115, 113, 115, 121, 119, 121, 103, 101, 103, 97, 95, 97, 103, 101, 103, 121, 119, 121

Offset: 0

Author

Rémy Sigrist, Apr 11 2021

Keywords

• nonn
• base

Comments

To compute a(n): in the balanced ternary representation of n, replace each nonzero digit by "+1" and each nonleading zero by "-1".

Examples

			The first terms, alongside their balanced ternary representation (with "T" instead of digits "-1"), are:
  n   a(n)  bter(n)  bter(a(n))
  --  ----  -------  ----------
   0     0        0           0
   1     1        1           1
   2     4       1T          11
   3     2       10          1T
   4     4       11          11
   5    13      1TT         111
   6    11      1T0         11T
   7    13      1T1         111
   8     7      10T         1T1
   9     5      100         1TT
  10     7      101         1T1
  11    13      11T         111
  12    11      110         11T
  13    13      111         111
  14    40     1TTT        1111
  15    38     1TT0        111T
		

Links

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

Crossrefs

Cf. A343316, A343231.

Programs

PARI

a(n) = if (n==0, 0, my (d=centerlift(Mod(n, 3))); if (d, +1, -1) + 3*a((n-d)\3))