A343229 A binary encoding of the digits "-1" in balanced ternary representation of n.

0, 0, 1, 0, 0, 3, 2, 2, 1, 0, 0, 1, 0, 0, 7, 6, 6, 5, 4, 4, 5, 4, 4, 3, 2, 2, 1, 0, 0, 1, 0, 0, 3, 2, 2, 1, 0, 0, 1, 0, 0, 15, 14, 14, 13, 12, 12, 13, 12, 12, 11, 10, 10, 9, 8, 8, 9, 8, 8, 11, 10, 10, 9, 8, 8, 9, 8, 8, 7, 6, 6, 5, 4, 4, 5, 4, 4, 3, 2, 2, 1, 0

Offset

0,6

Comments

The ones in the binary representation of a(n) correspond to the digits "-1" in the balanced ternary representation of n.

We can extend this sequence to negative indices: a(-n) = A343228(n) for any n >= 0.

Links

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

Wikipedia, Balanced ternary

Formula

a(n) = A289831(A060373(n)).

Example

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

Prog

(PARI) a(n) = { my (v=0, b=1, t); while (n, t=centerlift(Mod(n, 3)); if (t==-1, v+=b); n=(n-t)\3; b*=2); v }

Crossrefs

Cf. A059095, A060373, A140267, A289814, A289831, A343228, A343230, A343231, A005836 (indices of 0's).

Sequence in context: A323557 A155917 A291770 * A287823 A143378 A131961

Adjacent sequences: A343226 A343227 A343228 * A343230 A343231 A343232

Keyword

nonn,look,base

Author

Rémy Sigrist, Apr 08 2021

Status

approved