A343230 A binary encoding of the digits "0" in balanced ternary representation of n.

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

Offset

0,9

Comments

The ones in the binary representation of a(n) correspond to the nonleading digits "0" in the balanced ternary representation of n.

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

Links

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

Wikipedia, Balanced ternary

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     0      1T          0
   3     1      10          1
   4     0      11          0
   5     0     1TT          0
   6     1     1T0          1
   7     0     1T1          0
   8     2     10T         10
   9     3     100         11
  10     2     101         10
  11     0     11T          0
  12     1     110          1
  13     0     111          0
  14     0    1TTT          0
  15     1    1TT0          1

Prog

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

Crossrefs

Cf. A059095, A140267, A291770, A343228, A343229, A343231, A147991 (indices of 0's).

Sequence in context: A291293 A259572 A027413 * A019509 A071484 A372706

Adjacent sequences: A343227 A343228 A343229 * A343231 A343232 A343233

Keyword

nonn,look,base

Author

Rémy Sigrist, Apr 08 2021

Status

approved