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

Author

Rémy Sigrist, Apr 08 2021

Keywords

• nonn
• look
• base

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.

Examples

			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
		

Links

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

Crossrefs

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

Programs

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 }