A343231 A binary encoding of the nonzero digits in balanced ternary representation of n.

0, 1, 3, 2, 3, 7, 6, 7, 5, 4, 5, 7, 6, 7, 15, 14, 15, 13, 12, 13, 15, 14, 15, 11, 10, 11, 9, 8, 9, 11, 10, 11, 15, 14, 15, 13, 12, 13, 15, 14, 15, 31, 30, 31, 29, 28, 29, 31, 30, 31, 27, 26, 27, 25, 24, 25, 27, 26, 27, 31, 30, 31, 29, 28, 29, 31, 30, 31, 23

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 nonzero digits 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     1       1          1
   2     3      1T         11
   3     2      10         10
   4     3      11         11
   5     7     1TT        111
   6     6     1T0        110
   7     7     1T1        111
   8     5     10T        101
   9     4     100        100
  10     5     101        101
  11     7     11T        111
  12     6     110        110
  13     7     111        111
  14    15    1TTT       1111
  15    14    1TT0       1110
		

Links

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

Crossrefs

Cf. A059095, A140267, A289831, A343228, A343229, A343230.

Programs

PARI

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

Formula

a(n) = A343228(n) + A343229(n).