A343228 A binary encoding of the digits "+1" in balanced ternary representation of n.

0, 1, 2, 2, 3, 4, 4, 5, 4, 4, 5, 6, 6, 7, 8, 8, 9, 8, 8, 9, 10, 10, 11, 8, 8, 9, 8, 8, 9, 10, 10, 11, 12, 12, 13, 12, 12, 13, 14, 14, 15, 16, 16, 17, 16, 16, 17, 18, 18, 19, 16, 16, 17, 16, 16, 17, 18, 18, 19, 20, 20, 21, 20, 20, 21, 22, 22, 23, 16, 16, 17, 16

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 digits "+1" in the balanced ternary representation of n.

We can extend this sequence to negative indices: a(-n) = A343229(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     2      1T         10
   3     2      10         10
   4     3      11         11
   5     4     1TT        100
   6     4     1T0        100
   7     5     1T1        101
   8     4     10T        100
   9     4     100        100
  10     5     101        101
  11     6     11T        110
  12     6     110        110
  13     7     111        111
  14     8    1TTT       1000
  15     8    1TT0       1000
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..6561
• Rémy Sigrist, Scatterplot of (a(n), A343229(n)) for n = 0..3^10
• Wikipedia, Balanced ternary

Crossrefs

Cf. A059095, A060372, A140267, A289813, A289831, A343229, A343230, A343231.

Programs

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 }

Formula

a(n) = A289831(A060372(n)).