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

0,3

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.

Links

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

Wikipedia, Balanced ternary

Formula

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

Prog

(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 }

Crossrefs

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

Sequence in context: A275330 A141863 A071010 * A215934 A323895 A274508

Adjacent sequences: A343228 A343229 A343230 * A343232 A343233 A343234

Keyword

nonn,look,base

Author

Rémy Sigrist, Apr 08 2021

Status

approved