login
A343231
A binary encoding of the nonzero digits in balanced ternary representation of n.
6
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
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
KEYWORD
nonn,look,base
AUTHOR
Rémy Sigrist, Apr 08 2021
STATUS
approved