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A binary encoding of the digits "-1" in balanced ternary representation of n.
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%I #13 Apr 09 2021 11:38:23

%S 0,0,1,0,0,3,2,2,1,0,0,1,0,0,7,6,6,5,4,4,5,4,4,3,2,2,1,0,0,1,0,0,3,2,

%T 2,1,0,0,1,0,0,15,14,14,13,12,12,13,12,12,11,10,10,9,8,8,9,8,8,11,10,

%U 10,9,8,8,9,8,8,7,6,6,5,4,4,5,4,4,3,2,2,1,0

%N A binary encoding of the digits "-1" in balanced ternary representation of n.

%C The ones in the binary representation of a(n) correspond to the digits "-1" in the balanced ternary representation of n.

%C We can extend this sequence to negative indices: a(-n) = A343228(n) for any n >= 0.

%H Rémy Sigrist, <a href="/A343229/b343229.txt">Table of n, a(n) for n = 0..6561</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Balanced_ternary">Balanced ternary</a>

%F a(n) = A289831(A060373(n)).

%e The first terms, alongside the balanced ternary representation of n (with "T" instead of digits "-1") and the binary representation of a(n), are:

%e n a(n) ter(n) bin(a(n))

%e -- ---- ------ ---------

%e 0 0 0 0

%e 1 0 1 0

%e 2 1 1T 1

%e 3 0 10 0

%e 4 0 11 0

%e 5 3 1TT 11

%e 6 2 1T0 10

%e 7 2 1T1 10

%e 8 1 10T 1

%e 9 0 100 0

%e 10 0 101 0

%e 11 1 11T 1

%e 12 0 110 0

%e 13 0 111 0

%e 14 7 1TTT 111

%e 15 6 1TT0 110

%o (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 }

%Y Cf. A059095, A060373, A140267, A289814, A289831, A343228, A343230, A343231, A005836 (indices of 0's).

%K nonn,look,base

%O 0,6

%A _Rémy Sigrist_, Apr 08 2021