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A binary encoding of the nonzero digits in balanced ternary representation of n.
6

%I #12 Apr 09 2021 11:55:23

%S 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,

%T 9,11,10,11,15,14,15,13,12,13,15,14,15,31,30,31,29,28,29,31,30,31,27,

%U 26,27,25,24,25,27,26,27,31,30,31,29,28,29,31,30,31,23

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

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

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

%H Rémy Sigrist, <a href="/A343231/b343231.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) = A343228(n) + A343229(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 1 1 1

%e 2 3 1T 11

%e 3 2 10 10

%e 4 3 11 11

%e 5 7 1TT 111

%e 6 6 1T0 110

%e 7 7 1T1 111

%e 8 5 10T 101

%e 9 4 100 100

%e 10 5 101 101

%e 11 7 11T 111

%e 12 6 110 110

%e 13 7 111 111

%e 14 15 1TTT 1111

%e 15 14 1TT0 1110

%o (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 }

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

%K nonn,look,base

%O 0,3

%A _Rémy Sigrist_, Apr 08 2021