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A343228
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A binary encoding of the digits "+1" in balanced ternary representation of n.
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6
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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
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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FORMULA
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EXAMPLE
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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
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PROG
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(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 }
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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