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A289814
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A binary encoding of the twos in ternary representation of n (see Comments for precise definition).
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48
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0, 0, 1, 0, 0, 1, 2, 2, 3, 0, 0, 1, 0, 0, 1, 2, 2, 3, 4, 4, 5, 4, 4, 5, 6, 6, 7, 0, 0, 1, 0, 0, 1, 2, 2, 3, 0, 0, 1, 0, 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, 0
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OFFSET
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0,7
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COMMENTS
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The ones in the binary representation of a(n) correspond to the twos in the ternary representation of n; for example: ternary(42) = 1120 and binary(a(42)) = 10 (a(42) = 2).
See A289813 for the sequence encoding the ones in ternary representation of n and additional comments.
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LINKS
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FORMULA
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a(0) = 0.
a(3*n) = 2 * a(n).
a(3*n+1) = 2 * a(n).
a(3*n+2) = 2 * a(n) + 1.
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EXAMPLE
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The first values, alongside the ternary representation of n, and the binary representation of a(n), are:
n a(n) ternary(n) binary(a(n))
-- ---- ---------- ------------
0 0 0 0
1 0 1 0
2 1 2 1
3 0 10 0
4 0 11 0
5 1 12 1
6 2 20 10
7 2 21 10
8 3 22 11
9 0 100 0
10 0 101 0
11 1 102 1
12 0 110 0
13 0 111 0
14 1 112 1
15 2 120 10
16 2 121 10
17 3 122 11
18 4 200 100
19 4 201 100
20 5 202 101
21 4 210 100
22 4 211 100
23 5 212 101
24 6 220 110
25 6 221 110
26 7 222 111
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MATHEMATICA
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Table[FromDigits[#, 2] &[IntegerDigits[n, 3] /. d_ /; d > 0 :> d - 1], {n, 0, 81}] (* Michael De Vlieger, Jul 20 2017 *)
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PROG
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(PARI) a(n) = my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2)
(Python)
from sympy.ntheory.factor_ import digits
def a(n):
d = digits(n, 3)[1:]
return int("".join('1' if i == 2 else '0' for i in d), 2)
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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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