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A333441
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Numbers where each binary digit can be paired with a digit of the same value at another position so that two pairs can be nested but cannot otherwise overlap.
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1
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0, 3, 9, 12, 15, 33, 36, 39, 45, 48, 51, 54, 57, 60, 63, 129, 132, 135, 141, 144, 147, 150, 153, 156, 159, 165, 177, 180, 183, 189, 192, 195, 198, 201, 204, 207, 210, 216, 219, 222, 225, 228, 231, 237, 240, 243, 246, 249, 252, 255, 513, 516, 519, 525, 528, 531
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OFFSET
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1,2
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COMMENTS
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The term 0 is included by convention (we consider here that it has no digit).
This sequence is a binary variant of A333440.
This sequence has connections with A014486; in both sequences digits are balanced in some way.
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LINKS
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EXAMPLE
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The first terms, alongside their binary representation with a possible pairing, are:
n a(n) bin(a(n))
-- ---- ------------
1 0 0
2 3 (11)
3 9 (1(00)1)
4 12 (11)(00)
5 15 (11)(11)
6 33 (1(00)(00)1)
7 36 (1(00)1)(00)
8 39 (1(00)1)(11)
9 45 (1(0(11)0)1)
10 48 (11)(00)(00)
11 51 (11)(00)(11)
12 54 (11)(0(11)0)
13 57 (11)(1(00)1)
14 60 (11)(11)(00)
15 63 (11)(11)(11)
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PROG
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(PARI) is(n, base=2) = { my (u=0, s=0); while (n, my (d=n%base); if (u && s%base==d, u--; s\=base, u++; s=s*base+d); n\=base); u==0 }
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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