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A328596
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Numbers whose reversed binary expansion is a Lyndon word (aperiodic necklace).
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67
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1, 2, 4, 6, 8, 12, 14, 16, 20, 24, 26, 28, 30, 32, 40, 44, 48, 52, 56, 58, 60, 62, 64, 72, 80, 84, 88, 92, 96, 100, 104, 106, 108, 112, 116, 118, 120, 122, 124, 126, 128, 144, 152, 160, 164, 168, 172, 176, 180, 184, 188, 192, 200, 208, 212, 216, 218, 220, 224
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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First differs from A091065 in lacking 50.
A Lyndon word is a finite sequence that is lexicographically strictly less than all of its cyclic rotations.
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LINKS
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FORMULA
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EXAMPLE
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The sequence of terms together with their binary expansions and binary indices begins:
1: 1 ~ {1}
2: 10 ~ {2}
4: 100 ~ {3}
6: 110 ~ {2,3}
8: 1000 ~ {4}
12: 1100 ~ {3,4}
14: 1110 ~ {2,3,4}
16: 10000 ~ {5}
20: 10100 ~ {3,5}
24: 11000 ~ {4,5}
26: 11010 ~ {2,4,5}
28: 11100 ~ {3,4,5}
30: 11110 ~ {2,3,4,5}
32: 100000 ~ {6}
40: 101000 ~ {4,6}
44: 101100 ~ {3,4,6}
48: 110000 ~ {5,6}
52: 110100 ~ {3,5,6}
56: 111000 ~ {4,5,6}
58: 111010 ~ {2,4,5,6}
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MATHEMATICA
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aperQ[q_]:=Array[RotateRight[q, #]&, Length[q], 1, UnsameQ];
neckQ[q_]:=Array[OrderedQ[{q, RotateRight[q, #]}]&, Length[q]-1, 1, And];
Select[Range[100], aperQ[Reverse[IntegerDigits[#, 2]]]&&neckQ[Reverse[IntegerDigits[#, 2]]]&]
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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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