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A328596 Numbers whose reversed binary expansion is a Lyndon word (aperiodic necklace). 67
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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.
LINKS
FORMULA
Intersection of A328594 and A328595.
EXAMPLE
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}
MATHEMATICA
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]]]&]
CROSSREFS
A similar concept is A275692.
Aperiodic words are A328594.
Necklaces are A328595.
Binary Lyndon words are A001037.
Lyndon compositions are A059966.
Sequence in context: A318186 A139363 A091065 * A275692 A334267 A163823
KEYWORD
nonn,base
AUTHOR
Gus Wiseman, Oct 22 2019
STATUS
approved

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Last modified February 26 07:39 EST 2024. Contains 370335 sequences. (Running on oeis4.)