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%I #11 Oct 16 2021 11:55:37
%S 1,2,4,6,8,12,14,16,20,24,26,28,30,32,40,44,48,52,56,58,60,62,64,72,
%T 80,84,88,92,96,100,104,106,108,112,116,118,120,122,124,126,128,144,
%U 152,160,164,168,172,176,180,184,188,192,200,208,212,216,218,220,224
%N Numbers whose reversed binary expansion is a Lyndon word (aperiodic necklace).
%C First differs from A091065 in lacking 50.
%C A Lyndon word is a finite sequence that is lexicographically strictly less than all of its cyclic rotations.
%F Intersection of A328594 and A328595.
%e The sequence of terms together with their binary expansions and binary indices begins:
%e 1: 1 ~ {1}
%e 2: 10 ~ {2}
%e 4: 100 ~ {3}
%e 6: 110 ~ {2,3}
%e 8: 1000 ~ {4}
%e 12: 1100 ~ {3,4}
%e 14: 1110 ~ {2,3,4}
%e 16: 10000 ~ {5}
%e 20: 10100 ~ {3,5}
%e 24: 11000 ~ {4,5}
%e 26: 11010 ~ {2,4,5}
%e 28: 11100 ~ {3,4,5}
%e 30: 11110 ~ {2,3,4,5}
%e 32: 100000 ~ {6}
%e 40: 101000 ~ {4,6}
%e 44: 101100 ~ {3,4,6}
%e 48: 110000 ~ {5,6}
%e 52: 110100 ~ {3,5,6}
%e 56: 111000 ~ {4,5,6}
%e 58: 111010 ~ {2,4,5,6}
%t aperQ[q_]:=Array[RotateRight[q,#]&,Length[q],1,UnsameQ];
%t neckQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And];
%t Select[Range[100],aperQ[Reverse[IntegerDigits[#,2]]]&&neckQ[Reverse[IntegerDigits[#,2]]]&]
%Y A similar concept is A275692.
%Y Aperiodic words are A328594.
%Y Necklaces are A328595.
%Y Binary Lyndon words are A001037.
%Y Lyndon compositions are A059966.
%Y Cf. A000031, A000120, A000740, A008965, A027375, A121016.
%K nonn,base
%O 1,2
%A _Gus Wiseman_, Oct 22 2019
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