A328596 - OEIS

%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