cp's OEIS Frontend

A328596 Numbers whose reversed binary expansion is a Lyndon word (aperiodic necklace).

%I A328596 #11 Oct 16 2021 11:55:37
%S A328596 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 A328596 80,84,88,92,96,100,104,106,108,112,116,118,120,122,124,126,128,144,
%U A328596 152,160,164,168,172,176,180,184,188,192,200,208,212,216,218,220,224
%N A328596 Numbers whose reversed binary expansion is a Lyndon word (aperiodic necklace).
%C A328596 First differs from A091065 in lacking 50.
%C A328596 A Lyndon word is a finite sequence that is lexicographically strictly less than all of its cyclic rotations.
%F A328596 Intersection of A328594 and A328595.
%e A328596 The sequence of terms together with their binary expansions and binary indices begins:
%e A328596    1:      1 ~ {1}
%e A328596    2:     10 ~ {2}
%e A328596    4:    100 ~ {3}
%e A328596    6:    110 ~ {2,3}
%e A328596    8:   1000 ~ {4}
%e A328596   12:   1100 ~ {3,4}
%e A328596   14:   1110 ~ {2,3,4}
%e A328596   16:  10000 ~ {5}
%e A328596   20:  10100 ~ {3,5}
%e A328596   24:  11000 ~ {4,5}
%e A328596   26:  11010 ~ {2,4,5}
%e A328596   28:  11100 ~ {3,4,5}
%e A328596   30:  11110 ~ {2,3,4,5}
%e A328596   32: 100000 ~ {6}
%e A328596   40: 101000 ~ {4,6}
%e A328596   44: 101100 ~ {3,4,6}
%e A328596   48: 110000 ~ {5,6}
%e A328596   52: 110100 ~ {3,5,6}
%e A328596   56: 111000 ~ {4,5,6}
%e A328596   58: 111010 ~ {2,4,5,6}
%t A328596 aperQ[q_]:=Array[RotateRight[q,#]&,Length[q],1,UnsameQ];
%t A328596 neckQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And];
%t A328596 Select[Range[100],aperQ[Reverse[IntegerDigits[#,2]]]&&neckQ[Reverse[IntegerDigits[#,2]]]&]
%Y A328596 A similar concept is A275692.
%Y A328596 Aperiodic words are A328594.
%Y A328596 Necklaces are A328595.
%Y A328596 Binary Lyndon words are A001037.
%Y A328596 Lyndon compositions are A059966.
%Y A328596 Cf. A000031, A000120, A000740, A008965, A027375, A121016.
%K A328596 nonn,base
%O A328596 1,2
%A A328596 _Gus Wiseman_, Oct 22 2019