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A328607 Numbers whose reversed binary expansion, without the most significant digit, is a necklace.

%I A328607 #11 Oct 14 2021 19:08:17
%S A328607 0,1,2,3,4,6,7,8,12,14,15,16,24,26,28,30,31,32,48,52,56,58,60,62,63,
%T A328607 64,96,100,104,106,108,112,116,118,120,122,124,126,127,128,192,200,
%U A328607 208,212,216,220,224,228,232,234,236,240,244,246,248,250,252,254,255
%N A328607 Numbers whose reversed binary expansion, without the most significant digit, is a necklace.
%C A328607 Offset is 0 to be consistent with A257250.
%C A328607 A necklace is a finite sequence that is lexicographically minimal among all of its cyclic rotations.
%e A328607 The sequence of terms together with their binary expansions and binary indices begins:
%e A328607     0:        0 ~ {}
%e A328607     1:        1 ~ {1}
%e A328607     2:       10 ~ {2}
%e A328607     3:       11 ~ {1,2}
%e A328607     4:      100 ~ {3}
%e A328607     6:      110 ~ {2,3}
%e A328607     7:      111 ~ {1,2,3}
%e A328607     8:     1000 ~ {4}
%e A328607    12:     1100 ~ {3,4}
%e A328607    14:     1110 ~ {2,3,4}
%e A328607    15:     1111 ~ {1,2,3,4}
%e A328607    16:    10000 ~ {5}
%e A328607    24:    11000 ~ {4,5}
%e A328607    26:    11010 ~ {2,4,5}
%e A328607    28:    11100 ~ {3,4,5}
%e A328607    30:    11110 ~ {2,3,4,5}
%e A328607    31:    11111 ~ {1,2,3,4,5}
%e A328607    32:   100000 ~ {6}
%e A328607    48:   110000 ~ {5,6}
%e A328607    52:   110100 ~ {3,5,6}
%t A328607 neckQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And];
%t A328607 Select[Range[0,100],#<=1||neckQ[Reverse[Rest[IntegerDigits[#,2]]]]&]
%Y A328607 The dual non-reversed version is A257250.
%Y A328607 The dual non-reversed version involving all digits is A065609.
%Y A328607 The version involving all digits is A328595.
%Y A328607 The non-reversed version is A328668.
%Y A328607 Binary necklaces are A000031.
%Y A328607 Cf. A000120, A001037, A003714, A008965, A014081, A121016, A164707, A275692, A328594, A328596.
%K A328607 nonn
%O A328607 0,3
%A A328607 _Gus Wiseman_, Oct 30 2019