A328607 - OEIS

%I #11 Oct 14 2021 19:08:17

%S 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 64,96,100,104,106,108,112,116,118,120,122,124,126,127,128,192,200,

%U 208,212,216,220,224,228,232,234,236,240,244,246,248,250,252,254,255

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

%C Offset is 0 to be consistent with A257250.

%C A necklace is a finite sequence that is lexicographically minimal among all of its cyclic rotations.

%e The sequence of terms together with their binary expansions and binary indices begins:

%e     0:        0 ~ {}

%e     1:        1 ~ {1}

%e     2:       10 ~ {2}

%e     3:       11 ~ {1,2}

%e     4:      100 ~ {3}

%e     6:      110 ~ {2,3}

%e     7:      111 ~ {1,2,3}

%e     8:     1000 ~ {4}

%e    12:     1100 ~ {3,4}

%e    14:     1110 ~ {2,3,4}

%e    15:     1111 ~ {1,2,3,4}

%e    16:    10000 ~ {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    31:    11111 ~ {1,2,3,4,5}

%e    32:   100000 ~ {6}

%e    48:   110000 ~ {5,6}

%e    52:   110100 ~ {3,5,6}

%t neckQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And];

%t Select[Range[0,100],#<=1||neckQ[Reverse[Rest[IntegerDigits[#,2]]]]&]

%Y The dual non-reversed version is A257250.

%Y The dual non-reversed version involving all digits is A065609.

%Y The version involving all digits is A328595.

%Y The non-reversed version is A328668.

%Y Binary necklaces are A000031.

%Y Cf. A000120, A001037, A003714, A008965, A014081, A121016, A164707, A275692, A328594, A328596.

%K nonn

%O 0,3

%A _Gus Wiseman_, Oct 30 2019