cp's OEIS Frontend

A328668 Numbers whose binary expansion, without the most significant digit, is a necklace.

%I A328668 #10 Nov 14 2019 12:57:54
%S A328668 0,1,2,3,4,5,7,8,9,11,15,16,17,19,21,23,31,32,33,35,37,39,43,47,63,64,
%T A328668 65,67,69,71,73,75,77,79,85,87,91,95,127,128,129,131,133,135,137,139,
%U A328668 141,143,147,149,151,155,157,159,171,175,183,191,255,256,257
%N A328668 Numbers whose binary expansion, without the most significant digit, is a necklace.
%C A328668 Offset is 0 to be consistent with A257250.
%C A328668 A necklace is a finite sequence that is lexicographically minimal among all of its cyclic rotations.
%e A328668 The sequence of terms together with their binary expansions and binary indices begins:
%e A328668    0:       0 ~ {}
%e A328668    1:       1 ~ {1}
%e A328668    2:      10 ~ {2}
%e A328668    3:      11 ~ {1,2}
%e A328668    4:     100 ~ {3}
%e A328668    5:     101 ~ {1,3}
%e A328668    7:     111 ~ {1,2,3}
%e A328668    8:    1000 ~ {4}
%e A328668    9:    1001 ~ {1,4}
%e A328668   11:    1011 ~ {1,2,4}
%e A328668   15:    1111 ~ {1,2,3,4}
%e A328668   16:   10000 ~ {5}
%e A328668   17:   10001 ~ {1,5}
%e A328668   19:   10011 ~ {1,2,5}
%e A328668   21:   10101 ~ {1,3,5}
%e A328668   23:   10111 ~ {1,2,3,5}
%e A328668   31:   11111 ~ {1,2,3,4,5}
%e A328668   32:  100000 ~ {6}
%e A328668   33:  100001 ~ {1,6}
%e A328668   35:  100011 ~ {1,2,6}
%t A328668 neckQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And];
%t A328668 Select[Range[0,100],#<=1||neckQ[Rest[IntegerDigits[#,2]]]&]
%Y A328668 The dual version is A257250.
%Y A328668 The version involving all digits, taken in reverse, is A328595.
%Y A328668 The reversed version is A328607.
%Y A328668 Binary necklaces are A000031.
%Y A328668 Necklace compositions are A008965.
%Y A328668 Cf. A000120, A001037, A003714, A014081, A065609, A121016, A275692, A328594, A328596.
%K A328668 nonn
%O A328668 0,3
%A A328668 _Gus Wiseman_, Oct 26 2019