A329367 - OEIS

%I #4 Nov 15 2019 21:36:50

%S 6,10,12,13,14,18,20,22,24,25,26,27,28,29,30,34,36,38,40,41,42,44,45,

%T 46,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,66,68,70,72,74,76,78,

%U 80,81,82,83,84,86,88,89,90,92,93,94,96,97,98,99,100,101,102

%N Numbers whose binary expansion, without the most significant digit, is not a necklace.

%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 begins:

%e    6: (1,1,0)

%e   10: (1,0,1,0)

%e   12: (1,1,0,0)

%e   13: (1,1,0,1)

%e   14: (1,1,1,0)

%e   18: (1,0,0,1,0)

%e   20: (1,0,1,0,0)

%e   22: (1,0,1,1,0)

%e   24: (1,1,0,0,0)

%e   25: (1,1,0,0,1)

%e   26: (1,1,0,1,0)

%e   27: (1,1,0,1,1)

%e   28: (1,1,1,0,0)

%e   29: (1,1,1,0,1)

%e   30: (1,1,1,1,0)

%e   34: (1,0,0,0,1,0)

%e   36: (1,0,0,1,0,0)

%e   38: (1,0,0,1,1,0)

%e   40: (1,0,1,0,0,0)

%e   41: (1,0,1,0,0,1)

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

%t Select[Range[2,100],!neckQ[Rest[IntegerDigits[#,2]]]&]

%Y The complement is A328668.

%Y The version involving all digits is A062289.

%Y The reverse version is A328607.

%Y Binary necklaces are A000031.

%Y Necklace compositions are A008965.

%Y Numbers whose binary expansion is a necklace are A275692.

%Y Numbers whose reversed binary expansion is a necklace are A328595.

%Y Cf. A000120, A001037, A003714, A065609, A069010, A257739, A328596.

%K nonn

%O 1,1

%A _Gus Wiseman_, Nov 15 2019