cp's OEIS Frontend

A329367 Numbers whose binary expansion, without the most significant digit, is not a necklace.

%I A329367 #4 Nov 15 2019 21:36:50
%S A329367 6,10,12,13,14,18,20,22,24,25,26,27,28,29,30,34,36,38,40,41,42,44,45,
%T A329367 46,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,66,68,70,72,74,76,78,
%U A329367 80,81,82,83,84,86,88,89,90,92,93,94,96,97,98,99,100,101,102
%N A329367 Numbers whose binary expansion, without the most significant digit, is not a necklace.
%C A329367 A necklace is a finite sequence that is lexicographically minimal among all of its cyclic rotations.
%e A329367 The sequence of terms together with their binary expansions begins:
%e A329367    6: (1,1,0)
%e A329367   10: (1,0,1,0)
%e A329367   12: (1,1,0,0)
%e A329367   13: (1,1,0,1)
%e A329367   14: (1,1,1,0)
%e A329367   18: (1,0,0,1,0)
%e A329367   20: (1,0,1,0,0)
%e A329367   22: (1,0,1,1,0)
%e A329367   24: (1,1,0,0,0)
%e A329367   25: (1,1,0,0,1)
%e A329367   26: (1,1,0,1,0)
%e A329367   27: (1,1,0,1,1)
%e A329367   28: (1,1,1,0,0)
%e A329367   29: (1,1,1,0,1)
%e A329367   30: (1,1,1,1,0)
%e A329367   34: (1,0,0,0,1,0)
%e A329367   36: (1,0,0,1,0,0)
%e A329367   38: (1,0,0,1,1,0)
%e A329367   40: (1,0,1,0,0,0)
%e A329367   41: (1,0,1,0,0,1)
%t A329367 neckQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And];
%t A329367 Select[Range[2,100],!neckQ[Rest[IntegerDigits[#,2]]]&]
%Y A329367 The complement is A328668.
%Y A329367 The version involving all digits is A062289.
%Y A329367 The reverse version is A328607.
%Y A329367 Binary necklaces are A000031.
%Y A329367 Necklace compositions are A008965.
%Y A329367 Numbers whose binary expansion is a necklace are A275692.
%Y A329367 Numbers whose reversed binary expansion is a necklace are A328595.
%Y A329367 Cf. A000120, A001037, A003714, A065609, A069010, A257739, A328596.
%K A329367 nonn
%O A329367 1,1
%A A329367 _Gus Wiseman_, Nov 15 2019