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

6, 10, 12, 13, 14, 18, 20, 22, 24, 25, 26, 27, 28, 29, 30, 34, 36, 38, 40, 41, 42, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 66, 68, 70, 72, 74, 76, 78, 80, 81, 82, 83, 84, 86, 88, 89, 90, 92, 93, 94, 96, 97, 98, 99, 100, 101, 102

Offset: 1

Author

Gus Wiseman, Nov 15 2019

Keywords

• nonn

Comments

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

Examples

			The sequence of terms together with their binary expansions begins:
   6: (1,1,0)
  10: (1,0,1,0)
  12: (1,1,0,0)
  13: (1,1,0,1)
  14: (1,1,1,0)
  18: (1,0,0,1,0)
  20: (1,0,1,0,0)
  22: (1,0,1,1,0)
  24: (1,1,0,0,0)
  25: (1,1,0,0,1)
  26: (1,1,0,1,0)
  27: (1,1,0,1,1)
  28: (1,1,1,0,0)
  29: (1,1,1,0,1)
  30: (1,1,1,1,0)
  34: (1,0,0,0,1,0)
  36: (1,0,0,1,0,0)
  38: (1,0,0,1,1,0)
  40: (1,0,1,0,0,0)
  41: (1,0,1,0,0,1)
		

Crossrefs

The complement is A328668.

The version involving all digits is A062289.

The reverse version is A328607.

Binary necklaces are A000031.

Necklace compositions are A008965.

Numbers whose binary expansion is a necklace are A275692.

Numbers whose reversed binary expansion is a necklace are A328595.

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

Programs

Mathematica

neckQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And];
Select[Range[2,100],!neckQ[Rest[IntegerDigits[#,2]]]&]