A329401 Numbers whose binary expansion without the most significant (first) digit is a co-Lyndon word.

2, 3, 6, 12, 14, 24, 28, 30, 48, 52, 56, 58, 60, 62, 96, 104, 112, 114, 116, 120, 122, 124, 126, 192, 200, 208, 212, 224, 226, 228, 232, 234, 236, 240, 242, 244, 246, 248, 250, 252, 254, 384, 400, 416, 420, 424, 448, 450, 452, 456, 458, 464, 466, 468, 472, 474

Offset: 1

Author

Gus Wiseman, Nov 16 2019

Keywords

• nonn

Comments

A co-Lyndon word is a finite sequence that is lexicographically strictly greater than all of its cyclic rotations.

Examples

			The sequence of terms together with their binary expansions begins:
    2: (1,0)
    3: (1,1)
    6: (1,1,0)
   12: (1,1,0,0)
   14: (1,1,1,0)
   24: (1,1,0,0,0)
   28: (1,1,1,0,0)
   30: (1,1,1,1,0)
   48: (1,1,0,0,0,0)
   52: (1,1,0,1,0,0)
   56: (1,1,1,0,0,0)
   58: (1,1,1,0,1,0)
   60: (1,1,1,1,0,0)
   62: (1,1,1,1,1,0)
   96: (1,1,0,0,0,0,0)
  104: (1,1,0,1,0,0,0)
  112: (1,1,1,0,0,0,0)
  114: (1,1,1,0,0,1,0)
  116: (1,1,1,0,1,0,0)
  120: (1,1,1,1,0,0,0)
		

Crossrefs

The version involving all digits is A275692.

Binary Lyndon/co-Lyndon words are A001037.

A ranking of binary co-Lyndon words is A329318

Cf. A059966, A060223, A102659, A211097, A211100, A328594, A328596, A329312, A329325, A329326, A329359, A329395, A329396, A329400.

Programs

Mathematica

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