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

1,1

Comments

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

Links

Table of n, a(n) for n=1..56.

Example

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)

Mathematica

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

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.

Sequence in context: A015771 A020492 A110590 * A291174 A281110 A252792

Adjacent sequences: A329398 A329399 A329400 * A329402 A329403 A329404

Keyword

nonn

Author

Gus Wiseman, Nov 16 2019

Status

approved