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Numbers whose binary expansion without the most significant (first) digit is a co-Lyndon word.
4

%I #4 Nov 16 2019 13:49:13

%S 2,3,6,12,14,24,28,30,48,52,56,58,60,62,96,104,112,114,116,120,122,

%T 124,126,192,200,208,212,224,226,228,232,234,236,240,242,244,246,248,

%U 250,252,254,384,400,416,420,424,448,450,452,456,458,464,466,468,472,474

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

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

%e The sequence of terms together with their binary expansions begins:

%e 2: (1,0)

%e 3: (1,1)

%e 6: (1,1,0)

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

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

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

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

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

%e 48: (1,1,0,0,0,0)

%e 52: (1,1,0,1,0,0)

%e 56: (1,1,1,0,0,0)

%e 58: (1,1,1,0,1,0)

%e 60: (1,1,1,1,0,0)

%e 62: (1,1,1,1,1,0)

%e 96: (1,1,0,0,0,0,0)

%e 104: (1,1,0,1,0,0,0)

%e 112: (1,1,1,0,0,0,0)

%e 114: (1,1,1,0,0,1,0)

%e 116: (1,1,1,0,1,0,0)

%e 120: (1,1,1,1,0,0,0)

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

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

%Y The version involving all digits is A275692.

%Y Binary Lyndon/co-Lyndon words are A001037.

%Y A ranking of binary co-Lyndon words is A329318

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

%K nonn

%O 1,1

%A _Gus Wiseman_, Nov 16 2019