A328596 Numbers whose reversed binary expansion is a Lyndon word (aperiodic necklace).

1, 2, 4, 6, 8, 12, 14, 16, 20, 24, 26, 28, 30, 32, 40, 44, 48, 52, 56, 58, 60, 62, 64, 72, 80, 84, 88, 92, 96, 100, 104, 106, 108, 112, 116, 118, 120, 122, 124, 126, 128, 144, 152, 160, 164, 168, 172, 176, 180, 184, 188, 192, 200, 208, 212, 216, 218, 220, 224

Offset

1,2

Comments

First differs from A091065 in lacking 50.

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

Links

Table of n, a(n) for n=1..59.

Formula

Intersection of A328594 and A328595.

Example

The sequence of terms together with their binary expansions and binary indices begins:
   1:      1 ~ {1}
   2:     10 ~ {2}
   4:    100 ~ {3}
   6:    110 ~ {2,3}
   8:   1000 ~ {4}
  12:   1100 ~ {3,4}
  14:   1110 ~ {2,3,4}
  16:  10000 ~ {5}
  20:  10100 ~ {3,5}
  24:  11000 ~ {4,5}
  26:  11010 ~ {2,4,5}
  28:  11100 ~ {3,4,5}
  30:  11110 ~ {2,3,4,5}
  32: 100000 ~ {6}
  40: 101000 ~ {4,6}
  44: 101100 ~ {3,4,6}
  48: 110000 ~ {5,6}
  52: 110100 ~ {3,5,6}
  56: 111000 ~ {4,5,6}
  58: 111010 ~ {2,4,5,6}

Mathematica

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

Crossrefs

A similar concept is A275692.

Aperiodic words are A328594.

Necklaces are A328595.

Binary Lyndon words are A001037.

Lyndon compositions are A059966.

Cf. A000031, A000120, A000740, A008965, A027375, A121016.

Sequence in context: A318186 A139363 A091065 * A275692 A334267 A163823

Adjacent sequences: A328593 A328594 A328595 * A328597 A328598 A328599

Keyword

nonn,base

Author

Gus Wiseman, Oct 22 2019

Status

approved