OFFSET
1,3
COMMENTS
A finite sequence is aperiodic if all of its cyclic rotations are distinct. See A000740 or A027375 for details.
Also numbers k such that the k-th composition in standard order is aperiodic. The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions. - Gus Wiseman, Apr 28 2020
EXAMPLE
The sequence of terms together with their binary expansions and binary indices begins:
0: 0 ~ {}
1: 1 ~ {1}
2: 10 ~ {2}
4: 100 ~ {3}
5: 101 ~ {1,3}
6: 110 ~ {2,3}
8: 1000 ~ {4}
9: 1001 ~ {1,4}
11: 1011 ~ {1,2,4}
12: 1100 ~ {3,4}
13: 1101 ~ {1,3,4}
14: 1110 ~ {2,3,4}
16: 10000 ~ {5}
17: 10001 ~ {1,5}
18: 10010 ~ {2,5}
19: 10011 ~ {1,2,5}
20: 10100 ~ {3,5}
21: 10101 ~ {1,3,5}
22: 10110 ~ {2,3,5}
23: 10111 ~ {1,2,3,5}
24: 11000 ~ {4,5}
MATHEMATICA
aperQ[q_]:=Array[RotateRight[q, #]&, Length[q], 1, UnsameQ];
Select[Range[0, 100], aperQ[IntegerDigits[#, 2]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 22 2019
STATUS
approved