OFFSET
1,1
COMMENTS
First differs from A133811 in having 50.
A Lyndon word is a finite sequence that is lexicographically strictly less than all of its cyclic rotations.
A number's prime signature is the sequence of positive exponents in its prime factorization.
EXAMPLE
The prime signature of 30870 is (1,2,1,3), which is a Lyndon word, so 30870 is in the sequence.
The sequence of terms together with their prime indices begins:
2: {1}
3: {2}
4: {1,1}
5: {3}
7: {4}
8: {1,1,1}
9: {2,2}
11: {5}
13: {6}
16: {1,1,1,1}
17: {7}
18: {1,2,2}
19: {8}
23: {9}
25: {3,3}
27: {2,2,2}
29: {10}
31: {11}
32: {1,1,1,1,1}
MATHEMATICA
lynQ[q_]:=Array[Union[{q, RotateRight[q, #]}]=={q, RotateRight[q, #]}&, Length[q]-1, 1, And];
Select[Range[2, 100], lynQ[Last/@FactorInteger[#]]&]
CROSSREFS
Numbers whose reversed binary expansion is Lyndon are A328596.
Numbers whose prime signature is a necklace are A329138.
Numbers whose prime signature is aperiodic are A329139.
Lyndon compositions are A059966.
Prime signature is A124010.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 06 2019
STATUS
approved