A296977 List of normal Lyndon sequences ordered first by length and then lexicographically, where a finite sequence is normal if it spans an initial interval of positive integers.

1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 3, 1, 3, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 3, 1, 1, 3, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 2, 2, 3, 1, 2, 3, 2, 1, 2, 3, 3, 1, 2, 3, 4, 1, 2, 4, 3, 1, 3, 2, 2, 1, 3, 2, 3, 1, 3, 2, 4, 1, 3, 3, 2, 1, 3, 4, 2, 1, 4, 2, 3, 1, 4, 3, 2

Offset: 1

Author

Gus Wiseman, Dec 22 2017

Keywords

• nonn
• tabf

Comments

Row n is formed by A060223(n) sequences and has length A296975(n).

Examples

			Triangle of normal Lyndon sequences begins:
1,
12,
112,122,123,132,
1112,1122,1123,1132,1213,1222,1223,1232,1233,1234,1243,1322,1323,1324,1332,1342,1423,1432.
		

Crossrefs

Cf. A000670, A019536, A060223, A095684, A185700, A281013, A294859, A296372, A296656, A296818, A296975, A296976.

Programs

Mathematica

LyndonQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And]&&Array[RotateRight[q,#]&,Length[q],1,UnsameQ];
normseqs[n_]:=Union@@Permutations/@Function[s,Array[Count[s,y_/;y<=#]+1&,n]]/@Subsets[Range[n-1]+1];
Table[Select[normseqs[n],LyndonQ],{n,5}]