OFFSET
1,3
COMMENTS
First differs from A335467 in having 166, corresponding to the composition (2,3,1,2).
The leaders of weakly increasing runs in a sequence are obtained by splitting it into maximal weakly increasing subsequences and taking the first term of each.
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.
LINKS
EXAMPLE
The 4444th composition in standard order is (4,2,2,1,1,3), with weakly increasing runs ((4),(2,2),(1,1,3)), with leaders (4,2,1), so 4444 is in the sequence.
MATHEMATICA
stc[n_]:=Differences[Prepend[Join @@ Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
Select[Range[0, 166], UnsameQ@@First/@Split[stc[#], LessEqual]&]
CROSSREFS
A011782 counts compositions.
All of the following pertain to compositions in standard order:
- Ones are counted by A000120.
- Parts are listed by A066099.
- Length is A070939.
- Ranks of strict compositions are A233564.
- Ranks of constant compositions are A272919.
- Run-length transform is A333627.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 19 2024
STATUS
approved