OFFSET
1,3
COMMENTS
First differs from A335469 in having 150, which corresponds to the composition (3,2,1,2).
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 maximal weakly decreasing subsequences of the 1257th composition in standard order are ((3,1,1),(2),(3,1)), with leaders (3,2,3), so 1257 is not in the sequence.
MATHEMATICA
stc[n_]:=Differences[Prepend[Join @@ Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
Select[Range[0, 100], UnsameQ@@First/@Split[stc[#], GreaterEqual]&] (* Gus Wiseman, Jul 24 2024 *)
CROSSREFS
Compositions of this type are counted by A374743.
Other types of runs and their counts: A374249 (A274174), A374638 (A374518), A374698 (A374687), A374767 (A374761), A374768 (A374632).
A011782 counts compositions.
A335456 counts patterns matched by compositions.
A373949 counts compositions by run-compressed sum.
All of the following pertain to compositions in standard order:
- Length is A000120.
- Parts are listed by A066099.
- Run-length transform is A333627.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 24 2024
STATUS
approved