A374701 Numbers k such that the leaders of weakly decreasing runs in the k-th composition in standard order (A066099) are distinct.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71

Offset: 1

Author

Gus Wiseman, Jul 24 2024

Keywords

• nonn

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.

Examples

			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.
		

Links

• Gus Wiseman, Sequences counting and ranking compositions by their leaders (for six types of runs).

Crossrefs

Positions of distinct (strict) rows in A374740, opposite A374629.

Compositions of this type are counted by A374743.

For identical leaders we have A374744, counted by A374742.

Other types of runs and their counts: A374249 (A274174), A374638 (A374518), A374698 (A374687), A374767 (A374761), A374768 (A374632).

A011782 counts compositions.

A238130, A238279, A333755 count compositions by number of runs.

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.

- Sum is A029837(n+1) (or sometimes A070939).

- Parts are listed by A066099.

- Adjacent equal pairs are counted by A124762, unequal A333382.

- Number of max runs: A124765, A124766, A124767, A124768, A124769, A333381.

- Ranks of anti-run compositions are A333489, counted by A003242.

- Run-length transform is A333627.

- Run-compression transform is A373948, sum A373953, excess A373954.

Cf. A065120, A106356, A189076, A238343, A261982, A272919, A333213, A374630, A374635, A374637, A374748.

Programs

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 *)