A374639 Numbers k such that the leaders of maximal anti-runs in the k-th composition in standard order (A066099) are not distinct.

3, 7, 10, 14, 15, 21, 23, 27, 28, 29, 30, 31, 36, 39, 42, 43, 47, 51, 55, 56, 57, 58, 59, 60, 61, 62, 63, 71, 73, 79, 84, 85, 86, 87, 90, 94, 95, 99, 103, 106, 107, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 135

Offset: 1

Author

Gus Wiseman, Aug 06 2024

Keywords

• nonn

Comments

The leaders of maximal anti-runs in a sequence are obtained by splitting it into maximal consecutive anti-runs (sequences with no adjacent equal terms) 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.

Examples

			The sequence of terms together with the corresponding compositions begins:
   3: (1,1)
   7: (1,1,1)
  10: (2,2)
  14: (1,1,2)
  15: (1,1,1,1)
  21: (2,2,1)
  23: (2,1,1,1)
  27: (1,2,1,1)
  28: (1,1,3)
  29: (1,1,2,1)
  30: (1,1,1,2)
  31: (1,1,1,1,1)
		

Crossrefs

First differs from A335466 in lacking 166, complement A335467.

The complement for leaders of identical runs is A374249, counted by A274174.

For leaders of identical runs we have A374253, counted by A335548.

Positions of non-distinct (or non-strict) rows in A374515.

The complement is A374638, counted by A374518.

For identical instead of non-distinct we have A374519, counted by A374517.

For identical instead of distinct we have A374520, counted by A374640.

Compositions of this type are counted by A374678.

Other functional neighbors are A374768, A374698, A374701, A374767.

A065120 gives leaders of standard compositions.

A106356 counts compositions by number of maximal anti-runs.

A238279 counts compositions by number of maximal runs

All of the following pertain to compositions in standard order:

- Length is A000120.

- Sum is A029837(n+1).

- Parts are listed by A066099.

- Number of adjacent equal pairs is A124762, unequal A333382.

- Anti-runs are ranked by A333489, counted by A003242.

- Run-length transform is A333627, sum A070939.

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

Six types of maximal runs:

- Count: A124766, A124765, A124768, A124769, A333381, A124767.

- Leaders: A374629, A374740, A374683, A374757, A374515, A374251.

- Rank: A375123, A375124, A375125, A375126, A375127, A373948.

Cf. A029931, A114994, A228351, A233564, A238343, A272919, A335466, A373949.

Programs

Mathematica

stc[n_]:=Differences[Prepend[Join @@ Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
Select[Range[0,100],!UnsameQ@@First/@Split[stc[#],UnsameQ]&]