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A374520
Numbers k such that the leaders of maximal anti-runs in the k-th composition in standard order (A066099) are not identical.
9
11, 19, 23, 26, 35, 39, 43, 46, 47, 53, 58, 67, 71, 74, 75, 78, 79, 83, 87, 91, 92, 93, 94, 95, 100, 106, 107, 117, 122, 131, 135, 138, 139, 142, 143, 147, 149, 151, 154, 155, 156, 157, 158, 159, 163, 164, 167, 171, 174, 175, 179, 183, 184, 185, 186, 187, 188
OFFSET
1,1
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.
EXAMPLE
The sequence together with corresponding compositions begins:
11: (2,1,1)
19: (3,1,1)
23: (2,1,1,1)
26: (1,2,2)
35: (4,1,1)
39: (3,1,1,1)
43: (2,2,1,1)
46: (2,1,1,2)
47: (2,1,1,1,1)
53: (1,2,2,1)
58: (1,1,2,2)
67: (5,1,1)
71: (4,1,1,1)
74: (3,2,2)
75: (3,2,1,1)
78: (3,1,1,2)
79: (3,1,1,1,1)
83: (2,3,1,1)
87: (2,2,1,1,1)
91: (2,1,2,1,1)
MATHEMATICA
stc[n_]:=Differences[Prepend[Join @@ Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
Select[Range[0, 100], !SameQ@@First/@Split[stc[#], UnsameQ]&]
CROSSREFS
For leaders of maximal constant runs we have the complement of A272919.
Positions of non-constant rows in A374515.
The complement is A374519, counted by A374517.
For distinct instead of identical leaders we have A374639, counted by A374678, complement A374638, counted by A374518.
Compositions of this type are counted by A374640.
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.
- Ranks of contiguous compositions are A374249, counted by A274174.
Six types of maximal runs:
Sequence in context: A145059 A124139 A291682 * A335478 A136435 A246428
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 06 2024
STATUS
approved