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A374639
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Numbers k such that the leaders of maximal anti-runs in the k-th composition in standard order (A066099) are not distinct.
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1
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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)
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MATHEMATICA
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stc[n_]:=Differences[Prepend[Join @@ Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
Select[Range[0, 100], !UnsameQ@@First/@Split[stc[#], UnsameQ]&]
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CROSSREFS
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The complement for leaders of identical runs is A374249, counted by A274174.
Positions of non-distinct (or non-strict) rows in A374515.
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.
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:
Six types of maximal runs:
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KEYWORD
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nonn,new
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AUTHOR
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STATUS
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approved
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