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A374744
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Numbers k such that the leaders of weakly decreasing runs in the k-th composition in standard order (A066099) are identical.
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17
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0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 15, 16, 17, 18, 19, 21, 22, 23, 31, 32, 33, 34, 35, 36, 37, 39, 42, 43, 45, 46, 47, 63, 64, 65, 66, 67, 68, 69, 71, 73, 74, 75, 76, 79, 85, 86, 87, 90, 91, 93, 94, 95, 127, 128, 129, 130, 131, 132, 133, 135, 136, 137, 138
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OFFSET
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1,3
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COMMENTS
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The leaders of weakly decreasing runs in a sequence are obtained by splitting into maximal weakly decreasing subsequences 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 terms together with the corresponding compositions begin:
0: ()
1: (1)
2: (2)
3: (1,1)
4: (3)
5: (2,1)
7: (1,1,1)
8: (4)
9: (3,1)
10: (2,2)
11: (2,1,1)
15: (1,1,1,1)
16: (5)
17: (4,1)
18: (3,2)
19: (3,1,1)
21: (2,2,1)
22: (2,1,2)
23: (2,1,1,1)
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], SameQ@@First/@Split[stc[#], GreaterEqual]&]
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CROSSREFS
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For distinct (instead of identical) leaders we have A374701, count A374743.
Compositions of this type are counted by A374742.
A374748 counts compositions by sum of leaders of weakly decreasing runs.
All of the following pertain to compositions in standard order:
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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