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A357181
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Last run-length of the n-th composition in standard order.
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3
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0, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 1, 5, 1, 1, 1, 2, 2, 1, 1, 3, 1, 1, 3, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 1, 6, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1
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OFFSET
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0,4
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COMMENTS
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A composition of n is a finite sequence of positive integers summing to n. 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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Composition 87 in standard order is (2,2,1,1,1), so a(87) = 3.
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MATHEMATICA
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stc[n_]:=Differences[Prepend[Join @@ Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
Table[If[n==0, 0, Last[Length/@Split[stc[n]]]], {n, 0, 100}]
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CROSSREFS
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See link for sequences related to standard compositions.
This is the last part of row n of A333769.
The first instead of last run-length is A357180.
A051903 gives maximal part of prime signature.
A124767 counts runs in standard compositions.
A286470 gives maximal difference of prime indices.
A353847 ranks run-sums of standard compositions.
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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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