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%I #5 Sep 26 2022 08:20:30
%S 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,
%T 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,
%U 1,1,1,3,1,1,2,2,1,1,1,4,1,1,1,2,1,1,1
%N Last run-length of the n-th composition in standard order.
%C 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.
%H Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vTCPiJVFUXN8IqfLlCXkgP15yrGWeRhFS4ozST5oA4Bl2PYS-XTA3sGsAEXvwW-B0ealpD8qnoxFqN3/pub">Statistics, classes, and transformations of standard compositions</a>
%e Composition 87 in standard order is (2,2,1,1,1), so a(87) = 3.
%t stc[n_]:=Differences[Prepend[Join @@ Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
%t Table[If[n==0,0,Last[Length/@Split[stc[n]]]],{n,0,100}]
%Y See link for sequences related to standard compositions.
%Y For parts instead of run-lengths we have A001511, first A065120.
%Y For Heinz numbers of partitions we have A071178, first A067029.
%Y This is the last part of row n of A333769.
%Y For maximal instead of last we have A357137, minimal A357138.
%Y The first instead of last run-length is A357180.
%Y A051903 gives maximal part of prime signature.
%Y A061395 gives maximal prime index.
%Y A124767 counts runs in standard compositions.
%Y A286470 gives maximal difference of prime indices.
%Y A333766 gives maximal part of standard composition, minimal A333768.
%Y A353847 ranks run-sums of standard compositions.
%Y Cf. A000120, A003754, A029931, A070939, A329395, A356841, A356844, A357134, A357135, A357136.
%K nonn
%O 0,4
%A _Gus Wiseman_, Sep 24 2022
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