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A374701 Numbers k such that the leaders of weakly decreasing runs in the k-th composition in standard order (A066099) are distinct.

%I A374701 #8 Jul 26 2024 08:58:42
%S A374701 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,23,24,25,26,
%T A374701 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,47,48,49,50,51,
%U A374701 52,53,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71
%N A374701 Numbers k such that the leaders of weakly decreasing runs in the k-th composition in standard order (A066099) are distinct.
%C A374701 First differs from A335469 in having 150, which corresponds to the composition (3,2,1,2).
%C A374701 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 A374701 Gus Wiseman, <a href="/A374629/a374629.txt">Sequences counting and ranking compositions by their leaders (for six types of runs)</a>.
%e A374701 The maximal weakly decreasing subsequences of the 1257th composition in standard order are ((3,1,1),(2),(3,1)), with leaders (3,2,3), so 1257 is not in the sequence.
%t A374701 stc[n_]:=Differences[Prepend[Join @@ Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
%t A374701 Select[Range[0,100],UnsameQ@@First/@Split[stc[#],GreaterEqual]&] (* _Gus Wiseman_, Jul 24 2024 *)
%Y A374701 Positions of distinct (strict) rows in A374740, opposite A374629.
%Y A374701 Compositions of this type are counted by A374743.
%Y A374701 For identical leaders we have A374744, counted by A374742.
%Y A374701 Other types of runs and their counts: A374249 (A274174), A374638 (A374518), A374698 (A374687), A374767 (A374761), A374768 (A374632).
%Y A374701 A011782 counts compositions.
%Y A374701 A238130, A238279, A333755 count compositions by number of runs.
%Y A374701 A335456 counts patterns matched by compositions.
%Y A374701 A373949 counts compositions by run-compressed sum.
%Y A374701 All of the following pertain to compositions in standard order:
%Y A374701 - Length is A000120.
%Y A374701 - Sum is A029837(n+1) (or sometimes A070939).
%Y A374701 - Parts are listed by A066099.
%Y A374701 - Adjacent equal pairs are counted by A124762, unequal A333382.
%Y A374701 - Number of max runs: A124765, A124766, A124767, A124768, A124769, A333381.
%Y A374701 - Ranks of anti-run compositions are A333489, counted by A003242.
%Y A374701 - Run-length transform is A333627.
%Y A374701 - Run-compression transform is A373948, sum A373953, excess A373954.
%Y A374701 Cf. A065120, A106356, A189076, A238343, A261982, A272919, A333213, A374630, A374635, A374637, A374748.
%K A374701 nonn
%O A374701 1,3
%A A374701 _Gus Wiseman_, Jul 24 2024