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A374520 Numbers k such that the leaders of maximal anti-runs in the k-th composition in standard order (A066099) are not identical.

%I A374520 #5 Aug 06 2024 21:36:42
%S A374520 11,19,23,26,35,39,43,46,47,53,58,67,71,74,75,78,79,83,87,91,92,93,94,
%T A374520 95,100,106,107,117,122,131,135,138,139,142,143,147,149,151,154,155,
%U A374520 156,157,158,159,163,164,167,171,174,175,179,183,184,185,186,187,188
%N A374520 Numbers k such that the leaders of maximal anti-runs in the k-th composition in standard order (A066099) are not identical.
%C A374520 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.
%C A374520 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 A374520 Gus Wiseman, <a href="/A374629/a374629.txt">Sequences counting and ranking compositions by their leaders (for six types of runs)</a>.
%e A374520 The sequence together with corresponding compositions begins:
%e A374520   11: (2,1,1)
%e A374520   19: (3,1,1)
%e A374520   23: (2,1,1,1)
%e A374520   26: (1,2,2)
%e A374520   35: (4,1,1)
%e A374520   39: (3,1,1,1)
%e A374520   43: (2,2,1,1)
%e A374520   46: (2,1,1,2)
%e A374520   47: (2,1,1,1,1)
%e A374520   53: (1,2,2,1)
%e A374520   58: (1,1,2,2)
%e A374520   67: (5,1,1)
%e A374520   71: (4,1,1,1)
%e A374520   74: (3,2,2)
%e A374520   75: (3,2,1,1)
%e A374520   78: (3,1,1,2)
%e A374520   79: (3,1,1,1,1)
%e A374520   83: (2,3,1,1)
%e A374520   87: (2,2,1,1,1)
%e A374520   91: (2,1,2,1,1)
%t A374520 stc[n_]:=Differences[Prepend[Join @@ Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
%t A374520 Select[Range[0,100],!SameQ@@First/@Split[stc[#],UnsameQ]&]
%Y A374520 For leaders of maximal constant runs we have the complement of A272919.
%Y A374520 Positions of non-constant rows in A374515.
%Y A374520 The complement is A374519, counted by A374517.
%Y A374520 For distinct instead of identical leaders we have A374639, counted by A374678, complement A374638, counted by A374518.
%Y A374520 Compositions of this type are counted by A374640.
%Y A374520 A065120 gives leaders of standard compositions.
%Y A374520 A106356 counts compositions by number of maximal anti-runs.
%Y A374520 A238279 counts compositions by number of maximal runs
%Y A374520 All of the following pertain to compositions in standard order:
%Y A374520 - Length is A000120.
%Y A374520 - Sum is A029837(n+1).
%Y A374520 - Parts are listed by A066099.
%Y A374520 - Number of adjacent equal pairs is A124762, unequal A333382.
%Y A374520 - Anti-runs are ranked by A333489, counted by A003242.
%Y A374520 - Run-length transform is A333627, sum A070939.
%Y A374520 - Run-compression transform is A373948, sum A373953, excess A373954.
%Y A374520 - Ranks of contiguous compositions are A374249, counted by A274174.
%Y A374520 Six types of maximal runs:
%Y A374520 - Count: A124766, A124765, A124768, A124769, A333381, A124767.
%Y A374520 - Leaders: A374629, A374740, A374683, A374757, A374515, A374251.
%Y A374520 - Rank: A375123, A375124, A375125, A375126, A375127, A373948.
%Y A374520 Cf. A029931, A228351, A233564, A238343, A238424, A333213, A373949.
%K A374520 nonn
%O A374520 1,1
%A A374520 _Gus Wiseman_, Aug 06 2024