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A335486 Numbers k such that the k-th composition in standard order (A066099) is not weakly increasing.

%I A335486 #9 Jun 30 2020 09:55:26
%S A335486 5,9,11,13,17,18,19,21,22,23,25,27,29,33,34,35,37,38,39,41,43,44,45,
%T A335486 46,47,49,50,51,53,54,55,57,59,61,65,66,67,68,69,70,71,73,74,75,76,77,
%U A335486 78,79,81,82,83,85,86,87,88,89,90,91,92,93,94,95,97,98,99
%N A335486 Numbers k such that the k-th composition in standard order (A066099) is not weakly increasing.
%C A335486 Also compositions matching the pattern (2,1).
%C A335486 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 A335486 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation_pattern">Permutation pattern</a>
%H A335486 Gus Wiseman, <a href="https://oeis.org/A102726/a102726.txt">Sequences counting and ranking compositions by the patterns they match or avoid.</a>
%H A335486 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 A335486 The sequence of terms together with the corresponding compositions begins:
%e A335486    5: (2,1)
%e A335486    9: (3,1)
%e A335486   11: (2,1,1)
%e A335486   13: (1,2,1)
%e A335486   17: (4,1)
%e A335486   18: (3,2)
%e A335486   19: (3,1,1)
%e A335486   21: (2,2,1)
%e A335486   22: (2,1,2)
%e A335486   23: (2,1,1,1)
%e A335486   25: (1,3,1)
%e A335486   27: (1,2,1,1)
%e A335486   29: (1,1,2,1)
%e A335486   33: (5,1)
%e A335486   34: (4,2)
%e A335486   35: (4,1,1)
%t A335486 stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]];
%t A335486 Select[Range[0,100],MatchQ[stc[#],{___,x_,___,y_,___}/;x>y]&]
%Y A335486 The complement A225620 is the avoiding version.
%Y A335486 The (1,2)-matching version is A335485.
%Y A335486 Patterns matching this pattern are counted by A002051 (by length).
%Y A335486 Permutations of prime indices matching this pattern are counted by A008480(n) - 1.
%Y A335486 These compositions are counted by A056823 (by sum).
%Y A335486 Constant patterns are counted by A000005 and ranked by A272919.
%Y A335486 Permutations are counted by A000142 and ranked by A333218.
%Y A335486 Patterns are counted by A000670 and ranked by A333217.
%Y A335486 Non-unimodal compositions are counted by A115981 and ranked by A335373.
%Y A335486 Combinatory separations are counted by A269134.
%Y A335486 Patterns matched by standard compositions are counted by A335454.
%Y A335486 Minimal patterns avoided by a standard composition are counted by A335465.
%Y A335486 Cf. A034691, A056986, A108917, A114994, A238279, A334968, A335456, A335458.
%K A335486 nonn
%O A335486 1,1
%A A335486 _Gus Wiseman_, Jun 18 2020