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A335475 Numbers k such that the k-th composition in standard order (A066099) matches the pattern (1,2,2).

%I A335475 #7 Jun 30 2020 09:55:12
%S A335475 26,53,54,58,90,100,106,107,109,110,117,118,122,154,164,181,182,186,
%T A335475 201,202,204,210,212,213,214,215,218,219,221,222,228,234,235,237,238,
%U A335475 245,246,250,282,309,310,314,329,332,346,356,362,363,365,366,373,374,378
%N A335475 Numbers k such that the k-th composition in standard order (A066099) matches the pattern (1,2,2).
%C A335475 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.
%C A335475 We define a pattern to be a finite sequence covering an initial interval of positive integers. Patterns are counted by A000670 and ranked by A333217. A sequence S is said to match a pattern P if there is a not necessarily contiguous subsequence of S whose parts have the same relative order as P. For example, (3,1,1,3) matches (1,1,2), (2,1,1), and (2,1,2), but avoids (1,2,1), (1,2,2), and (2,2,1).
%H A335475 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation_pattern">Permutation pattern</a>
%H A335475 Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vTCPiJVFUXN8IqfLlCXkgP15yrGWeRhFS4ozST5oA4Bl2PYS-XTA3sGsAEXvwW-B0ealpD8qnoxFqN3/pub">Statistics, classes, and transformations of standard compositions</a>
%H A335475 Gus Wiseman, <a href="/A102726/a102726.txt">Sequences counting and ranking compositions by the patterns they match or avoid.</a>
%e A335475 The sequence of terms together with the corresponding compositions begins:
%e A335475    26: (1,2,2)
%e A335475    53: (1,2,2,1)
%e A335475    54: (1,2,1,2)
%e A335475    58: (1,1,2,2)
%e A335475    90: (2,1,2,2)
%e A335475   100: (1,3,3)
%e A335475   106: (1,2,2,2)
%e A335475   107: (1,2,2,1,1)
%e A335475   109: (1,2,1,2,1)
%e A335475   110: (1,2,1,1,2)
%e A335475   117: (1,1,2,2,1)
%e A335475   118: (1,1,2,1,2)
%e A335475   122: (1,1,1,2,2)
%e A335475   154: (3,1,2,2)
%e A335475   164: (2,3,3)
%t A335475 stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]];
%t A335475 Select[Range[0,100],MatchQ[stc[#],{___,x_,___,y_,___,y_,___}/;x<y]&]
%Y A335475 The complement A335525 is the avoiding version.
%Y A335475 The (2,2,1)-matching version is A335477.
%Y A335475 Patterns matching this pattern are counted by A335509 (by length).
%Y A335475 Permutations of prime indices matching this pattern are counted by A335453.
%Y A335475 These compositions are counted by A335472 (by sum).
%Y A335475 Constant patterns are counted by A000005 and ranked by A272919.
%Y A335475 Permutations are counted by A000142 and ranked by A333218.
%Y A335475 Patterns are counted by A000670 and ranked by A333217.
%Y A335475 Non-unimodal compositions are counted by A115981 and ranked by A335373.
%Y A335475 Combinatory separations are counted by A269134.
%Y A335475 Patterns matched by standard compositions are counted by A335454.
%Y A335475 Minimal patterns avoided by a standard composition are counted by A335465.
%Y A335475 Cf. A034691, A056986, A108917, A114994, A238279, A333224, A333257, A335446, A335456, A335458.
%K A335475 nonn
%O A335475 1,1
%A A335475 _Gus Wiseman_, Jun 18 2020