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A335482 Numbers k such that the k-th composition in standard order (A066099) matches the pattern (2,3,1).

%I A335482 #9 Jun 29 2020 22:13:15
%S A335482 41,81,83,89,105,145,161,163,165,166,167,169,177,179,185,209,211,217,
%T A335482 233,289,290,291,297,305,321,323,325,326,327,329,331,332,333,334,335,
%U A335482 337,339,345,353,355,357,358,359,361,369,371,377,401,417,419,421,422,423
%N A335482 Numbers k such that the k-th composition in standard order (A066099) matches the pattern (2,3,1).
%C A335482 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 A335482 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 A335482 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation_pattern">Permutation pattern</a>
%H A335482 Gus Wiseman, <a href="https://oeis.org/A102726/a102726.txt">Sequences counting and ranking compositions by the patterns they match or avoid.</a>
%H A335482 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 A335482 The sequence of terms together with the corresponding compositions begins:
%e A335482    41: (2,3,1)
%e A335482    81: (2,4,1)
%e A335482    83: (2,3,1,1)
%e A335482    89: (2,1,3,1)
%e A335482   105: (1,2,3,1)
%e A335482   145: (3,4,1)
%e A335482   161: (2,5,1)
%e A335482   163: (2,4,1,1)
%e A335482   165: (2,3,2,1)
%e A335482   166: (2,3,1,2)
%e A335482   167: (2,3,1,1,1)
%e A335482   169: (2,2,3,1)
%e A335482   177: (2,1,4,1)
%e A335482   179: (2,1,3,1,1)
%e A335482   185: (2,1,1,3,1)
%t A335482 stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]];
%t A335482 Select[Range[0,100],MatchQ[stc[#],{___,x_,___,y_,___,z_,___}/;z<x<y]&]
%Y A335482 The version counting permutations is A056986.
%Y A335482 Patterns matching this pattern are counted by A335515 (by length).
%Y A335482 Permutations of prime indices matching this pattern are counted by A335520.
%Y A335482 These compositions are counted by A335514 (by sum).
%Y A335482 Constant patterns are counted by A000005 and ranked by A272919.
%Y A335482 Permutations are counted by A000142 and ranked by A333218.
%Y A335482 Patterns are counted by A000670 and ranked by A333217.
%Y A335482 Non-unimodal compositions are counted by A115981 and ranked by A335373.
%Y A335482 Permutations matching (1,3,2,4) are counted by A158009.
%Y A335482 Combinatory separations are counted by A269134.
%Y A335482 Patterns matched by standard compositions are counted by A335454.
%Y A335482 Minimal patterns avoided by a standard composition are counted by A335465.
%Y A335482 Other permutations:
%Y A335482 - A335479 (1,2,3)
%Y A335482 - A335480 (1,3,2)
%Y A335482 - A335481 (2,1,3)
%Y A335482 - A335482 (2,3,1)
%Y A335482 - A335483 (3,1,2)
%Y A335482 - A335484 (3,2,1)
%Y A335482 Cf. A034691, A056986, A108917, A114994, A158005, A238279, A333224, A333257, A334968, A335456, A335458.
%K A335482 nonn
%O A335482 1,1
%A A335482 _Gus Wiseman_, Jun 18 2020