cp's OEIS Frontend

A335484 Numbers k such that the k-th composition in standard order (A066099) matches the pattern (3,2,1).

%I A335484 #8 Jun 30 2020 01:55:18
%S A335484 37,69,75,77,101,133,137,139,141,149,150,151,155,157,165,197,203,205,
%T A335484 229,261,265,267,269,274,275,277,278,279,281,283,285,293,297,299,300,
%U A335484 301,302,303,309,310,311,315,317,325,331,333,357,389,393,395,397,405,406
%N A335484 Numbers k such that the k-th composition in standard order (A066099) matches the pattern (3,2,1).
%C A335484 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 A335484 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 A335484 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation_pattern">Permutation pattern</a>
%H A335484 Gus Wiseman, <a href="https://oeis.org/A102726/a102726.txt">Sequences counting and ranking compositions by the patterns they match or avoid.</a>
%H A335484 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 A335484 The sequence of terms together with the corresponding compositions begins:
%e A335484    37: (3,2,1)
%e A335484    69: (4,2,1)
%e A335484    75: (3,2,1,1)
%e A335484    77: (3,1,2,1)
%e A335484   101: (1,3,2,1)
%e A335484   133: (5,2,1)
%e A335484   137: (4,3,1)
%e A335484   139: (4,2,1,1)
%e A335484   141: (4,1,2,1)
%e A335484   149: (3,2,2,1)
%e A335484   150: (3,2,1,2)
%e A335484   151: (3,2,1,1,1)
%e A335484   155: (3,1,2,1,1)
%e A335484   157: (3,1,1,2,1)
%e A335484   165: (2,3,2,1)
%t A335484 stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]];
%t A335484 Select[Range[0,100],MatchQ[stc[#],{___,x_,___,y_,___,z_,___}/;z<y<x]&]
%Y A335484 The version counting permutations is A056986.
%Y A335484 Patterns matching this pattern are counted by A335515 (by length).
%Y A335484 Permutations of prime indices matching this pattern are counted by A335520.
%Y A335484 These compositions are counted by A335514 (by sum).
%Y A335484 Constant patterns are counted by A000005 and ranked by A272919.
%Y A335484 Permutations are counted by A000142 and ranked by A333218.
%Y A335484 Patterns are counted by A000670 and ranked by A333217.
%Y A335484 Non-unimodal compositions are counted by A115981 and ranked by A335373.
%Y A335484 Permutations matching (1,3,2,4) are counted by A158009.
%Y A335484 Combinatory separations are counted by A269134.
%Y A335484 Patterns matched by standard compositions are counted by A335454.
%Y A335484 Minimal patterns avoided by a standard composition are counted by A335465.
%Y A335484 Other permutations:
%Y A335484 - A335479 (1,2,3)
%Y A335484 - A335480 (1,3,2)
%Y A335484 - A335481 (2,1,3)
%Y A335484 - A335482 (2,3,1)
%Y A335484 - A335483 (3,1,2)
%Y A335484 - A335484 (3,2,1)
%Y A335484 Cf. A034691, A056986, A108917, A114994, A158005, A238279, A333224, A333257, A334968, A335456, A335458.
%K A335484 nonn
%O A335484 1,1
%A A335484 _Gus Wiseman_, Jun 18 2020