OFFSET
1,3
COMMENTS
First differs from A374701 in having 150, corresponding to (3,2,1,2). - Gus Wiseman, Sep 18 2024
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.
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).
LINKS
EXAMPLE
See A335468 for an example of the complement.
MATHEMATICA
stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]];
Select[Range[0, 100], !MatchQ[stc[#], {___, x_, ___, y_, ___, x_, ___}/; x>y]&]
CROSSREFS
The complement A335468 is the matching version.
The (1,2,1)-avoiding version is A335467.
These compositions are counted by A335473.
Patterns matched by standard compositions are counted by A335454.
Minimal patterns avoided by a standard composition are counted by A335465.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 16 2020
STATUS
approved