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A335479 Numbers k such that the k-th composition in standard order (A066099) matches the pattern (1,2,3). 12
52, 104, 105, 108, 116, 180, 200, 208, 209, 210, 211, 212, 216, 217, 220, 232, 233, 236, 244, 308, 328, 360, 361, 364, 372, 400, 401, 404, 408, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 428, 432, 433, 434, 435, 436, 440, 441, 444, 456, 464, 465, 466 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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
The sequence of terms together with the corresponding compositions begins:
52: (1,2,3)
104: (1,2,4)
105: (1,2,3,1)
108: (1,2,1,3)
116: (1,1,2,3)
180: (2,1,2,3)
200: (1,3,4)
208: (1,2,5)
209: (1,2,4,1)
210: (1,2,3,2)
211: (1,2,3,1,1)
212: (1,2,2,3)
216: (1,2,1,4)
217: (1,2,1,3,1)
220: (1,2,1,1,3)
MATHEMATICA
stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]];
Select[Range[0, 100], MatchQ[stc[#], {___, x_, ___, y_, ___, z_, ___}/; x<y<z]&]
CROSSREFS
The version counting permutations is A056986.
Patterns matching this pattern are counted by A335515 (by length).
Permutations of prime indices matching this pattern are counted by A335520.
These compositions are counted by A335514 (by sum).
Constant patterns are counted by A000005 and ranked by A272919.
Permutations are counted by A000142 and ranked by A333218.
Patterns are counted by A000670 and ranked by A333217.
Non-unimodal compositions are counted by A115981 and ranked by A335373.
Combinatory separations are counted by A269134.
Patterns matched by standard compositions are counted by A335454.
Minimal patterns avoided by a standard composition are counted by A335465.
Other permutations:
- A335479 (1,2,3)
- A335480 (1,3,2)
- A335481 (2,1,3)
- A335482 (2,3,1)
- A335483 (3,1,2)
- A335484 (3,2,1)
Sequence in context: A236461 A044141 A044522 * A272140 A252343 A252336
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 18 2020
STATUS
approved

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Last modified July 12 14:24 EDT 2024. Contains 374251 sequences. (Running on oeis4.)