A335486 Numbers k such that the k-th composition in standard order (A066099) is not weakly increasing.

5, 9, 11, 13, 17, 18, 19, 21, 22, 23, 25, 27, 29, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 53, 54, 55, 57, 59, 61, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99

Offset

1,1

Comments

Also compositions matching the pattern (2,1).

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.

Links

Table of n, a(n) for n=1..65.

Wikipedia, Permutation pattern

Gus Wiseman, Sequences counting and ranking compositions by the patterns they match or avoid.

Gus Wiseman, Statistics, classes, and transformations of standard compositions

Example

The sequence of terms together with the corresponding compositions begins:
   5: (2,1)
   9: (3,1)
  11: (2,1,1)
  13: (1,2,1)
  17: (4,1)
  18: (3,2)
  19: (3,1,1)
  21: (2,2,1)
  22: (2,1,2)
  23: (2,1,1,1)
  25: (1,3,1)
  27: (1,2,1,1)
  29: (1,1,2,1)
  33: (5,1)
  34: (4,2)
  35: (4,1,1)

Mathematica

stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]];
Select[Range[0, 100], MatchQ[stc[#], {___, x_, ___, y_, ___}/; x>y]&]

Crossrefs

The complement A225620 is the avoiding version.

The (1,2)-matching version is A335485.

Patterns matching this pattern are counted by A002051 (by length).

Permutations of prime indices matching this pattern are counted by A008480(n) - 1.

These compositions are counted by A056823 (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.

Cf. A034691, A056986, A108917, A114994, A238279, A334968, A335456, A335458.

Sequence in context: A257292 A234285 A314584 * A347771 A294277 A373674

Adjacent sequences: A335483 A335484 A335485 * A335487 A335488 A335489

Keyword

nonn

Author

Gus Wiseman, Jun 18 2020

Status

approved