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 A335485 Numbers k such that the k-th composition in standard order (A066099) is not weakly decreasing. 4
 6, 12, 13, 14, 20, 22, 24, 25, 26, 27, 28, 29, 30, 38, 40, 41, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 70, 72, 76, 77, 78, 80, 81, 82, 83, 84, 86, 88, 89, 90, 91, 92, 93, 94, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also compositions matching the pattern (1,2). 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..63. Keiichi Shigechi, Noncommutative crossing partitions, arXiv:2211.10958 [math.CO], 2022. 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: 6: (1,2) 12: (1,3) 13: (1,2,1) 14: (1,1,2) 20: (2,3) 22: (2,1,2) 24: (1,4) 25: (1,3,1) 26: (1,2,2) 27: (1,2,1,1) 28: (1,1,3) 29: (1,1,2,1) 30: (1,1,1,2) 38: (3,1,2) 40: (2,4) MATHEMATICA stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]]; Select[Range[0, 100], MatchQ[stc[#], {___, x_, ___, y_, ___}/; x

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Last modified June 9 16:40 EDT 2023. Contains 363183 sequences. (Running on oeis4.)