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 A335466 Numbers k such that the k-th composition in standard order (A066099) matches (1,2,1). 4
 13, 25, 27, 29, 45, 49, 51, 53, 54, 55, 57, 59, 61, 77, 82, 89, 91, 93, 97, 99, 101, 102, 103, 105, 107, 108, 109, 110, 111, 113, 115, 117, 118, 119, 121, 123, 125, 141, 153, 155, 157, 162, 165, 166, 173, 177, 178, 179, 181, 182, 183, 185, 187, 189, 193, 195 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 Wikipedia, Permutation pattern EXAMPLE The sequence of terms together with the corresponding compositions begins:   13: (1,2,1)   25: (1,3,1)   27: (1,2,1,1)   29: (1,1,2,1)   45: (2,1,2,1)   49: (1,4,1)   51: (1,3,1,1)   53: (1,2,2,1)   54: (1,2,1,2)   55: (1,2,1,1,1)   57: (1,1,3,1)   59: (1,1,2,1,1)   61: (1,1,1,2,1)   77: (3,1,2,1)   82: (2,3,2) MATHEMATICA stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]]; Select[Range[0, 100], MatchQ[stc[#], {___, x_, ___, y_, ___, x_, ___}/; x

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Last modified September 18 02:19 EDT 2020. Contains 337164 sequences. (Running on oeis4.)