The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A335482 Numbers k such that the k-th composition in standard order (A066099) matches the pattern (2,3,1). 6
 41, 81, 83, 89, 105, 145, 161, 163, 165, 166, 167, 169, 177, 179, 185, 209, 211, 217, 233, 289, 290, 291, 297, 305, 321, 323, 325, 326, 327, 329, 331, 332, 333, 334, 335, 337, 339, 345, 353, 355, 357, 358, 359, 361, 369, 371, 377, 401, 417, 419, 421, 422, 423 (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 Wikipedia, Permutation pattern EXAMPLE The sequence of terms together with the corresponding compositions begins: 41: (2,3,1) 81: (2,4,1) 83: (2,3,1,1) 89: (2,1,3,1) 105: (1,2,3,1) 145: (3,4,1) 161: (2,5,1) 163: (2,4,1,1) 165: (2,3,2,1) 166: (2,3,1,2) 167: (2,3,1,1,1) 169: (2,2,3,1) 177: (2,1,4,1) 179: (2,1,3,1,1) 185: (2,1,1,3,1) MATHEMATICA stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]]; Select[Range[0, 100], MatchQ[stc[#], {___, x_, ___, y_, ___, z_, ___}/; z

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 9 13:46 EST 2022. Contains 358700 sequences. (Running on oeis4.)