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 A335374 Numbers k such that the k-th composition in standard order (A066099) is not co-unimodal. 2
 13, 25, 27, 29, 41, 45, 49, 50, 51, 53, 54, 55, 57, 59, 61, 77, 81, 82, 83, 89, 91, 93, 97, 98, 99, 101, 102, 103, 105, 107, 108, 109, 110, 111, 113, 114, 115, 117, 118, 119, 121, 123, 125, 141, 145, 153, 155, 157, 161, 162, 163, 165, 166, 167, 169, 173, 177 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A sequence of integers is co-unimodal if it is the concatenation of a weakly decreasing and a weakly increasing sequence, implying that its negation is unimodal. 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 EXAMPLE The sequence together with the corresponding compositions begins:   13: (1,2,1)   25: (1,3,1)   27: (1,2,1,1)   29: (1,1,2,1)   41: (2,3,1)   45: (2,1,2,1)   49: (1,4,1)   50: (1,3,2)   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)   81: (2,4,1)   82: (2,3,2)   83: (2,3,1,1)   89: (2,1,3,1) MATHEMATICA unimodQ[q_]:=Or[Length[q]<=1, If[q[[1]]<=q[[2]], unimodQ[Rest[q]], OrderedQ[Reverse[q]]]]; stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse; Select[Range[0, 100], !unimodQ[-stc[#]]&] CROSSREFS This is the dual version of A335373. The case that is not unimodal either is A335375. Unimodal compositions are A001523. Unimodal normal sequences are A007052. Unimodal permutations are A011782. Non-unimodal permutations are A059204. Non-unimodal compositions are A115981. Non-unimodal normal sequences are A328509. Numbers with non-unimodal unsorted prime signature are A332282. Co-unimodal compositions are A332578. Numbers with non-co-unimodal unsorted prime signature are A332642. Non-co-unimodal compositions are A332669. Cf. A000120, A029931, A048793, A066099, A070939, A334299. Cf. A112798, A227038, A329398, A332281, A332286, A332287, A332638, A332639, A332643, A332670, A332873, A333146. Sequence in context: A018991 A018948 A256475 * A335466 A186403 A032478 Adjacent sequences:  A335371 A335372 A335373 * A335375 A335376 A335377 KEYWORD nonn AUTHOR Gus Wiseman, Jun 03 2020 STATUS approved

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Last modified September 20 16:05 EDT 2020. Contains 337265 sequences. (Running on oeis4.)