

A335373


Numbers k such that the kth composition in standard order (A066099) is not unimodal.


33



22, 38, 44, 45, 46, 54, 70, 76, 77, 78, 86, 88, 89, 90, 91, 92, 93, 94, 102, 108, 109, 110, 118, 134, 140, 141, 142, 148, 150, 152, 153, 154, 155, 156, 157, 158, 166, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 198
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OFFSET

1,1


COMMENTS

A sequence of integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.
The kth composition in standard order (graded reverselexicographic, 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..56.


EXAMPLE

The sequence together with the corresponding compositions begins:
22: (2,1,2)
38: (3,1,2)
44: (2,1,3)
45: (2,1,2,1)
46: (2,1,1,2)
54: (1,2,1,2)
70: (4,1,2)
76: (3,1,3)
77: (3,1,2,1)
78: (3,1,1,2)
86: (2,2,1,2)
88: (2,1,4)
89: (2,1,3,1)
90: (2,1,2,2)
91: (2,1,2,1,1)
92: (2,1,1,3)
93: (2,1,1,2,1)
94: (2,1,1,1,2)


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, 200], !unimodQ[stc[#]]&]


CROSSREFS

The dual version (noncounimodal compositions) is A335374.
The case that is not counimodal either is A335375.
Unimodal compositions are A001523.
Unimodal normal sequences are A007052.
Unimodal permutations are A011782.
Nonunimodal permutations are A059204.
Nonunimodal compositions are A115981.
Nonunimodal normal sequences are A328509.
Numbers with nonunimodal unsorted prime signature are A332282.
Partitions with nonunimodal 0appended first differences are A332284.
Nonunimodal permutations of the multiset of prime indices of n are A332671.
Cf. A000120, A029931, A048793, A066099, A070939, A334299.
Cf. A072704, A332281, A332286, A332287, A332639, A332642, A332669, A332672.
Sequence in context: A084141 A259736 A082261 * A337460 A063252 A078540
Adjacent sequences: A335370 A335371 A335372 * A335374 A335375 A335376


KEYWORD

nonn


AUTHOR

Gus Wiseman, Jun 03 2020


STATUS

approved



