

A335374


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


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
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OFFSET

1,1


COMMENTS

A sequence of integers is counimodal if it is the concatenation of a weakly decreasing and a weakly increasing sequence, implying that its negation is unimodal.
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..57.


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.
Nonunimodal permutations are A059204.
Nonunimodal compositions are A115981.
Nonunimodal normal sequences are A328509.
Numbers with nonunimodal unsorted prime signature are A332282.
Counimodal compositions are A332578.
Numbers with noncounimodal unsorted prime signature are A332642.
Noncounimodal 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



