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A335486
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Numbers k such that the k-th composition in standard order (A066099) is not weakly increasing.
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2
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5, 9, 11, 13, 17, 18, 19, 21, 22, 23, 25, 27, 29, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 53, 54, 55, 57, 59, 61, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99
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OFFSET
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1,1
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COMMENTS
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Also compositions matching the pattern (2,1).
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.
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LINKS
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EXAMPLE
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The sequence of terms together with the corresponding compositions begins:
5: (2,1)
9: (3,1)
11: (2,1,1)
13: (1,2,1)
17: (4,1)
18: (3,2)
19: (3,1,1)
21: (2,2,1)
22: (2,1,2)
23: (2,1,1,1)
25: (1,3,1)
27: (1,2,1,1)
29: (1,1,2,1)
33: (5,1)
34: (4,2)
35: (4,1,1)
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MATHEMATICA
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stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]];
Select[Range[0, 100], MatchQ[stc[#], {___, x_, ___, y_, ___}/; x>y]&]
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CROSSREFS
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The complement A225620 is the avoiding version.
The (1,2)-matching version is A335485.
Patterns matching this pattern are counted by A002051 (by length).
Permutations of prime indices matching this pattern are counted by A008480(n) - 1.
These compositions are counted by A056823 (by sum).
Non-unimodal compositions are counted by A115981 and ranked by A335373.
Combinatory separations are counted by A269134.
Patterns matched by standard compositions are counted by A335454.
Minimal patterns avoided by a standard composition are counted by A335465.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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