

A353744


Numbers k such that the kth composition in standard order has all equal runlengths.


4



0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 15, 16, 17, 18, 20, 22, 24, 25, 31, 32, 33, 34, 36, 37, 38, 40, 41, 42, 43, 44, 45, 48, 49, 50, 52, 54, 58, 63, 64, 65, 66, 68, 69, 70, 72, 76, 77, 80, 81, 82, 88, 89, 96, 97, 98, 101, 102, 104, 105, 108, 109, 127, 128
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OFFSET

1,3


COMMENTS

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



EXAMPLE

Composition 2362 in standard order is (3,3,1,1,2,2), with runlengths (2,2,2), so 2362 is in the sequence.


MATHEMATICA

stc[n_]:=Differences[Prepend[Join@@ Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
Select[Range[0, 100], SameQ@@Length/@Split[stc[#]]&]


CROSSREFS

Standard compositions are listed by A066099.
These compositions are counted by A329738.
For distinct instead of equal runlengths we have A351596.
A005811 counts runs in binary expansion.
A353838 ranks partitions with all distinct runsums, counted by A353837.
A353847 represents the composition runsum transformation.
A353860 counts collapsible compositions.


KEYWORD

nonn


AUTHOR



STATUS

approved



