OFFSET
1,3
COMMENTS
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.
EXAMPLE
Composition 2362 in standard order is (3,3,1,1,2,2), with run-lengths (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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 11 2022
STATUS
approved