OFFSET
1,2
COMMENTS
An ordered tree is balanced if all leaves have the same distance from the root.
We define the n-th standard ordered rooted tree to be obtained by taking the (n-1)-th composition in standard order (graded reverse-lexicographic, A066099) as root and replacing each part with its own standard ordered rooted tree. This ranking is an ordered variation of Matula-Goebel numbers, giving a bijective correspondence between positive integers and unlabeled ordered rooted trees.
LINKS
EXAMPLE
The terms together with their corresponding ordered trees begin:
1: o
2: (o)
3: ((o))
4: (oo)
5: (((o)))
8: (ooo)
9: ((oo))
11: ((o)(o))
16: (oooo)
17: ((((o))))
32: (ooooo)
35: ((oo)(o))
37: (((o))((o)))
41: ((o)(oo))
43: ((o)(o)(o))
MATHEMATICA
stc[n_]:=Differences[Prepend[Join @@ Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
srt[n_]:=If[n==1, {}, srt/@stc[n-1]];
Select[Range[100], SameQ@@Length/@Position[srt[#], {}]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 19 2022
STATUS
approved