OFFSET
1,2
COMMENTS
We define an unlabeled ordered rooted tree to be weakly transitive if every branch of a branch of the root is itself a branch of 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)
4: (oo)
6: ((o)o)
7: (o(o))
8: (ooo)
12: ((o)oo)
14: (o(o)o)
15: (oo(o))
16: (oooo)
18: ((oo)o)
22: ((o)(o)o)
23: ((o)o(o))
24: ((o)ooo)
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], Complement[Union@@srt[#], srt[#]]=={}&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 18 2022
STATUS
approved