|
| |
|
|
A358521
|
|
Sorted list of positions of first appearances in the sequence of Matula-Goebel numbers of standard ordered trees (A358506).
|
|
4
|
|
|
|
1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 16, 17, 18, 19, 20, 22, 24, 32, 33, 34, 35, 36, 37, 38, 40, 43, 44, 48, 64, 66, 67, 68, 69, 70, 72, 74, 75, 76, 80, 86, 88, 96, 128, 129, 131, 132, 133, 134, 136, 137, 138, 139, 140, 144, 147, 148, 150, 152, 160, 171, 172
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
The Matula-Goebel number of a rooted tree is the product of primes indexed by the Matula-Goebel numbers of the branches of its root, which gives a bijective correspondence between positive integers and unlabeled rooted trees.
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 standard ordered trees begin:
1: o
2: (o)
3: ((o))
4: (oo)
5: (((o)))
6: ((o)o)
8: (ooo)
9: ((oo))
10: (((o))o)
11: ((o)(o))
12: ((o)oo)
16: (oooo)
17: ((((o))))
18: ((oo)o)
19: (((o))(o))
20: (((o))oo)
|
|
|
MATHEMATICA
|
stc[n_]:=Differences[Prepend[Join @@ Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
srt[n_]:=If[n==1, {}, srt/@stc[n-1]];
mgnum[t_]:=If[t=={}, 1, Times@@Prime/@mgnum/@t];
fir[q_]:=Select[Range[Length[q]], !MemberQ[Take[q, #-1], q[[#]]]&];
fir[Table[mgnum[srt[n]], {n, 100}]]
|
|
|
CROSSREFS
|
Positions of first appearances in A358506.
Cf. A001263, A014486, A061775, A127301, A196050, A206487, A358371, A358372, A358378, A358379, A358505.
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
