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A318048 Size of the span of the unlabeled rooted tree with Matula-Goebel number n. 2
1, 2, 3, 2, 4, 4, 4, 2, 6, 6, 5, 4, 6, 3, 9, 2, 6, 6, 4, 6, 6, 8, 10, 4, 12, 6, 10, 4, 9, 9, 6, 2, 12, 6, 9, 6, 6, 4, 9, 6, 9, 7, 6, 8, 15, 10, 15, 4, 5, 12, 9, 7, 4, 10, 16, 4, 7, 9, 8, 9, 10, 10, 11, 2, 13, 12, 6, 7, 14, 10, 9, 6, 10, 7, 21, 3, 12, 10, 12, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The span of a tree is defined to be the set of possible terminal subtrees of initial subtrees, or, which is the same, the set of possible initial subtrees of terminal subtrees.
LINKS
EXAMPLE
42 is the Matula-Goebel number of (o(o)(oo)), which has span {o, (o), (oo), (ooo), (oo(oo)), (o(o)o), (o(o)(oo))}, so a(42) = 7.
MATHEMATICA
ext[c_, {}]:=c; ext[c_, s:{__}]:=Extract[c, s]; rpp[c_, v_, {}]:=v; rpp[c_, v_, s:{__}]:=ReplacePart[c, v, s];
RLO[ear_, rue:{__}]:=Union@@(Function[x, rpp[ear, x, #2]]/@ReplaceList[ext[ear, #2], #1]&@@@Select[Tuples[{rue, Position[ear, _]}], MatchQ[ext[ear, #[[2]]], #[[1, 1]]]&]);
RL[ear_, rue:{__}]:=FixedPoint[Function[keeps, Union[keeps, Join@@(RLO[#, rue]&/@keeps)]], {ear}];
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
MGTree[n_]:=If[n==1, {}, MGTree/@primeMS[n]];
Table[Length[Union[Cases[RL[MGTree[n], {List[__List]:>List[]}], _List, {1, Infinity}]]], {n, 100}]
CROSSREFS
Sequence in context: A087437 A304739 A304735 * A235805 A168231 A235728
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 13 2018
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)