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A318048
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Size of the span of the unlabeled rooted tree with Matula-Goebel number n.
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2
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A000081, A007097, A007853, A049076, A061773, A061775, A109082, A109129, A206491, A317713, A318046.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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