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A366142 Matula-Goebel numbers of rooted trees which are symmetrical about a straight line passing through the root. 0
1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 16, 17, 18, 19, 20, 23, 25, 27, 28, 31, 32, 36, 37, 44, 45, 48, 49, 50, 53, 59, 61, 63, 64, 67, 68, 71, 72, 75, 76, 80, 81, 83, 92, 97, 98, 99, 100, 103, 107, 108, 112, 121, 124, 125, 127, 128, 131, 144, 147, 148, 151, 153, 157, 162, 169, 171, 175, 176, 180 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The Matula-Goebel number of a tree is Product prime(k_i), where the k_i are the Matula-Goebel numbers of the child subtrees of the root.
A tree is symmetric about a line iff the root has 2 copies of each child subtree (one each side of the line), and an optional "middle" child subtree on the line and in turn symmetric too.
LINKS
Ramzan Guekhaev, Flowery numbers.docx.
FORMULA
a(1) = 1; k > 1 is a term iff (k/p^2 is a term for some p) OR (k = prime(j) where j is a term).
EXAMPLE
12 is a term since it's the Matula-Goebel number of the following tree which is, per the layout shown, symmetric about the vertical.
(*)
|
(*) (*) (*)
\ | /
\ | /
(*) root
CROSSREFS
Cf. A000040.
Sequence in context: A346782 A229757 A319272 * A141819 A097904 A094387
KEYWORD
nonn
AUTHOR
Ramzan Guekhaev, Sep 30 2023
STATUS
approved

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Last modified July 15 00:37 EDT 2024. Contains 374323 sequences. (Running on oeis4.)