A366142 Matula-Goebel numbers of rooted trees which are symmetrical about a straight line passing through the root.

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

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

Table of n, a(n) for n=1..69.

Ramzan Guekhaev, Flowery numbers.docx.

Ramzan Guekhaev, Table for n, a(n) for n = 1..455

Index entries for sequences related to Matula-Goebel numbers

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

Adjacent sequences: A366139 A366140 A366141 * A366143 A366144 A366145

Keyword

nonn,changed

Author

Ramzan Guekhaev and Loïc Apothéloz, Sep 30 2023

Status

approved