

A352456


Smallest MatulaGoebel number of a rooted binary tree (everywhere 0 or 2 children) of n childless vertices.


1



1, 4, 14, 49, 301, 1589, 9761, 51529, 452411, 3041573, 23140153, 143573641, 1260538619, 8474639717, 64474684537
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OFFSET

1,2


COMMENTS

In the formula below, the two subtrees of the root have x and y childless vertices. The minimum MatulaGoebel number for that partition uses the minimum numbers for each subtree. The question is then which x+y partition is the overall minimum.


REFERENCES

Audace A. V. DossouOlory. The topological trees with extreme Matula numbers. J. Combin. Math. Combin. Comput., 115 (2020), 215225.


LINKS



FORMULA

a(n) = Min_{x+y=n} prime(a(x))*prime(a(y)).


EXAMPLE

For n = 6, the tree a(6) = 1589 is
.
* root
/ \
* * 6 childless
/ \ / \ vertices "@"
@ @ * *
/ \ / \
@ @ @ @
.


PROG

(PARI) See links.
(Python)
from sympy import prime
from itertools import count, islice
def agen(): # generator of terms
alst, plst = [0, 1], [0, 2]
yield 1
for n in count(2):
an = min(plst[x]*plst[nx] for x in range(1, n//2+1))
yield an
alst.append(an)
plst.append(prime(an))


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



