OFFSET
1,2
COMMENTS
In the formula below, the two subtrees of the root have x and y childless vertices. The minimum Matula-Goebel 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. Dossou-Olory. The topological trees with extreme Matula numbers. J. Combin. Math. Combin. Comput., 115 (2020), 215-225.
LINKS
Audace Amen Vioutou Dossou-Olory, The topological trees with extremal Matula numbers, arXiv:1806.03995 [math.CO], 2018.
Kevin Ryde, PARI/GP Code
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[n-x] for x in range(1, n//2+1))
yield an
alst.append(an)
plst.append(prime(an))
print(list(islice(agen(), 10))) # Michael S. Branicky, Mar 17 2022
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Kevin Ryde, Mar 16 2022
EXTENSIONS
a(14) from Michael S. Branicky, Mar 17 2022
a(15) from Andrew Howroyd, Sep 17 2023
STATUS
approved