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A352456 Smallest Matula-Goebel 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 (list; graph; refs; listen; history; text; internal format)
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
Column 1 of A245824.
Cf. A111299 (all binary trees), A005517 (smallest all trees), A000040 (primes).
Sequence in context: A215493 A079309 A026630 * A034459 A120747 A229314
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

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Last modified February 21 04:30 EST 2024. Contains 370219 sequences. (Running on oeis4.)