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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 Table of n, a(n) for n=1..15. Audace Amen Vioutou Dossou-Olory, The topological trees with extremal Matula numbers, arXiv:1806.03995 [math.CO], 2018. Kevin Ryde, PARI/GP Code Index entries for sequences related to Matula-Goebel numbers 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 Adjacent sequences: A352453 A352454 A352455 * A352457 A352458 A352459 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.)