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A352289 a(1) = 1 and thereafter a(n) = 2*prime(a(n-1)). 2
1, 4, 14, 86, 886, 13766, 298154, 8455786, 300427382, 12942000398, 659492202274, 38995629272042, 2634767648759954, 200877694833442486, 17101872791349773894 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
In Matula-Goebel tree codes, a(n) is a rooted caterpillar consisting of a path of n-1 internal vertices down, and n childless vertices under them so each has exactly 2 children.
Mir, Rosselló, and Rotger show that among phylogenic trees (meaning series-reduced, no vertex with just 1 child) with n childless vertices, tree a(n) has the largest total cophenetic index A352288(a(n)) = binomial(n,3).
LINKS
Arnau Mir, Francesc Rosselló, and Lucía Rotger, A New Balance Index for Phylogenetic Trees, arXiv:1202.1223 [q-bio.PE], 2012.
EXAMPLE
For n=3, a(3) = 14 is the Matula-Goebel code of the following tree
root 14
/ \ tree numbers of subtrees shown,
4 1 with "1" being childless,
/ \ and n=3 of those
1 1
MATHEMATICA
NestList[2 Prime[#] &, 1, 10] (* Michael De Vlieger, Apr 18 2022 *)
PROG
(PARI) a(n) = my(ret=1); for(i=2, n, ret=2*prime(ret)); ret;
(Python)
from functools import lru_cache
from sympy import prime
@lru_cache(maxsize=None)
def A352289(n): return 1 if n == 1 else 2*prime(A352289(n-1)) # Chai Wah Wu, Apr 18 2022
CROSSREFS
Cf. A352288 (total cophenetic index).
Cf. A331937.
Sequence in context: A024421 A259353 A339193 * A330465 A202139 A331637
KEYWORD
nonn,more
AUTHOR
Kevin Ryde, Mar 16 2022
EXTENSIONS
a(10)-a(15) from Daniel Suteu, Mar 19 2022
STATUS
approved

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Last modified March 19 07:41 EDT 2024. Contains 370958 sequences. (Running on oeis4.)