A352289 a(1) = 1 and thereafter a(n) = 2*prime(a(n-1)).

1, 4, 14, 86, 886, 13766, 298154, 8455786, 300427382, 12942000398, 659492202274, 38995629272042, 2634767648759954, 200877694833442486, 17101872791349773894

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

Table of n, a(n) for n=1..15.

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

Adjacent sequences: A352286 A352287 A352288 * A352290 A352291 A352292

Keyword

nonn,more

Author

Kevin Ryde, Mar 16 2022

Extensions

a(10)-a(15) from Daniel Suteu, Mar 19 2022

Status

approved