cp's OEIS Frontend

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

%I A352289 #20 Sep 11 2024 13:36:40
%S A352289 1,4,14,86,886,13766,298154,8455786,300427382,12942000398,
%T A352289 659492202274,38995629272042,2634767648759954,200877694833442486,
%U A352289 17101872791349773894,1611548301646589127698,166820830882144877428234
%N A352289 a(1) = 1 and thereafter a(n) = 2*prime(a(n-1)).
%C A352289 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.
%C A352289 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).
%H A352289 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A352289.py">Python program</a>.
%H A352289 Arnau Mir, Francesc Rosselló, and Lucía Rotger, <a href="http://arxiv.org/abs/1202.1223">A New Balance Index for Phylogenetic Trees</a>, arXiv:1202.1223 [q-bio.PE], 2012.
%e A352289 For n=3, a(3) = 14 is the Matula-Goebel code of the following tree
%e A352289   root  14
%e A352289        /  \     tree numbers of subtrees shown,
%e A352289       4    1    with "1" being childless,
%e A352289      / \        and n=3 of those
%e A352289     1   1
%t A352289 NestList[2 Prime[#] &, 1, 10] (* _Michael De Vlieger_, Apr 18 2022 *)
%o A352289 (PARI) a(n) = my(ret=1); for(i=2,n, ret=2*prime(ret)); ret;
%o A352289 (Python)
%o A352289 from functools import lru_cache
%o A352289 from sympy import prime
%o A352289 @lru_cache(maxsize=None)
%o A352289 def A352289(n): return 1 if n == 1 else 2*prime(A352289(n-1)) # _Chai Wah Wu_, Apr 18 2022
%Y A352289 Cf. A352288 (total cophenetic index).
%Y A352289 Cf. A331937.
%K A352289 nonn,more,hard
%O A352289 1,2
%A A352289 _Kevin Ryde_, Mar 16 2022
%E A352289 a(10)-a(15) from _Daniel Suteu_, Mar 19 2022
%E A352289 a(16) and a(17) from _Lucas A. Brown_, Sep 04 2024