

A300402


Smallest integer i such that TREE(i) >= n.


2



1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


COMMENTS

The sequence grows very slowly.
A rooted tree is a tree containing one special node labeled the "root".
TREE(n) gives the largest integer k where a sequence T(1), T(2), ..., T(k) of rooted trees, each one assigned a label from a set of n labels and each one having at most i vertices, exists such that T(i) <= T(j) does not hold for any i < j <= k.


LINKS

Table of n, a(n) for n=0..86.
Eric Weisstein's World of Mathematics, Rooted Tree
Wikipedia, Hyperoperation  Notations
Wikipedia, Kruskal's tree theorem


EXAMPLE

TREE(1) = 1, so a(n) = 1 for n <= 1.
TREE(2) = 3, so a(n) = 2 for 2 <= n <= 3.
TREE(3) > A(A(...A(1)...)), where A(x) = 2[x+1]x is a variant of Ackermann's function, a[n]b denotes a hyperoperation and the number of nested A() functions is 187196, so a(n) = 3 for at least 4 <= n <= A^A(187196)(1).


CROSSREFS

Cf. A090529, A300403, A300404.
Sequence in context: A115230 A304733 A165024 * A211020 A157639 A010096
Adjacent sequences: A300399 A300400 A300401 * A300403 A300404 A300405


KEYWORD

nonn


AUTHOR

Felix FrÃ¶hlich, Mar 05 2018


STATUS

approved



