

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
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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 such that a sequence T(1), T(2), ..., T(k) of vertexcolored (using up to n colors) rooted trees, each one T(i) having at most i vertices, exists such that T(i) <= T(j) does not hold for any i < j <= k.  Edited by Gus Wiseman, Jul 06 2020


LINKS

Table of n, a(n) for n=0..86.
Priyabrata Biswas, Towards Data Science: How Big Is The Number — Tree(3)
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.
Labeled rooted trees are counted by A000169 and A206429.
Cf. A000081, A000311, A060313, A060356, A317713.
Sequence in context: A304733 A350737 A165024 * A326166 A211020 A157639
Adjacent sequences: A300399 A300400 A300401 * A300403 A300404 A300405


KEYWORD

nonn


AUTHOR

Felix Fröhlich, Mar 05 2018


STATUS

approved



