The function TREE(k) gives the length of the longest sequence of trees T1, T2, ... where each vertex is labelled with one of k colours, the tree Ti has at most i vertices, and no tree is a minor of any tree following it in the sequence.
TREE(1) = 1, with e.g. T1 =
TREE(2) = 3: e.g. T1 =
(1); T2 =
(2)--(2); T3 =
TREE(3) is a big big number. Even bigger than Graham's number. Your job is to output a number even bigger than it!
This is a code-golf so the goal is to write the shortest program in any language that deterministically outputs a number bigger than or equal to TREE(3) (to the stdout).
- You aren't allowed to take input.
- Your program must eventually terminate but you can assume the machine has infinite memory.
- You might assume your language's number type can hold any finite value but need to explain how this exactly works in your language (ex: does a float have infinite precision?)
- Infinities are not allowed as output.
- Underflow of a number type throws an exception. It does not wrap around.
- Because TREE(3) is such a complex number you can use the fast growing hierarchy approximation fϑ(Ωω ω)+1(3) as the number to beat.
- You need to provide an explanation of why your number is so big and an ungolfed version of your code to check if your solution is valid (since there is no computer with enough memory to store TREE(3))
Note: None of the answers currently found here work.