The following iterative sequence is defined for the set of positive integers:

n → n/2 (n is even)
n → 3n + 1 (n is odd)

Using the rule above and starting with 13, we generate the following sequence:

13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1

It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.

Which starting number, under one million, produces the longest chain?

NOTE: Once the chain starts the terms are allowed to go above one million.



In [1]:

    
let isEven n = n % 2UL = 0UL

let rec collatz x =
    if (x = 1UL) then 1UL
    else if (isEven x) then 1UL + (collatz (x / 2UL))
    else 1UL + (collatz ((3UL * x) + 1UL))
    
[1UL .. 1000000UL]
|> List.map (fun n -> (n, (collatz n)))
|> List.sortBy (fun t -> (snd t))
|> List.last
|> fst









    Out[1]:





837799UL



In [ ]: