I coded this solution in just a couple of minutes, but ran into trouble with F#’s unchecked Int32 operations. We can do checked operations using Checked.(+) for + for example. After changing to Int64, this runs in about 4 and a half seconds.

let problem14a = let collatz n = let rec collatz n count = let count = count + 1L if n = 1L then count elif n % 2L = 0L then collatz (n/2L) count else collatz ((3L*n)+1L) count collatz n 0L {1L..999999L} |> Seq.map (fun i -> (i, collatz i)) |> Seq.maxBy snd |> fst

Since subsequences are frequently shared between inputs of *n, *this is a good opportunity to apply a memoization technique.

let problem14b = let mem = new System.Collections.Generic.Dictionary<int64,int64>() let collatz m = let rec collatz n count = let count = count + 1L if mem.ContainsKey n then let count = mem.[n] + count - 1L mem.Add(m, count) count elif n = 1L then mem.Add(m, count) count elif n % 2L = 0L then collatz (n/2L) count else collatz ((3L*n)+1L) count collatz m 0L {1L..999999L} |> Seq.map (fun i -> (i, collatz i)) |> Seq.maxBy snd |> fstThat ran in about 1 and a half seconds.

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