Problem 25: What is the first term in the Fibonacci sequence to contain 1000 digits?

The key to this one, unlike the traditional non-tail-recursive definition of the Fibonacci sequence, is to generate the next element in the sequence given the previous two. 

let problem25a =
    let rec find n1 n2 term =
        let n0 = n1 + n2
        if (n0 |> string).Length = 1000 then term
        else find n0 n1 (term+1)
    find 1I 1I 3

Playing around with recursive sequences, I came up with this neat solution which runs on average the same as solution (a).

let problem25b =
    let fibseq =    
        let rec fibseq n1 n2 = 
            seq {
                let n0 = n1 + n2 
                yield n0
                yield! fibseq n0 n1 }
        seq {yield 1I ; yield 1I ; yield! (fibseq 1I 1I)}
                
    (fibseq |> Seq.findIndex (fun i -> (i |> string).Length = 1000)) + 1