Project Euler – Problem 25 Solution

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Problem

The Fibonacci sequence is defined by the recurrence relation:

Fn = Fn-1 + Fn-2, where F1 = 1 and F2 = 1.

Hence the first 12 terms will be:

F1 = 1

F2 = 1

F3 = 2

F4 = 3

F5 = 5

F6 = 8

F7 = 13

F8 = 21

F9 = 34

F10 = 55

F11 = 89

F12 = 144

The 12th term, F12, is the first term to contain three digits.

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

Solution

let fibonacciSeq =
    Seq.unfold (fun (current, next) -> Some(current, (next, current + next))) (0I, 1I)
    |> Seq.filter (fun f -> f > 0I)

let answer = (Seq.findIndex (fun f -> f.ToString().Length >= 1000) fibonacciSeq) + 1

In my solution here I first created a Fibonacci sequence which starts with 1, 1, … all the way to infinity, and the second expression gives us the answer to the problem by using Seq.findIndex to find the index (zero-based) of the first element which contains 1000 digits. The ‘+ 1’ at the end simply converts the zero-based index to the one-based index which the problem is asking for.

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