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 index of the first term in the Fibonacci sequence to contain 1000 digits?



In [4]:

    
open System.Numerics

let numLen (n:BigInteger) = n.ToString().Length

let bigOne = new BigInteger(1)

let bigTwo = new BigInteger(2)

let rec fibLen1000 index previous current =
    if (numLen current) >= 1000 then index
    else fibLen1000 (index + bigOne) current (previous + current)
    
fibLen1000 bigTwo bigOne bigOne









    Out[4]:





4782



In [ ]: