Euler 25

The Fibonacci sequence consists of elements \(F_n\) defined by

\(F_n = F_{n-1} + F_{n-1}\) Where \(F_1 = 1\) and \(F_2 = 1\).

What is the lowest n that results in \(F_n\) containing 1000 digits?

Those are large numbers - so we use fibnum() from the gmp package. We wrap that in a function that returns the number of digits;

library(gmp)

fib_n_dig <- function(n){
    nchar(as.character(fibnum(n)))
}

And then we calculate the number of digits in \(F_n\) for increasing n until the number of digits is 1000:

n_d <- 0
n <- 0
while(n_d != 1000){
        n <- n + 1
    n_d <- fib_n_dig(n)

}
answer <- n