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/**
* Problem 25 - 1000-digit Fibonacci number
*
* @see {@link https://projecteuler.net/problem=25}
*
* 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?
*/
// brute force method
function fibonacciIndex (t = 1000) {
const digits = 10n ** BigInt(t - 1)
let fib0 = BigInt(0)
let fib1 = BigInt(1)
let index = 1
while (fib1 < digits) { // using this to compare number of digits instead of .toString() significantly improved run time
const tempfib = fib1
fib1 = fib1 + fib0
fib0 = tempfib
index += 1
}
return (index)
}
export { fibonacciIndex }