104 Pandigital Fibonacci ends.sf

#!/usr/bin/ruby

# Author: Trizen
# Date: 18 March 2022
# https://github.com/trizen

# https://projecteuler.net/problem=104

# Runtime: 5.904s

# Solution using Binet's formula to compute the first 9 digits of fib(n),
# and also modular exponentiation to compute the last 9 digits of fib(n).

func f(n) {
    n*log((1+sqrt(5))/2) - log(5)/2
}

func nth_fib_first_k_digits(n,k,b=10) {
    var v = f(n)
    var l = b.log
    int(b**(k-1) * exp(v - l*floor(v/l)))
}

var t = @(1..9).join

for (var k = 2749; true; ++k) {
    if ((fibmod(k, 1e9).to_s.sort == t) && (nth_fib_first_k_digits(k, 9).to_s.sort == t)) {
        say k
        break
    }
}