686 Powers of Two.sf

#!/usr/bin/ruby

# Daniel "Trizen" Șuteu
# Date: 05 November 2019
# https://github.com/trizen

# https://projecteuler.net/problem=686

# Runtime: 1 minute, 19 seconds.

# The first few exponents are: 90, 379, 575, 864, 1060, 1545, 1741, 2030, 2226, 2515, 2711, 3000, 3196, 3681, 3877, 4166, 4362, 4651, 4847, 5136, ...
# The set of differences between consecutive exponents is: {196, 289, 485}.

define ln2  = log(2)
define ln5  = log(5)
define ln10 = log(10)

func isok(n) {
    #floor(2**(n - floor((n*ln2)/ln10) + 2) * 5**(2 - floor((n*ln2)/ln10))) == 123
    floor(exp(ln2*(n - floor((n*ln2)/ln10) + 2) + ln5*(2 - floor((n*ln2)/ln10)))) == 123
}

var count = 1
var k = (1..Inf -> first(isok))
var nth = 678910

loop {

    if (isok(k+196)) {
        ++count
        k += 196
    }
    elsif (isok(k+289)) {
        ++count
        k += 289
    }
    elsif (isok(k+485)) {
        ++count
        k += 485
    }

    #say "#{count} out of #{nth} with k = #{k}"

    if (count == nth) {
        say "Final result: #{k}"
        break
    }
}