Terms approximation

(function() {
    // Returns whether or not the given N is lower than the target
    function tooLow(N) {
        return (Math.log(N) + 1) / N >= 0.001;
    }

    // Track a lower and upper bound, and squeeze them together
    let lower = 0;
    let upper = 1;

    // Seek an upper bound
    while(tooLow(upper)) {
        // If we aren't there yet, go bigger!
        upper *= 2;

        // Log the new bounds
        console.log(`${lower} < N < ${upper}`);
    }

    // We've found an upper bound!
    console.log("Upper bound found!");

    // Close in on the value
    while(upper - lower > 1) {
        // Make a guess as a new bound
        let guess = Math.round((upper + lower) / 2);

        // Tighten the bounds
        if(tooLow(guess)) lower = guess;
        else              upper = guess;

        // Log the new bounds
        console.log(`${lower} < N < ${upper}`);
    }

    // All set!
    console.log("Done!");
})();