Hi, I have a question regarding nested doseq loops. In the start function, once I find an answer I set the atom to true, so that the outer loop validation with :while fails. However it seems that it doesn't break it, and the loops keep on going. What's wrong with it?

I am also quite confused with the usage of atoms, refs, agents (Why do they have different names for the update functions when then the mechanism is almost the same?) etc. Is it okay to use an atom in this situation as a flag? Obviously I need a a variable like object to store a state.

(def pentagonal-list (map (fn [a] (/ (* a (dec (* 3 a))) 2)) (iterate inc 1)))


(def found (atom false))


(defn pentagonal? [a]
  (let [y (/ (inc (Math/sqrt (inc (* 24 a)))) 6)
        x (mod (* 10 y) 10)]
  (if (zero? x)
    true
    false)))


(defn both-pent? [a b]
  (let [sum (+ b a)
       diff (- a b)]
    (if (and (pentagonal? sum) (pentagonal? diff))
        true
        false)))

(defn start []
 (doseq [x pentagonal-list :while (false? @found)]
  (doseq [y pentagonal-list :while (<= y x)]
       (if (both-pent? x y)
           (do
            (reset! found true)
             (println (- x y)))))))