Project Euler Problem 14 in Clojure

euler_14.clj

(defn collatz [n]
    (if (even? n)
        (/ n 2)
        (inc (* 3 n))))

(defn collatz-seq [start ls]
    (let [next-number (collatz start)]
    (if (= start 1)
        (conj ls 1)
        (collatz-seq next-number (conj ls start)))))

(defn length-of-collatz [start-number]
    (count (collatz-seq start-number [])))

(defn collatz-length-map [num end lengths]
    (let [collatz-length (length-of-collatz num)]
    (if (= num end)
        lengths
        (recur (inc num) end (assoc lengths collatz-length num)))))

(defn problem16 [start end]
    (let [lengths (collatz-length-map start end {})
          largest-key (apply max (keys lengths))]
    (get lengths largest-key)))

(println (problem16 1 1000000))