base-conversion-core.clj

(ns base-conversion.core)

(def characters
  (concat (map char (range 48 58)) (map char (range 65 91))))

(def conversion-table
  (zipmap
   characters
   (range)))

(defn base-n-to-base-10
  [^String string ^Integer base]
  (let [string (clojure.string/upper-case string)]
    (assert (every? #(< (conversion-table %) base) string))
    (loop [num string
           acc 0]
      (if (seq num)
        (recur (drop 1 num) (+ (* base acc) (get conversion-table (first num))))
        acc))))

(defn base-10-to-base-n
  [^Integer number ^Integer base]
  (loop [num number
         acc []]
    (if (zero? num)
      (clojure.string/join (reverse acc))
      (recur (int (/ num base))
             (conj acc (nth characters (mod num base)))))))

@rkneufeld, Oh yes, I knew that, but how you said it was just an exercise...
Actually integer/parseInt is implemented pretty much like my function.