using binary method (not always shortest)

AdditionChains.clj

(defn double [i]
  (bit-shift-left i 1))

(defn to-binary-seq [^long x]
  (map #(- (int %) (int \0))
       (Long/toBinaryString x)))

(defn addition-chain [x]
  (reduce #(if (zero? %2)
             (conj %1 (double (peek %1)))
             (conj %1 (double (peek %1)) (inc (double (peek %1)))))
          [1]
          (next (to-binary-seq x))))