a constant-time solution to prob1.clj

(defn nth-val [first-val step val-count]
  (+ first-val (* step (dec val-count))))

(defn arithmetic-series [first-val step val-count]
  (let [last-val (nth-val first-val step val-count)]
    (* val-count
       (/ (+ first-val last-val) 2))))

(defn arithmetic-series-of-multiples-less-than [ceiling]
  (fn [val]
    (arithmetic-series val val (quot (dec ceiling) val))))

(defn prob1 [val1 val2 ceiling]
  (let [calc-series (arithmetic-series-of-multiples-less-than ceiling)
        val1-series (calc-series val1)
        val2-series (calc-series val2)
        multiples-series (calc-series (* val1 val2))]
    (- (+ val1-series val2-series) multiples-series)))

(time (prob1 3 5 1e3))
(time (prob1 3 5 1e30))