jneira-4clojure-solution67.clj

;; jneira's solution to http://4clojure.com/problem/67

(fn primes [n]
  (letfn
      [(next-prime
	[prs nxt]
	(if (empty? (filter #(= 0 (mod nxt %)) prs))
	  (conj prs nxt)
	  (recur prs (inc nxt))))]
    (->> (iterate
	  (fn [prs] (next-prime prs (inc (last prs)))) [2])
	 (take n)
	 (last))))

(fn primes2 [n]
  (last
   (take
    n
    (map first
	 ((fn iter-when [pred f x]
	    (let [iter #(iter-when pred f %)
		  n-cons (f x)]
	      (if (pred n-cons x)
		(cons x (lazy-seq (iter n-cons)))
		(iter n-cons))))
	  #(not= (first %1) (first %2))
	  (fn [[prs nxt :as c]]
	    (let [n-prs (if (empty? (filter #(zero? (mod nxt %)) prs))
			  (conj prs nxt) prs)]
	     [n-prs (inc nxt)]))
	  [[2] 3])))))

(defn primes3 [n]
  (let
      [next-prime
       (fn [prs]
	 (letfn
	     [(aux [[f & r :as c] nxt]
		   (cond
		    (empty? c) (conj prs nxt)
		    (zero? (mod nxt f)) (recur prs (inc nxt))
		    :else (recur (take-while #(< % (quot nxt f)) r)
				 nxt)))]
	   (aux prs (inc (last prs)))))]
    (->> (iterate next-prime [2])
	 (take n)
	 (last))))