Snippets for Project Euler 1-3 in Clojure

euler-1.clj

(defn prog-sum 
  "Calculates the sum of an arithmetic progression"
  ([n a] (prog-sum n a a)) 
  ([n a d] (/ (* n (+ (* 2 a) (* (dec n) d))) 2)))

(defn euler-1 [n f1 f2]
  (let [
    b (dec n)
    d1 (quot b f1)
    d2 (quot b f2)
    f3 (* f1 f2)
    d3 (quot b f3)]

    (- (+ (prog-sum d1 f1) (prog-sum d2 f2)) (prog-sum d3 f3))))

euler-2.clj

(defn fib-seq []
  ((fn rfib [a b] (cons a (lazy-seq (rfib b (+ a b))))) 0 1))

(defn euler-2 []
  (reduce + (filter even? (take-while #(< % 4000000) (fib-seq)))))

euler-3.clj

(defn prime? [x]
  (cond 
    (< x 2) false
    (= x 2) true 
    :else (not (some zero? 
      (map #(rem x %) (range 2 (inc (int (Math/sqrt x)))))))))


(defn euler-3 [n]
  (let [sqrt (int (Math/sqrt n))]
    (first (filter #(and (zero? (rem n %)) (prime? %)) (range sqrt 0 -1)))))

prime-factors.clj

(defn prime-factors [n]
  (loop [factors [] n n div 2]
    (cond
      (= n 1) factors
      (zero? (rem n div)) (recur (conj factors div) (/ n div) div)
      (> (* div div) n) (conj factors n)
      :else (recur factors n (inc div)))))

prime.clj

(defn prime? [x]
  (cond 
    (< x 2) false
    (= x 2) true 
    :else (not (some zero? 
      (map #(rem x %) (range 2 (inc (int (Math/sqrt x)))))))))

prog-sum.clj

(defn prog-sum 
  "Calculates the sum of an arithmetic progression"
  ([n a] (prog-sum n a a)) 
  ([n a d] (/ (* n (+ (* 2 a) (* (dec n) d))) 2)))