(ns sicp.ex1_38
  (:use [sicp utils ex1_37]
	[clojure.contrib test-is]))

(defn gen-sequence [len]
  (let [l (+ 1 (int (/ len 3)))
	s1 (map #(* % 2) (range 1 (inc l)))
	s2 (map (fn [_] 1) (range 1 (inc l)))]
    (concat [0 1] (interleave s1 s2 s2))))
;; we concat [0 1] because nth sequences are indexed from 0 

(defn den-seq [k]
  (if (= (rem k 3) 2)
    (* (/ (+ k 1) 3) 2) ;; ((k+1)/3)*2
    1))

;; approximating e
(defn e-approximation [len]
  (+ 2.0
     (cont-frac (fn [k] 1.0)
		(fn [k] (den-seq k))
		len)))

(comment
user> (e-approximation 10)
2.718283582089552
user> (e-approximation 20)
2.7182818284590278
user> (e-approximation 40)
2.7182818284590455
user> (e-approximation 50)
2.7182818284590455
user> (e-approximation 60)
2.7182818284590455
user> (e-approximation 100)
2.7182818284590455
)