math_6.clj

(ns math-6.core
  (:require [clojure.math.numeric-tower :refer [abs]]))

(def boundaries (range -100 100))

(defn- get-cs-after-second
  [c-before-before c-before]
  (when-let [c (mod c-before-before c-before)]
    (if (zero? c)
      [0]
      (lazy-seq (cons c (get-cs-after-second c-before c))))))

(defn get-cs
  [A B]
  (concat [A B] (get-cs-after-second A B)))

(defn- get-k
  [cs i c]
  (if (< i 3)
    1
    (/ (- (nth cs (- i 2)) c)
       (nth cs (dec i)))))

(defn get-ks
  [cs]
  (map-indexed #(get-k cs %1 %2) cs))

(defn- find-a-b
  [A B c]
  (->> (for [a boundaries
             b boundaries
             :when (= c (+ (* a A) (* b B)))]
         [a b])
       (sort-by #(abs (first %)))
       first))

(defn get-a-bs
  [cs]
  (map-indexed #(cond
                  (zero? %1) [1 0]
                  (= 1 %1) [0 1]
                  :else (find-a-b (first cs) (second cs) %2))
               cs))

(defn get-table
  [A B]
  (let [cs (get-cs A B)
        ks (get-ks cs)
        a-bs (get-a-bs cs)]
    (map #(apply vector %1 %2 %3) cs ks a-bs)))


(defn get-expected-table
  []
  (->> (for [A (range 2 100)
             B (range 1 A)]
         (get-table A B))
       (filter #(= (count %) 7))
       first))

(defn print-table!
  [table]
  (println "c\tk_i\ta_i\tb_i\t")
  (doseq [[c k a b] table]
    (println c "\t" k "\t" a "\t" b)))

(print-table! (get-expected-table))