The Collatz conjecture is fairly well known (one example). Given a positive integer *n*, as long as *n* is greater than 1 repeatedly replace *n* by 3*n* + 1 if n is odd or by *n*/2 otherwise. The sequence of integers created is called the **cycle** for *n*.

Whether all cycles where *n* is a positive integer eventually terminate at 1 is currently unproven and among the most well-known open problems in mathematics. Paul ErdÅ‘s offered a reward of $500 for its solution.

Given two positive integers *i* and *j*, the **max-cycle** for *i* and *j* is the largest cycle for all integers between *i* and *j* inclusive at both ends. Write a program that reads pairs of integers and finds the max-cycle for each pair read.

(use-modules (ice-9 format)) (define (main port) (define (int-reader f) (let ((i (read port))) (if (integer? i) (f i)))) (let loop () (int-reader (lambda (i) (int-reader (lambda (j) (format #t "~d ~d ~d" i j (max-cycle i j)) (newline) (loop))))))) (define (max-cycle i j) (define (max-cycle' i j max-cyc) (if (> i j) max-cyc (max-cycle' (+ i 1) j (max max-cyc (cycle i))))) (max-cycle' (min i j) (max i j) 0)) (define (cycle i) (define (cycle' i len) (if (= i 1) len (cycle' (if (odd i) (+ (* 3 i) 1) (/ i 2)) (+ len 1)))) (if (> i 0) (cycle' i 1) 0)) (define (odd n) (= 1 (remainder n 2))) guile> (define inp (open-file "t" "r")) guile> (main inp) 1 10 20 100 200 125 201 210 89 900 1000 174 guile>