(defun longest_collatz(n)
  (reverse
   (maxlist
    (loop for x from 1 to n
       collect (list x (length (collatz x)))))))

(defun collatz (n)
  (if (<= n 1)
      '(1)
      (if (= (mod n 2) 0)
          (cons (/ n 2) (collatz (/ n 2)))
          (cons (+ (* n 3) 1) (collatz (+ (* n 3) 1))))))

(defun maxlist (z)
  (if (> (length z) 1)
      (if (< (cadr (elt z 0)) (cadr (elt z 1)))
          (maxlist (cdr z))
          (maxlist (cons (elt z 0) (cddr z))))
      (car z)))

(defun collatz (n &optional acc)
  (unless (plusp n)
    (error "~s(~s): positive argument is required" 'collatz n))
  (if (= n 1)
      (nreverse (cons 1 acc))
      (let ((next (if (evenp n)
                      (ash n -1) ; same as (mod n 2)
                      (1+ (* n 3)))))
        (collatz next (cons next acc)))))

(defun collatz_length2 (n cnt)
  (if (<= n 1)
    cnt
    (if (= (mod n 2) 0)
      (collatz_length2 (/ n 2) (1+ cnt))
      (collatz_length2 (+ (* n 3) 1) (1+ cnt)))))

(defun collatz_length (n) (collatz_length2 n 1))