(defun ! (n) (reduce #'* (loop for i from 1 to n collect i)))

(defun C () (* 426880 (rationalize (sqrt 10005))))
(defun M (k) (/ (! (* 6 k)) (! (* 3 k)) (expt (! k) 3)))
(defun L (k) (+ (* 545140134 k) 13591409))
(defun X (k) (expt  -262537412640768000 k))

(defun pi-fraction (k)
  (* (C) (/ 1 (loop for i from 0 to k sum
                   (/ (* (M i) (L i)) (X i))))))

(defun power-of-2 (n)
  (loop for i from 1
     when (/= (denominator (/ n (expt 2 i))) 1)
     return (1- i)))
(defun power-of-5 (n)
  (loop for i from 1
     when (/= (denominator (/ n (expt 5 i))) 1)
     return (1- i)))

(defun fract2digits (fract)
  (let ((p2 (power-of-2 (denominator fract)))
        (p5 (power-of-5 (denominator fract))))
    (round (*
            fract
            (expt 10 (+
                      (max p2 p5)
                      (loop for i from 1 when
                           (zerop (mod
                                   (1- (expt 10 i))
                                   (/ (denominator fract) (expt 2 p2) (expt 5 p5))))
                           return i)))))))
  

(defun 3- (n) (1- (1- (1- n))))
(format t "~a~%" (fract2digits (3- (pi-fraction 10))))