enumerate-rationals.lisp

(defun n->r (n)
  (let* ((band      (isqrt n))
         (bandstart (expt band 2))
         (nextstart (expt (1+ band) 2)))
    (list (min band (- n bandstart))
          (min band (- nextstart n 1)))))

(defun init-rar (size)
  (let ((ar (make-array (list size size))))
    (dotimes (n (expt size 2))
      (destructuring-bind (x y) (n->r n)
        (setf (aref ar y x) n)))
    ar))

(let ((ar (init-rar 5)))
  (print ar))
;; => #2A(( 0  3  8 15 24)
;;        ( 1  2  7 14 23)
;;        ( 4  5  6 13 22)
;;        ( 9 10 11 12 21)
;;        (16 17 18 19 20))