One easy algorithm to implement as a recursive function is factorial.

```
;;Compute the factorial for any n >= 0. Precondition: n >= 0, n is an integer.
(defun factorial (n)
(cond
((= n 0) 1) ;; Special case, 0! = 1
((= n 1) 1) ;; Base case, 1! = 1
(t
;; Recursive case
;; Multiply n by the factorial of n - 1.
(* n (factorial (- n 1)))
)
)
)
```