I tried implementing the sieve of Eratosthenes in Clojure. The approach is 
to loop while (A) keeping my current list of numbers which have not yet 
been eliminated, and (B) keeping track of the number I'm "on" (checking for 
multiples thereof).

Here's what I came up with (in a foo.clj file):

~~~clojure
(declare remove-multiples-of)
(declare next-one-after)

(defn main
  [max-num]
  (let [starting-nums (range 2 max-num)]
    (loop [new-nums (remove-multiples-of 2 starting-nums)
           new-num  (next-one-after 2 new-nums)]
      (if (or (nil? new-num)
              (> new-num (* 0.5 max-num)))
        new-nums
        (recur (remove-multiples-of new-num new-nums)
               (next-one-after new-num new-nums))))))

(defn remove-multiples-of
  "Removes all multiples of n (but not $n * 1$) from xs."
  [n xs]
  (remove (fn [x] (and (> x n)
                       (zero? (rem x n))))
          xs))

(defn next-one-after
  "It's assumed that xs is an ordered sequential collection of positive
integers, and that n is among xs. Returns the element right after n, unless
n is the last element --- if that's the case, just returns nil."
  [n xs]
  (second (drop-while (fn [x]
                        (not= x n))
                      xs)))

;;---------------------------
(println (last (main 5000)))
~~~

Running that (via `lein exec foo.clj`), it appears to work.

However, if I change that 5000 to 50000, I get a long disapproving-looking 
stack trace starting with java.lang.StackOverflowError. Why is it 
overflowing?

Thanks!

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