Thanks, Sergio - this is a good way to construct the sieve.

It took me a little while to convince myself that it's the same, but it's 
definitely a good solution.

In general, I guess it's not possible to generate an infinite sequence that 
utilizes the tail-call optimization.... it makes sense as there is no 
"tail".

Have a good day,

Matty

On Wednesday, November 4, 2015 at 10:07:46 AM UTC-5, Sergio Rupena wrote:
>
> Hi
>
> You can try the following
>
> (defn dividers   [primes n]
>   (take-while #(<= (* % %) n) primes))
>
> (defn prime? [primes n]
>   (every? #(pos? (rem n %))
>           (dividers primes n)))
>
> (defn range-peek [coll]
>   (iterate inc (-> coll peek inc)))
>
> (defn sieve
>   ([] (cons 2 (lazy-seq (sieve [2]))))
>   ([primes]
>    (let [p (->> primes
>                 range-peek
>                 (filter (partial prime? primes))
>                 first)]
>      (cons p (lazy-seq (sieve (conj primes p)))))))
>
> (last (take 10000 (sieve)))
>
> This version keeps the visited primes in a vector so it will grow in 
> memory but won’t overflow otherwise.
>
> Sergio
>
> On 04 Nov 2015, at 15:44, Matthew Ulrich <matty...@gmail.com <javascript:>> 
> wrote:
>
> All - 
>
> I'm trying to generate a lazy sequence of primes using Erastosthenes Sieve 
> (from Abelson & Sussman) and am encountering some issues with lazy sequence.
>
> Here's what I have:
> ---
>
> (defn divisible?
>   [input numerator]
>   (= 0 (mod input numerator)))
>
> (defn sieve
>   [stream]
>   (lazy-seq
>     (cons
>       (first stream)
>       (sieve (filter #(not (divisible? % (first stream))) (rest 
> stream))))))
>
> (def primes (sieve (iterate inc 2)))
>
> ---
>
> This is fine now when I:
>
> => (take 5 (drop 1000 primes))
> (7927 7933 7937 7949 7951)
>
>
> But when I:
>
> => (take 5 (drop 4000 primes))
> StackOverflowError    clojure.lang.LazySeq.sval  (LazySeq.java:40)
>
>
> --
>
> I understand how the StackOverflow occurs with the filter on the 
> recursively generated sequence... however I can't think of a way to make 
> this work..
>
> I'm pretty new to clojure so I'm not very familiar with all of the 
> language features; is there some tool to help me realize this or should I 
> just go about the implementation in a different way?
>
> Thanks - have a great morning!
>
> Matty
>
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