[racket] making Racket code more idiomatic

Hi,

To continue our conversation about creating idiomatic Racket code, here is
some code I wrote last night to solve projecteuler.net problem #29:

(define (euler29a)
  ; calculate 99^2 - duplicates
  (- (sqr 99)
     (for/sum ([d '(2 3 5 6 7 10)])
              (let ([lst '()])
                (let loop ([exp 1])
                  (if (> (expt d exp) 100) (- (length lst) (length
(remove-duplicates lst)))
                      (begin
                        (for ([i (in-range 2 101)]) (set! lst (cons (* i
exp) lst)))
                        (loop (add1 exp)))))))))

It's fast (it avoids calculating a bunch of huge numbers), it gives the
correct answer, so what's not to love?!

Well, it starts off OK, but my eye stumbles over the following:

1) predeclaring lst and accessing it twice, related to each other
2) ugly single parameter named-let loop
3) ugly "begin" - not a big deal, but I just dislike when having to use
begin
4) use of set!

Here is a quick rewrite:

(define (euler29b)
  ; calculate 99^2 - duplicates
  (- (sqr 99)
     (for/sum ([d '(2 3 5 6 7 10)])
              (let ([lst '()])
                (do ([exp 1 (add1 exp)])
                  ((> (expt d exp) 100) (- (length lst) (length
(remove-duplicates lst))))
                  (for ([i (in-range 2 101)]) (set! lst (cons (* i exp)
lst))))))))

It solves #2 and #3 above, but it is still fundamentally clunky.

Can someone help and teach us all some tricks?  My instincts say it should
be possible to use append-map, for/list and/or foldl to build a list of the
duplicates then simply count them in the for/sum loop, but am still unable
to do it.

Thanks,
-Joe
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