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#lang racket
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(define (van-der-Corput n base)
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(if (zero? n)
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0
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(let-values ([(q r) (quotient/remainder n base)])
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(/ (+ r (van-der-Corput q base))
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base))))
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#lang racket
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(define (digit-length n base)
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(if (< n base) 1 (add1 (digit-length (quotient n base) base))))
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(define (digit n i base)
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(remainder (quotient n (expt base i)) base))
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(define (van-der-Corput n base)
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(for/sum ([i (digit-length n base)]) (/ (digit n i base) (expt base (+ i 1)))))
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(for ([base (in-range 2 (add1 5))])
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(printf "Base ~a: " base)
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(for ([n (in-range 0 10)])
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(printf "~a " (van-der-Corput n base)))
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(newline))
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#| Base 2: 0 1/2 1/4 3/4 1/8 5/8 3/8 7/8 1/16 9/16
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Base 3: 0 1/3 2/3 1/9 4/9 7/9 2/9 5/9 8/9 1/27
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Base 4: 0 1/4 1/2 3/4 1/16 5/16 9/16 13/16 1/8 3/8
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Base 5: 0 1/5 2/5 3/5 4/5 1/25 6/25 11/25 16/25 21/25 |#
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