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; project euler problem 1

(define (one n)
  (let ((sieve (make-vector n 0)))
    (do ((i 3 (+ i 3))) ((<= n i))
      (vector-set! sieve i i))
    (do ((i 5 (+ i 5))) ((<= n i))
      (vector-set! sieve i i))
    (let loop ((i 0) (sum 0))
      (if (= i n) sum
        (loop (+ i 1) (+ sum (vector-ref sieve i)))))))

(display (one 1000)) (newline)

(define (two-iter n)
  (let loop ((i 1) (sum 0))
    (cond ((= i n) sum)
          ((or (zero? (modulo i 3))
               (zero? (modulo i 5)))
            (loop (+ i 1) (+ sum i)))
          (else (loop (+ i 1) sum)))))

(display (two-iter 1000)) (newline)

(define (two-recur n)
  (cond ((zero? n) 0)
        ((or (zero? (modulo n 3))
             (zero? (modulo n 5)))
          (+ n (two-recur (- n 1))))
        (else (two-recur (- n 1)))))

(display (two-recur 999)) (newline)

(define (three n)
  (define (gauss n) (* n (+ n 1) 1/2))
  (+ (* 3 (gauss (quotient n 3)))
     (* 5 (gauss (quotient n 5)))
     (- (* 15 (gauss (quotient n 15))))))

(display (three 999)) (newline)

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