►zthomae’s SICP solutions
▼3 Chapter 3
3.1 Exercise 3.1
3.2 Exercise 3.2
3.3 Exercise 3.3
3.4 Exercise 3.4
3.5 Exercise 3.5
3.6 Exercise 3.6
3.7 Exercise 3.7
3.8 Exercise 3.8
3.9 Exercise 3.9
3.10 Exercise 3.10
3.11 Exercise 3.11
3.12 Exercise 3.12
3.13 Exercise 3.13
3.14 Exercise 3.14
3.15 Exercise 3.15
3.16 Exercise 3.16
3.17 Exercise 3.17
3.18 Exercise 3.18
3.19 Exercise 3.19
3.20 Exercise 3.20
3.21 Exercise 3.21
3.22 Exercise 3.22
3.23 Exercise 3.23
3.24 Exercise 3.24
3.25 Exercise 3.25
3.26 Exercise 3.26
3.27 Exercise 3.27
3.28 Exercise 3.28
3.29 Exercise 3.29
3.30 Exercise 3.30
3.31 Exercise 3.31
3.32 Exercise 3.32
3.33 Exercise 3.33
3.34 Exercise 3.34
3.35 Exercise 3.35
3.36 Exercise 3.36
3.37 Exercise 3.37
3.38 Exercise 3.38
3.39 Exercise 3.39
3.40 Exercise 3.40
3.41 Exercise 3.41
3.42 Exercise 3.42
3.43 Exercise 3.43
3.44 Exercise 3.44
3.45 Exercise 3.45
3.46 Exercise 3.46
3.47 Exercise 3.47
3.48 Exercise 3.48
3.49 Exercise 3.49
3.50 Exercise 3.50
3.51 Exercise 3.51
3.52 Exercise 3.52
3.53 Exercise 3.53
3.54 Exercise 3.54
3.55 Exercise 3.55
3.56 Exercise 3.56
3.57 Exercise 3.57
3.58 Exercise 3.58
3.59 Exercise 3.59
3.60 Exercise 3.60
3.61 Exercise 3.61
3.62 Exercise 3.62
3.63 Exercise 3.63
3.64 Exercise 3.64
3.65 Exercise 3.65
3.66 Exercise 3.66
3.67 Exercise 3.67
3.68 Exercise 3.68
3.69 Exercise 3.69
3.70 Exercise 3.70
3.71 Exercise 3.71
3.72 Exercise 3.72
3.73 Exercise 3.73
3.74 Exercise 3.74
3.75 Exercise 3.75
3.76 Exercise 3.76
3.77 Exercise 3.77
3.78 Exercise 3.78
3.79 Exercise 3.79
3.80 Exercise 3.80
3.81 Exercise 3.81
3.82 Exercise 3.82
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3.71 Exercise 3.71

In order to find integers that can be written as the sum of two cubes in two different ways as generally as possible, we can write a find-consecutive procedure that takes a stream and returns a stream of the values in the stream that appear consecutively. (In this case, I will take consecutively to mean two or more times in a row).

(define (weight-cubed p)
  (let ((cube (lambda (x) (* x x x))))
    (+ (cube (car p)) (cube (cadr p)))))
(define (drop-while f s)
  (cond ((stream-null? s) the-empty-stream)
        ((f (stream-car s)) (drop-while f (stream-cdr s)))
        (else s)))
(define (find-consecutive s)
  (if (stream-null? s)
      the-empty-stream
      (let ((first (stream-car s))
            (rest (stream-cdr s)))
        (if (stream-null? rest)
            the-empty-stream
            (let ((second (stream-car rest)))
              (if (= first second)
                  (cons-stream first
                               (find-consecutive (drop-while (lambda (x) (= x first))
                                                             (stream-cdr rest))))
                  (find-consecutive rest)))))))
(define ramanujan-pairs
  (find-consecutive (stream-map weight-cubed
                                (weighted-pairs weight-cubed integers integers))))

We can then see the one number provided and the five after it:

> (display-stream (take-stream ramanujan-pairs 6))

1729

4104

13832

20683

32832

39312

'done

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