Initial data commit

Task/Stern-Brocot-sequence/Scheme/stern-brocot-sequence-1.ss

@@ -0,0 +1,14 @@
+; Recursive function to return the Nth Stern-Brocot sequence number.
+
+(define stern-brocot
+  (lambda (n)
+    (cond
+      ((<= n 0)
+        0)
+      ((<= n 2)
+        1)
+      ((even? n)
+        (stern-brocot (/ n 2)))
+      (else
+        (let ((earlier (/ (1+ n) 2)))
+          (+ (stern-brocot earlier) (stern-brocot (1- earlier))))))))

Task/Stern-Brocot-sequence/Scheme/stern-brocot-sequence-2.ss

@@ -0,0 +1,48 @@
+; Show the first 15 Stern-Brocot sequence numbers.
+
+(printf "First 15 Stern-Brocot numbers:")
+(do ((index 1 (1+ index)))
+    ((> index 15))
+  (printf " ~a" (stern-brocot index)))
+(newline)
+
+; Show the indices of where the numbers 1 to 10 first appear in the Stern-Brocot sequence.
+
+(let ((indices (make-vector 11 #f))
+       (found 0))
+  (do ((index 1 (1+ index)))
+      ((>= found 10))
+    (let ((number (stern-brocot index)))
+      (when (and (<= number 10) (not (vector-ref indices number)))
+        (vector-set! indices number index)
+        (set! found (1+ found)))))
+  (printf "Indices of where the numbers 1 to 10 first appear:")
+  (do ((index 1 (1+ index)))
+      ((> index 10))
+  (printf " ~a" (vector-ref indices index))))
+(newline)
+
+; Show the index of where the number 100 first appears in the Stern-Brocot sequence.
+
+(do ((index 1 (1+ index)) (found #f))
+    (found)
+  (let ((number (stern-brocot index)))
+    (when (= number 100)
+      (printf "Index where the number 100 first appears: ~a~%" index)
+      (set! found #t))))
+
+; Check that the GCD of all two consecutive members up to the 1000th member is always one.
+
+(let ((any-bad #f)
+      (gcd (lambda (a b)
+             (if (= b 0)
+               a
+               (gcd b (remainder a b))))))
+  (do ((index 1 (1+ index)))
+      ((> index 1000))
+    (let ((sbgcd (gcd (stern-brocot index) (stern-brocot (1+ index)))))
+      (when (not (= 1 sbgcd))
+        (printf "GCD of Stern-Brocot ~a and ~a+1 is ~a -- Not 1~%" index index sbgcd)
+        (set! any-bad #t))))
+  (when (not any-bad)
+    (printf "GCDs of all Stern-Brocot consecutive pairs from 1 to 1000 are 1~%")))