Data update

Task/Farey-sequence/MATLAB/farey-sequence.m

@@ -0,0 +1,32 @@
+clear all;close all;clc;
+
+% Print Farey sequences for 1 to 11
+    for i = 1:11
+        farey_sequence = farey(i);
+        fprintf('%2d: %s\n', i, strjoin(farey_sequence, ' '));
+    end
+    fprintf('\n');
+
+    % Print the number of fractions in Farey sequences for 100 to 1000 step 100
+    for i = 100:100:1000
+        farey_sequence = farey(i);
+        fprintf('%4d: %6d fractions\n', i, length(farey_sequence));
+    end
+
+function farey_sequence = farey(n)
+    a = 0;
+    b = 1;
+    c = 1;
+    d = n;
+    farey_sequence = {[num2str(a) '/' num2str(b)]}; % Initialize the sequence with "0/1"
+    while c <= n
+        k = fix((n + b) / d);
+        aa = a;
+        bb = b;
+        a = c;
+        b = d;
+        c = k * c - aa;
+        d = k * d - bb;
+        farey_sequence{end+1} = [num2str(a) '/' num2str(b)]; % Append the fraction to the sequence
+    end
+end