(50g) Fun with Farey sequences

[Didier Lachieze]

Thanks for the links. Great video !

I've adapted the Python program for the Prime:

Code:

#pragma mode( separator(.,;) integer(h32) )
EXPORT farey(n)
BEGIN
     LOCAL a:=0,b:=1,c:=1,d:=n,k,l;
     l:={ a/b };
     WHILE c < n DO
         k:=IP((n+b)/d);
         c:=−a+k*(a:=c); d:=-b+k*(b:=d);
         l:=CONCAT(l,a/b);
     END;  
     exact(l);
END;

The result is a list of reals, you need to press the "a b/c" key to display it as fractions. I don't know how to do it programmatically.
EDIT: edited to add exact() to the result as suggested by Joe below.