#Displays terms in Farey_sequence of order n
farey_sequence := proc(n)
  local a,b,c,d,k;
  a,b,c,d := 0,1,1,n;
  printf("%d/%d", a,b);
  while c <= n do
    k := iquo(n+b,d);
    a,b,c,d := c,d,c*k-a,d*k-b;
    printf(", %d/%d", a,b)
  end do;
  printf("\n");
end proc:

#Returns the length of a Farey sequence
farey_len := proc(n)
  return 1 + add(NumberTheory:-Totient(k), k=1..n);
end proc;

for i to 11 do
  farey_sequence(i);
end do;
printf("\n");
for j from 100 to 1000 by 100 do
  printf("%d\n", farey_len(j));
end do;