User blog comment:Flavio61/Louis Epstein number list/@comment-27173506-20160118190252/@comment-27173506-20160119055532

The reason is that you are repeatedly iterating the first stage. What you should do is iterate those iterations. As I posted above, if n x+1u y was equal to  n x+1u  n x+1u  n x+1u n... n x+1u n, then it would reach f_w(n). Why is that?

n u n~f_4(n)

n uu n=n u n u n u n...n u n~f_4n(n)=f_5(n)

n uuu n=n uu n uu n uu n...n uu n~f_5n(n)=f_6(n)

And so forth. Instead of repeatedly iterating on f_4(n), I'm iterating on the iterations of the iterations of the...of f_4(n).