User blog comment:Primussupremus/f3(n) up to f3(8)/@comment-1605058-20170313152328

There are at least two mistakes. First, you have forgotten one application of \(f_2(2)\) when computing \(f_3(3)\); that number is \(f_2(402653184)=402653184\cdot 2^{402653184}\).

Second, you are miscalculating \(f_2(n)\) for large numbers \(n\) = from what I see, once you write \(n=a\cdot 10^b\) you compute \(f_2(n)=2^a\cdot a\cdot 10^{2b}\), but this is completely wrong. For \(n=2\cdot 10^1\), compare \(2^2\cdot 2\cdot 10^2=800\) and \(2^n\cdot n=20971520\).