User blog comment:Primussupremus/f2(n)/@comment-24920136-20170307184054/@comment-28606698-20170307204058

$$f_2(4)=4*2^{4}=4*16=64$$

$$f_2^2(4)=f_2(f_2(4))=64*2^{64}=1.180591620717 \times 10^{21}$$

$$f_2^3(4)=f_2(f_2^2(4))=(64*2^{64})*2^{64*2^{64}}=10^{3.553934904655\times 10^{20}}$$

$$f_3(4)=f_2^4(4)=f_2(f_2^3(4))=$$

$$=((64*2^{64})*2^{64*2^{64}})*2^{(64*2^{64})*2^{64*2^{64}}}=$$

$$=10^{10^{3.553934904655\times 10^{20}}}$$