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Transcribes FGH f_3(n) to TeX
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| def oh_great(n) | |
| if n == 1 | |
| "2^n n" | |
| else | |
| prev = oh_great(n - 1) | |
| "2^{#{prev}} {#{prev}}" | |
| end | |
| end | |
| def output(n) | |
| puts "f_2^{#{n}}(n) = #{oh_great(n)}" | |
| end | |
| (1..16).each do |n| | |
| output(n) | |
| puts | |
| puts | |
| end |
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| f_2^{1}(n) = 2^n n | |
| f_2^{2}(n) = 2^{2^n n} {2^n n} | |
| f_2^{3}(n) = 2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}} | |
| f_2^{4}(n) = 2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} | |
| f_2^{5}(n) = 2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} | |
| f_2^{6}(n) = 2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} | |
| f_2^{7}(n) = 2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} | |
| f_2^{8}(n) = 2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} | |
| f_2^{9}(n) = 2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} | |
| f_2^{10}(n) = 2^{2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}}} | |
| f_2^{11}(n) = 2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n 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{2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n 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n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n 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{2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} 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| f_2^{12}(n) = 2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n 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| f_2^{13}(n) = 2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n 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{2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} 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{2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n 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| f_2^{14}(n) = 2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n 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{2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n 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{2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} 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{2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}}}}}}} | |
| f_2^{15}(n) = 2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n 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{2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} 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{2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n 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{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n 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{2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n 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| f_2^{16}(n) = 2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}} {2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}}}} {2^{2^{2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}} {2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}} {2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}} {2^{2^{2^n n} {2^n n}} {2^{2^n n} {2^n n}}}}}} {2^{2^{2^{2^{2^{2^n n} {2^n n}} {2^{2^n n} 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