MathDB
2021 Team P5

Source:

March 2, 2021
number theory

Problem Statement

Let NN be the fifth largest number that can be created by combining 20212021 11's using addition, multiplication, and exponentiation, in any order (parentheses are allowed). If f(x)=log⁡2(x)f(x)=\log_2(x), and kk is the least positive integer such that fk(N)f^k(N) is not a power of 22, what is the value of fk(N)f^k(N)?
(Note: fk(N)=f(f(⋯(f(N))))f^k(N)=f(f(\cdots(f(N)))), where ff is applied kk times.)
Proposed by Adam Bertelli
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