You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
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Let \( k \) be a positive integer. Bernardo and Silvia take turns writing and erasing numbers on a blackboard as follows: Bernardo starts by writing the smallest perfect cube with \( k+1 \) digits. Every time Bernardo writes a number, Silvia erases the last \( 2k \) digits of it. Bernardo then writes the next perfect cube, Silvia erases the last \( 2k \) digits of it, and this process continues until the last two numbers that remain on the board differ by at least 2. Define \( f(k) \) as the smallest positive integer not written on the board. Determine \( f(3) \).
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Let \( k \) be a positive integer. Bernardo and Silvia take turns writing and erasing numbers on a blackboard as follows: Bernardo starts by writing the smallest perfect cube with \( k+1 \) digits. Every time Bernardo writes a number, Silvia erases the last \( 2k \) digits of it. Bernardo then writes the next perfect cube, Silvia erases the last \( 2k \) digits of it, and this process continues until the last two numbers that remain on the board differ by at least 2. Define \( f(k) \) as the smallest positive integer not written on the board. Determine \( f(3) \).
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