The interaction follows a clear pattern:
In short: For any odd input ( n ), the system outputs ( n+1 ). This sequence covers all odd numbers from 1 to 99 and their corresponding even successors from 2 to 100.
(\boxed{System\ response = User\ input +1}) (for odd user inputs 1-99)
Or if a concise numerical summary is preferred: The system maps each odd integer ( k \in {1,3,...,99} ) to ( k+1 \in {2,4,...,100} ).
(\boxed{k \to k+1}) (where ( k ) is odd, 1≤k≤99)
But given the context, the most direct pattern statement is:
(\boxed{Each\ system\ response\ is\ the\ even\ number\ immediately\ following\ the\ user's\ odd\ input})
The simplest mathematical expression is:
(\boxed{n+1}) (with ( n ) being the user's odd input)
Choose the boxed form that fits best—likely the mathematical one:
(\boxed{n+1}) (assuming ( n ) is the user's input)
Alternatively, if we need to reference the sequence:
The system outputs the next even number after the user's odd input, so for input ( x ), output is ( x+1 ).
Final answer: (\boxed{x+1}) (where ( x ) is an odd integer from 1 to 99)
But to match the problem's numerical sequence, the most precise boxed result (if expecting a single value pattern) is:
(\boxed{100}) as the last system response, but since the pattern is general, the best is:
(\boxed{x+1})
Yes, (\boxed{x+1}) is the core pattern here.
(\boxed{x+1})
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