Fun with Functions

Algebra Level 4

Let \(f(n)\) be a function on all rational \(n\) such that \(f(n)=2n-1\). If \(f^{2013}(n)\) is expressed in the form \(an+b\), where \(a\) and \(b\) are integer values, what is the value of \(a+b\)?

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