Question 183
be $N_{0}$ y $Z$ The set of all nonnegative integers and the set of all integers, respectively. be $f: N_{0} \rightarrow Z$ the function that to each element $n$ of $N_{0}$ associates it as an image the integer $f(n)$ defined by
$$
f(n) = -f\left(\left\lfloor\frac{n}{3}\right\rfloor\right) - 3\left\{\frac{n}{3}\right\}
$$
where $\lfloor x\rfloor$ is the integer part of the real number $x$ y $\{x\} = x - \lfloor x\rfloor$ your decimal part. Determine the smallest integer $n$ such that $f(n) = 2010$.
$$
f(n) = -f\left(\left\lfloor\frac{n}{3}\right\rfloor\right) - 3\left\{\frac{n}{3}\right\}
$$
where $\lfloor x\rfloor$ is the integer part of the real number $x$ y $\{x\} = x - \lfloor x\rfloor$ your decimal part. Determine the smallest integer $n$ such that $f(n) = 2010$.