MathDB

Let

\mathbb{N}_0

and

\mathbb{Z}

be the set of all non-negative integers and the set of all integers, respectively. Let

f:\mathbb{N}_0\rightarrow\mathbb{Z}

be a function defined as

f(n)=-f\left(\left\lfloor\frac{n}{3}\right\rfloor \right)-3\left\{\frac{n}{3}\right\}

where

\lfloor x \rfloor

is the greatest integer smaller than or equal to

x

and

\{ x\}=x-\lfloor x \rfloor

. Find the smallest integer

n

such that

f(n)=2010

Problem Statement