Get ready Part 17

The infinite sequence of 2’s and 3’s $2,3,3,2,3,3,3,2,3,3,3,2,3,3,2,3,3,3,2,3,3,3,2,3,3,3,2,3,3,2,3,3,3,2,\dots$ has the property that,if one forms a second sequence that records the number of 3’s between successive 2’s,the result is identical to the given sequence.Is there exists a real number $r$ such that,for any $n$ ,the $n^{th}$ term of the sequence is 2 if and only if $n = 1 +\lfloor rm \rfloor$ for some nonnegative integer $m$ .

Note

• $\lfloor x \rfloor$ denotes the floor function