Question 3
A sequence of real numbers $a_0,a_1,\ldots$ is good if:
(i) $a_0$ is a positive integer;
(ii) for every nonnegative integer $i$, either $a_{i+1}=2a_i+1$ or $a_{i+1}=a_i/(a_i+2)$;
(iii) $a_k=2014$ for some positive integer $k$.
Find the smallest positive integer $n$ for which a good sequence can have $a_n=2014$.
Proposed by Wang Wei Hua, Hong Kong.
(i) $a_0$ is a positive integer;
(ii) for every nonnegative integer $i$, either $a_{i+1}=2a_i+1$ or $a_{i+1}=a_i/(a_i+2)$;
(iii) $a_k=2014$ for some positive integer $k$.
Find the smallest positive integer $n$ for which a good sequence can have $a_n=2014$.
Proposed by Wang Wei Hua, Hong Kong.