Question 5
Determine all sequences $a_0,a_1,a_2,\ldots$ of positive integers with $a_0\ge2015$ such that for every integer $n\ge1$:
(i) $a_n$ divides $a_{n+2}$;
(ii) $|s_{n+1}-(n+1)a_n|=1$, where
$$s_{n+1}=a_{n+1}-a_n+a_{n-1}-\cdots+(-1)^{n+1}a_0.$$
Proposed by Pakawut Jiradilok and Warut Suksompong, Thailand.
(i) $a_n$ divides $a_{n+2}$;
(ii) $|s_{n+1}-(n+1)a_n|=1$, where
$$s_{n+1}=a_{n+1}-a_n+a_{n-1}-\cdots+(-1)^{n+1}a_0.$$
Proposed by Pakawut Jiradilok and Warut Suksompong, Thailand.