Seniors do understand some English

Is there a sequence $a_1, \ldots, a_{2016}$ of positive integers, such that every sum
$$a_r + a_{r+1} + \ldots + a_{s-1} + a_s$$
(with $1 \leq r \leq s \leq 2016$) is a composite number, but

$GCD (a_i, a_{i+1}) = 1$ for all $i=1,2,\ldots, 2015$;
$GCD (a_i, a_{i+1})= 1$ for all $i=1,2,\ldots, 2015$ and $GCD (a_i, a_{i+2})= 1$ for all $i=1,2,\ldots, 2014$?

$GCD(x,y)$ denotes the greatest common divisor of $x,y$.