Školjka

%V0 Let $n$ be an integer greater than 2. A positive integer is said to be attainable if it is 1 or can be obtained from 1 by a sequence of operations with the following properties: 1.) The first operation is either addition or multiplication. 2.) Thereafter, additions and multiplications are used alternately. 3.) In each addition, one can choose independently whether to add 2 or $n$ 4.) In each multiplication, one can choose independently whether to multiply by 2 or by $n$. A positive integer which cannot be so obtained is said to be unattainable. a.) Prove that if $n\geq 9$, there are infinitely many unattainable positive integers. b.) Prove that if $n=3$, all positive integers except 7 are attainable.