Let `a_1, a_2,a_3,…` be a sequence of positive integers in arithmetic progression with common difference 2. Also, let `b_1,b_2,b_3,…` be a sequence of positive integers in geometric progression with common ratio 2. If `a_1=b_1=c`, then the number of all possible values of `c`, for which the equality `2(a_1+ a_2+⋯+a_n)=b_1+ b_2+⋯+b_n` holds for some positive integer `n`, is _____

Answer

1