Let $a_1,a_2,a_3,\mathrm{.............}$ be a sequence of positive integers in arithmetic progression with common difference 2. Also, let $b_1,b_2,b_3\mathrm{.........}$ 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 $2(a_1+a_2+\mathrm{......}+a_n)=b_1+b_2+\mathrm{........}+b_n$ holds for some positive integer n, is ___________