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_______