Let $a_1, a_2, a_3, \ldots$. be a sequence of positive integers in arithmetic progression with common difference 2 . Also, let $b_1, b_2, b_3, \ldots$. 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 $$ 2\left(\mathrm{a}_1+\mathrm{a}_2+\ldots .+\mathrm{a}_{\mathrm{n}}\right)=\mathrm{b}_1+\mathrm{b}_2+\ldots . .+\mathrm{b}_{\mathrm{n}} $$ holds for some positive integer n , is $\_\_\_\_$