$\text{⨍ }$ is a function defined as $\sum _{\mathrm{k}=1}^{\mathrm{n}}{\text{⨍ (a+k)=16(2}}^{\mathrm{n}}\text{-1)}$ and $\text{⨍ (x+y)=⨍ (x).⨍ (y)}$ and $\text{⨍ (1)=2}$ the integral value of a

$\text{⨍ (x+y)=⨍ (x).⨍ (y)}$ and $\text{⨍ (1)=2}$

${\text{⇒⨍ (x)=2}}^{\mathrm{x}}$

$$\begin{gathered} \sum _{\mathrm{k}=1}^{\mathrm{n}}{\text{⨍ (a+k)=16(2}}^{\mathrm{n}}\text{-1)} \\ {2}^a\sum _{\mathrm{k}=1}^{\mathrm{n}}{2}^k={\mathrm{16(2}}^{\mathrm{n}}\text{-1)} \\ {2}^a\left(2+2^2+2^3+.....+2^n\right)=16{(2}^{\mathrm{n}}\text{-1)} \\ {2}^a\left(\frac{2{(2}^{\mathrm{n}}\text{-1)}}{2-1}\right)=16{(2}^{\mathrm{n}}\text{-1)⇒a=3} \end{gathered}$$