Two Versus Three

\[ \begin{array} { l l l l l } & \color{red}{y} & +\frac { 1 }{ 2 } & +\frac { \color{red}{y} }{ 4 } & +\frac { 1 }{ 8 } & +\frac { \color{red}{y} }{ 16 } & +\frac { 1 }{ 32 }& + \dots\\
= & 1 & +\frac { \color{blue} {x} }{ 3 } & +\frac { 1 }{ 9 } & +\frac { \color{blue} {x} }{ 27 } & +\frac { 1 }{ 81 } & +\frac { \color{blue} {x} }{ 243 } & +\dots \end{array} \]

Find the smallest positive integer \(\color{blue} {x}\), such that there exists an integer \(\color{red}{y}\) which satisfies the above equation.

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