Are there any integer solutions to $2^x+1=3^y$ for $y>2$? for what values of $ x $ and $ y $ the equality holds 

$2^x+1=3^y$

It is quiet obvious the equality holds for $x=1,y=1$ and $x=3,y=2$.
But further I cannot find why $x$ and $y$ cannot take higher values than this values.

With $y \gt 2$, there are only $684$ possible values of $3^y - 2^x$ mod $(262143 = 2^{18} - 1)$, so it is reduced the the finite problem of checking that none of them are $1$.
