Are there infinitely many $n > 2$ such that $n - 2^k$ is prime for all $k \geq 1$ with $2^k < n$?

$21$ satisfies the Erdős 1142 property: $21 - 2 = 19$, $21 - 4 = 17$, $21 - 8 = 13$, $21 - 16 = 5$.