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

$75$ satisfies the Erdős 1142 property: $75 - 2 = 73$, $75 - 4 = 71$, $75 - 8 = 67$, $75 - 16 = 59$, $75 - 32 = 43$, $75 - 64 = 11$.