Is it true that :
For every $n$ there exists a number $k<3n$ such that:
$k\cdot 2^n-1$ or $k\cdot 2^n+1$ is prime,where $k,n\in \mathbf{N}$
Maple code that prints least $k$ such that $k\cdot 2^n-1$ is prime and $k<3n$ :
for $n=624$ we have exception,there is no prime of the form $k\cdot 2^{624}-1$ such that $k<3\cdot 624$ , but number $85\cdot 2^{624}+1$ is prime number and $85<3\cdot 624$
Any idea how to prove or disprove statement above ?