Seems like this should be easy, but I couldn't find a single power of 2 that is divisible by 3, unless I am doing it wrong, or there is some special rule that I am overlooking.

I even wrote a C# script to try every power of 2 to see if its divisible by 3. It went up until my 64 bit computer couldn't count any higher, the last power of 2 it checked was 2^1023 or 8.98846567×10^307

Then just for a test of it ran it again looking for multiples of 5, then 6, then 7, every number up until 20 (with the obvious exception of 4, 8, & 16) and none returned multiples before hitting 2^1023

I'm assuming I didnt just make some profound discovery but there is a name for this phenomenon?

p.s, I have no idea what to tag this, new to MathOverflow.