[mankeysee]

Well haha still seems like a lot of brain was put into it.

Also, there's a simpler pattern to the sequence that is easily observable without even opening OEIS.

[gjm11]

Unfortunately, if you spot that pattern then you will not guess the correct generalization. It seems that this may be a puzzle that's easier to solve if you aren't good at spotting easy things.

[mankeysee]

Well tbh, it seems 2^k-1 does actually match the sequence as far as it is shown. Perhaps there is a proof that n=2^k-1 for the numbers where 2^n is divisible by (n+1). I'll have to see.

[oisdk]

What's the simpler pattern?

[paideic]

Presumably multiplying by two and adding one? That's the pattern that jumped out to me, unless they're talking about something more subtle.

[oisdk]

Oh, of course! Looking at it now that's pretty obvious, lol.

Although I think even if I had spotted that I still would have put it into oeis to see if there was a quick membership test.

[mankeysee]

Which is to say, 2^n-1.