[seqfan] Doomed by odd integers

[Eric Angelini]

Hello SeqFans,
Say I start with an even integer and successively add
halves like this:

16+8=24
     24+12=36
           36+18=54
                 54+27=81 END

... am I doomed to always END (on an odd integer)?

Is there a sequence of terms a(n) where a(n) is the
smallest integer ENDING in n steps?

Best,
É.