Python 2, 2927 bytes (@xnor)
f=lambda n:n>n%3/2>-f(n/3)
Swaps True and False.
Python 2, 29 bytes (@xnor)
f=lambda n:n<1or n%3<2*f(n/3)
Thanks to @Jonathan Allan for convincing me that @xnor's switching to A005836 (without its first element) is actually perfectly good.
Python 2, 31 bytes (@KevinCruijssen)
f=lambda n:n<2or n%3>0<f(n/3+1)
Improved logic is inspired by @alephalpha's PARI/GP answer. Could save another two bytes by allowing any nonzero value for True.
Python, 33 bytes
f=lambda n:n<2or n%3and f(n//3+1)
Uses the base 3 characterisation at OEIS. Returns 0 and True.