BALTIC-WAY 1997 Problem 9

The worlds in the Worlds' Sphere are numbered $1,2,3, \ldots$ and connected so that for any integer $n \geqslant 1$, Gandalf the Wizard can move in both directions between any worlds with numbers $n, 2 n$ and $3 n+1$. Starting his travel from an arbitrary world, can Gandalf reach every other world?