Return to Revisions

This is an old unsolved problem. Erdos conjectured (see the first problem in that paper) that for all $n\ge 9$ the ternary expansion of $2^n$ contains the ternary digit $2$ (this is equivalent to for every $n\ge 10$ the ternary expansion of $2^n$ contains a $1$). For recent work related to this (and references) see these papers of Abram and Lagarias, and Lagarias.