Abram, William C. and Lagarias, Jeffrey C., Intersections of multiplicative translates of 3-adic Cantor sets. J. Fractal Geom. 1 (2014), no. 4, 349-390; doi:10.4171/JFG/11.

Guy, Richard K., Unsolved problems in number theory. 3rd ed., Problem Books in Mathematics, Springer, New York (2004), xviii+437 pp. Section B33 "Largest divisor of a binomial coefficient", printed p. 135: "Erdős has also conjectured that for $k>8$, $2^k$ is not the sum of distinct powers of 3 [$2^8=3^5+3^2+3+1$]", a stronger form of the page's question (no such power beyond $2^8$, where the page asks only for finitely many), stated for its consequence that $3\mid\binom{2^{k+1}}{2^k}$ for $k\ge9$. Library home: Guy 2004.

Lagarias, Jeffrey C., Ternary expansions of powers of 2. J. Lond. Math. Soc. (2) (2009), 562-588.

Narkiewicz, W., A note on a paper of H. Gupta concerning powers of two and three: ``Powers of $2$\ and sums of distinct powers of $3$''\ [Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 602-633 (1978), 151-158 (1979);\ MR 81g:10016]. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. (1980), 173-174.

Saye, Robert I., On two conjectures concerning the ternary digits of powers of two. J. Integer Seq. (2022), Art. 22.3.4, 9.