Conjecture related to Lychrel numbers
The smallest counter-example is $10039547$, which gets into a cycle:
$$ \begin{array}{} \color{red}{84632548} \\ 69156196 \\ 38321392 \\ 67633775 \\ 25367451 \\ 40843803 \\ 71678607 \\ 42366224 \\ \color{red}{84632548} \\ \end{array} $$ Found by exhaustive brute-force search.