# Palindromes in Base 10 and Base 3

## Theorem

The following $n \in \Z$ are palindromic in both decimal and ternary:

$0, 1, 2, 4, 8, 121, 151, 212, 242, 484, 656, 757, \ldots$

## Proof

$n_{10}$ $n_3$
$0$ $0$
$1$ $1$
$2$ $2$
$4$ $11$
$8$ $22$
$121$ $11 \, 111$
$151$ $12 \, 121$
$212$ $21 \, 212$
$242$ $22 \, 222$
$484$ $122 \, 221$
$656$ $220 \, 022$
$757$ $1 \, 001 \, 001$

$\blacksquare$