1. The number of five-digit numbers where the sum of any two adjacent digits is divisible by 3 is $\qquad$ (answer with a number) .
1. 1254 .

If we classify the digits by their remainders, then the five-digit number $\overline{a b c d e}$ that meets the condition satisfies
$$
a \equiv c \equiv e \equiv 2 \quad(\bmod 3), \quad b \equiv d \equiv 1 \quad(\bmod 3),
$$

or
$$
a \equiv c \equiv e \equiv 1 \quad(\bmod 3), \quad b \equiv d \equiv 2 \quad(\bmod 3),
$$

or
$$
a \equiv b \equiv c \equiv d \equiv e \equiv 0 \quad(\bmod 3) .
$$

If it is equation (1), then there are $3^{5}$ five-digit numbers that meet the condition. If it is equation (2), then there are $3^{5}$ five-digit numbers that meet the condition. If it is equation (3), then there are $3 \times 4^{4}$ five-digit numbers that meet the condition.
Therefore, the total number of five-digit numbers that meet the condition is $3^{5}+3^{5}+3 \times 4^{4}=1254$.