Counting Numbers Whose Double Is Also a Palindrome

A palindrome is a number or expression which reads the same forwards and backwards, like the numbers 9, 282, 4554, and 11611, as well as the strings RACECAR and WXXW. How many 3-digit positive integers $ N $ are there such that both $ N $ and $ 2N $ are palindromes? (The first digit cannot be 0.)