Algorithm to find Lucky Numbers

Question

I came across this question.A number is called lucky if the sum of its digits, as well as the sum of the squares of its digits is a prime number. How many numbers between A

Answer 1

First I would like to add that a lucky number can be calculated by a sieve, the explanation of the sieve can be found here: http://en.wikipedia.org/wiki/Lucky_number

so you can improve your solution speed using a sieve to determine the numbers,