I've just discovered that there is a proper mathematical definition for a lucky number. It's any number in a sequence determined by a formula called a 'sieve'. It works like this:
Take a normal natural number sequence from 1 to whatever, i.e.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27 ...etc

You keep the first number (1) and remove every second number after it (all the evens):
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41 ...etc
Then you keep the second number, which is 3, and remove every third number, i.e.
1, 3, 7, 9, 13, 15, 19, 21, 25, 27, 31, 33, 37, 39 ...etc
You keep the third number, which is 7, and remove every seventh number, i.e.
1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 35, 37...etc
Then you keep the fourth number (9) and so on,
ad infinitum, i.e.
1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, 87, 93, 99 ...etc.
The numbers that are left are called 'lucky numbers'. Although, what use they are to anyone remains a mystery.