Lucky number

Lucky numbers are numbers left after a 'number massacre". First, 1 is a lucky number.

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,... Remove every second number:

1,3,5,7,9,11,13,15,17,19,... Thus 3 is a lucky number. Remove every 3rd number left:

1,3,7,9,13,15,19,... 7 is a lucky number. Every 7th number left:

1, 3, 7, 13, 15,... Every 13th number...

...

We are left with the lucky numbers after an infinite round of this. Surprisingly, 13, a number usually considered unlucky, is a lucky number.

Lucky numbers below 100:

1,3,7,9,13,15,21,25,31,33,37,43,49,51,63,67,69,73,75,79,87,93,99.