# Definition:Lucky Number

## Definition

$1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, \ldots$

Remove every $2$nd number from $2$ onwards (that is, all the even integers):

$1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, \ldots$

The $2$nd term is $3$. Starting from the $3$rd element in this list (which is $5$), remove every $3$rd element from what is left:

$1, 3, 7, 9, 13, 15, 19, 21, 25, \ldots$

The $3$rd number is now $7$. Starting from the $7$th element in this list (which is $19$), remove every $7$th element from what is left:

$1, 3, 7, 9, 13, 15, 21, 25, \ldots$

The numbers remaining are the lucky numbers.

### Sequence of Lucky Numbers

The sequence of lucky numbers begins:

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

## Also see

• Results about lucky numbers can be found here.