# Definition:Lucky Number

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## Definition

Start with the list of (strictly) positive integers:

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

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.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $9$ - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $33$ - 1994: Richard K. Guy:
*Unsolved Problems in Number Theory*(2nd ed.) - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $9$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $33$

- Weisstein, Eric W. "Lucky Number." From
*MathWorld*--A Wolfram Web Resource. http://mathworld.wolfram.com/LuckyNumber.html