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. https://mathworld.wolfram.com/LuckyNumber.html