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This article is about the formal mathematical concept defined by
Stanislaw Ulam; a discussion of the more common meaning is also available.
A lucky number is a natural number which is
generated in a similar way as primes are generated from the Sieve of Eratosthenes. We begin with a list of integers starting with 1:
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,
Then we cross out all even numbers, leaving only the odd integers:
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25,
The second term in this sequence is 3.
Now we cross out every third number which remains in the list:
1, 3, 7, 9, 13, 15, 19, 21, 25,
The third surviving number is now 7 so we again cross out every remaining seventh
number:
1, 3, 7, 9, 13, 15, 21, 25,
Finally we get all lucky numbers:
- 1,3,7,9,13,15,21,25,31,33,37,43,49,51,63,67,69,73,75,79,87,93,99,...
Lucky numbers were named so by Stanislaw Ulam around 1955.
Lucky numbers share some similar properties with primes as their asymptotic behaviour, according to the prime number theorem or the Goldbach's conjecture. There are infinitely many lucky numbers. It is not known whether there
are also infinitely many lucky primes:
- 3,7,13,31,37,43,67,73,79,127,151,163,193,...
External links
Eight (八 pinyin ba1) is considered a
lucky number in Chinese culture because it sounds
like the word "prosper" (發 pinyin fa1).
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