Lucky number

In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve". This sieve is similar to the Sieve of Eratosthenes that generates the primes, but it eliminates numbers based on their position in the remaining set, instead of their value (or position in the initial set of natural numbers).

One way that the application of the procedure differs to that of the Sieve of Eratosthenes is, for n being the number being multiplied on a specific pass, the first number eliminated on the pass is the n-th remaining number that hasn't yet been eliminated, as opposed to the number 2n. That is to say that the numbers this sieve counts through is different on each pass (for example 1, 3, 7, 9, 13, 15, 19... on the third pass), whereas in the Sieve of Eratosthenes, the sieve always counts through the entire original list (1, 2, 3...).

When this procedure has been carried out completely, the survivors are the lucky numbers:

The term was introduced in 1956 in a paper by Gardiner, Lazarus, Metropolis and Ulam. They suggest also calling its defining sieve, "the sieve of Josephus Flavius" because of its similarity with the counting-out game in the Josephus problem.

Lucky number (disambiguation)

Lucky number may refer to:

Mathematics

Film, TV and cartoon

Music

Albums

Songs

Lucky

Lucky may refer to:

Fictional characters

Lucky Numbers

Lucky Numbers is a 2000 comedy film directed by Nora Ephron. The screenplay by Adam Resnick was inspired by the 1980 Pennsylvania Lottery scandal.

Plot

Russ Richards (John Travolta), the weatherman for a Harrisburg, Pennsylvania television station, is revered as a local celebrity by his viewers, and fame affords him such perks as a reserved parking spot and his own booth at Denny's, where an omelet bears his name. His eternally optimistic demeanor conceals the fact his snowmobile dealership is on the verge of bankruptcy due to an unusually warm winter.

His friend Gig (Tim Roth), a shady strip club owner, suggests an insurance scam will free Russ of his financial problems, but when the scheme fails to pay off, Russ finds himself even deeper in debt and the target of a hitman named Dale (Michael Rapaport). Gig then proposes Russ rig the Pennsylvania Lottery with the help of his amoral girlfriend Crystal Latroy (Lisa Kudrow), a ditzy model who pulls and announces the winning numbers on television, and her oddball cousin Walter (Michael Moore), who will pose as the owner of the lucky ticket.