Check if a number is lucky or generate lucky numbers using the Josephus sieve
Number to Check
Max Range
Result
Verdict
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Lucky Numbers in Range
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Sieve Process
Lucky Number Sieve Process
Start: all odd numbers 1,3,5,7,9,11,13,15...
Step 2: remove every 3rd (n=3): remove 5,11,17...
Step 3: next survivor=7, remove every 7th
Continue: next survivor determines step size
Lucky numbers are generated by a sieve process similar to the Sieve of Eratosthenes but using ordinal position instead of divisibility. They were discovered by mathematician Stanislaw Ulam.
⚠Lucky numbers are not the same as prime numbers. They share similar density but are computed differently. The range should be large enough to include the number.
What Is a Lucky Number?
Lucky numbers are generated by a sieve that removes numbers based on position rather than divisibility. The process is named after the Josephus problem. The numbers that survive all elimination rounds are called lucky.
Sieve Method
Start with odds. Remove every 3rd, then every 7th, then every 9th, then every 13th, etc. Step size = next surviving number.
Lucky Primes
Numbers that are both lucky and prime: 3,7,13,31,37,43,67,73,79,127,151. About 57% of lucky numbers under 1000 are also prime.
History
Discovered by Stanislaw Ulam (of Manhattan Project fame) in 1955. He studied them during lunch breaks at Los Alamos National Laboratory.
Twin Lucky
Twin lucky numbers differ by 2: (1,3), (7,9), (13,15), (31,33), (49,51). Like twin primes, they become rarer as numbers grow.
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