Lucky Number Checker

Test membership in the lucky-number sieve that starts with positive odd integers and repeatedly removes every kth survivor; input is capped at 100,000.

Description

Lucky numbers survive a positional sieve: after removing even numbers, each next surviving step removes every kth current survivor.

Lucky numbers survive a positional sieve: after removing even numbers, each next surviving step removes every kth current survivor. This differs from removing numeric multiples of primes.^[1]

The tool returns isLucky. The indexing and output conventions below determine how to read these values.

When to use Lucky Number Checker

Use this for the following task: Test membership in the lucky-number sieve that starts with positive odd integers and repeatedly removes every kth survivor; input is capped at 100,000. Use the input and output conventions below to reproduce the intended mathematical quantity.

How to use Lucky Number Checker and understand its results

Choose the required indexes, integers or sequence entries. Preserve decimal-string encodings where the field table specifies strings.
Enter n according to the field table, then run the tool.
Read isLucky. A true flag means the candidate meets the stated property; false means it does not.
If the flag is false, review the candidate and definition. A well-formed nonmember is different from a rejected input.

Input field	Meaning	Value type and bounds	Requirement
n	Nonnegative integer (sieve resource limit 100000)	integer; minimum 0; maximum 100000	Required

Exclude zero and even n. Build odd survivors through n, repeatedly filter one-based positions using the next surviving step, then test whether n remains.

start with positive odds; for successive surviving k, remove positions divisible by k

The symbols and boundary conditions refer to the supplied fields and the implementation described above.

Output field	Meaning	Value type
isLucky	Whether n survives the lucky-number sieve	boolean

json

{
  "input": {
    "n": 21
  },
  "output": {
    "isLucky": true
  }
}

Limitations and assumptions

The candidate is at most 100000. This tests lucky-sieve membership without any probabilistic luck, prime property or generated lucky-number list.

Use the declared integer bounds and string formats. Large exact outputs remain decimal strings; numerical approximations use ordinary floating-point arithmetic. A rejected input is different from a valid zero count or false membership flag.

Alternative or Complementary methods

Choose Prime Counting by the Sieve of Eratosthenes when you need its operation: Count primes at most n exactly with the sieve of Eratosthenes, excluding zero and one and limiting n to 1,000,000. Choose Recamán Sequence Term for the complementary operation: Return a(0)=0 and a(n)=a(n−1)−n when that value is positive and unused, otherwise a(n−1)+n; the index is capped at 100,000.

Background reference: OEIS A000959.

References

OEIS A000959 — OEIS Foundation

Similar or alternative tools

Prime Counting by the Sieve of Eratosthenes
Count primes at most n exactly with the sieve of Eratosthenes, excluding zero and one and limiting n to 1,000,000.
Recamán Sequence Term
Return a(0)=0 and a(n)=a(n−1)−n when that value is positive and unused, otherwise a(n−1)+n; the index is capped at 100,000.