lucky number
Let an agent define lucky numbers in the mathematical sense, generate and test them, relate them to primes, and separate this sense from cultural beliefs about fortunate numbers, which are presented with attribution.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
Researched by: Claude
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Define The sieve.
Sieve
The procedure.
Sieve
Sieve.
- How does the lucky number sieve work, step by step? definition
- Is the question about the mathematical sense or about fortunate numbers in culture? boundary
Examples
First terms.
Examples
Examples.
- What are the lucky numbers below a given bound? measurement
- Which entry fits integer sequences? action
Properties Known results.
Distribution
Distribution.
Distribution
Distribution.
- How does the density of lucky numbers compare with primes, and what is proved versus conjectured? provenance
- Which references are standard? provenance
Lucky primes
Lucky primes.
Primes
Primes.
- Which numbers are both lucky and prime, and what is known about them? provenance
- Which entry fits prime numbers? action
Compute Algorithms.
Algorithm
Generating.
Algorithm
Algorithm.
- How is the sieve implemented efficiently, and how is membership tested? action
- What are the complexity and limits? measurement
Variants
Variants.
Variants
Variants.
- What variants of the sieve exist, and how do they relate? provenance
- Should a variant be a separate entry? boundary
Context History and culture.
History
Origin.
History
History.
- How did Ulam and colleagues introduce lucky numbers, and why the name? provenance
- Which entry fits Stanislaw Ulam? action
Culture
Cultural sense.
Culture
Culture.
- How do cultures regard certain numbers as lucky, presented with attribution and without endorsement? provenance
- Is the presentation neutral? boundary
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.QTY
What it is Filled
In number theory, a positive integer that survives a sieve similar to the sieve of Eratosthenes but based on position: starting from the odd numbers, every k-th remaining number is deleted where k is the next surviving number, leaving 1, 3, 7, 9, 13, 15, 21 and so on; the term is also used in popular culture for numbers people regard as fortunate, which is a different sense.
Why it exists Filled
Let an agent define lucky numbers in the mathematical sense, generate and test them, relate them to primes, and separate this sense from cultural beliefs about fortunate numbers, which are presented with attribution.
Distinguishing features Filled
- Defined by a sieve on positions, not divisibility
- Shares distribution properties with primes
- All lucky numbers are odd
- Distinct from cultural lucky numbers
What robots and AI may and may not do Filled
Must not
- Confuse sieve lucky numbers with numbers considered lucky by superstition.
- Present unproven conjectures about them as theorems.
- Use the term to promote gambling or numerology.
Only with a human decision
- Publishing new results about them.
May
- Explain the lucky number sieve and compute lucky numbers.
- Compare their properties with primes, with sources.
Moral aspects Filled
- Confusion with luck can support gambling and superstition.
- Rigorous treatment matters for students learning number theory.
Who is affected
- Students
- People prone to gambling
Owners Filled
Steward
Nobody: a mathematical concept held in common.
Links to other meta-models Filled
parent
- Q16317911 - registry parent class
related
- positive integer - a property of integers
- prime number - similar distribution
- On-Line Encyclopedia of Integer Sequences - sequence A000959
- numerology - cultural beliefs about numbers
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.lucky-number
- Wikidata: Q1428157 (https://www.wikidata.org/wiki/Q1428157)
- OEIS: A000959 lucky numbers
Direct properties not applicable Not applicable
- first terms: 1, 3, 7, 9, 13, 15, 21 integers
Plane XCT: no invented physical properties.
Recognition optional Filled
- Produced by the position-based sieve
- Sequence 1, 3, 7, 9, 13, 15, 21, 25, 31
- Culturally lucky numbers such as 7 or 8 are a different sense
- Not visible; a property of integers.
Capabilities and actions required Filled
- generate lucky numbers by the sieve
- test whether an integer is lucky
- compare their distribution with primes
- distinguish the mathematical from the cultural sense
Hazards and failure modes required Filled
- Mixing the mathematical and cultural senses
- Off-by-one errors in the sieve
- Presenting conjectures as theorems
Standards and interfaces required Filled
- No regulation; definitions follow the literature and the OEIS
Context of use required Filled
- Not for anything; an object of number theory.
- lucky numbers of the Ulam sieve
- lucky primes, which are both lucky and prime
- variants of the sieve starting from other sets
- cultural lucky numbers, a separate sense
Sources Filled
- Wikidata item Q1428157: lucky number - identity and sense of the item
- Wikipedia: Lucky number - general description of the item
Open questions
- Should the cultural sense be a separate entry?
- How should OEIS entries be linked?
- Which conjectures about lucky numbers should be recorded?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q1428157/spec.json