narcissistic number
Let an agent define narcissistic numbers, list examples and the finite set in base 10, explain why the set is finite and base-dependent, and help test or generate them.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Define What narcissistic numbers are.
Definition
Definition and examples.
Definition
Definition.
- What is a narcissistic number, and what are the examples in base 10? definition
- Is the question about narcissistic numbers or another digit-based class? boundary
Finite
Why the set is finite.
Finite
Finite.
- Why are there finitely many narcissistic numbers in any base, and how is the bound found? definition
- Which entry fits perfect digital invariant? action
Compute Testing and generating.
Test
Testing a number.
Test
Test.
- How is a number tested for the property, and how are all such numbers generated? action
- Is the number in question narcissistic? measurement
Programming
Programming exercise.
Programming
Programming.
- Why are Armstrong numbers a common programming exercise, and what pitfalls arise? provenance
- Which references are standard? provenance
Theory Related classes.
Bases
Other bases.
Bases
Bases.
- How do narcissistic numbers differ across bases? provenance
- Which sources are cited? provenance
Related
Related curiosities.
Related
Related.
- How do happy, Kaprekar, Dudeney and other digit-based numbers relate? provenance
- Which entry fits the specific class? action
Context History and status.
History
History.
History
History.
- Who studied these numbers, and where does the name Armstrong come from? provenance
- Which entry fits recreational mathematics? action
Status
Mathematical status.
Status
Status.
- Why do mathematicians regard the property as a curiosity, with positions attributed? 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
A number that equals the sum of its own digits each raised to the power of the number of digits, such as 153, which equals 1 cubed plus 5 cubed plus 3 cubed, also called an Armstrong number or pluperfect digital invariant; in base 10 there are exactly 88 such numbers, the largest with 39 digits, and the concept is a recreational curiosity that depends on the base rather than a deep property of numbers.
Why it exists Filled
Let an agent define narcissistic numbers, list examples and the finite set in base 10, explain why the set is finite and base-dependent, and help test or generate them.
Distinguishing features Filled
- Digit-power invariant
- Finite in any base
- Base dependent
- Recreational status
What robots and AI may and may not do Filled
Must not
- State a wrong count or a wrong largest member without checking a source.
- Confuse the term with narcissism as a personality trait.
- Fabricate properties or proofs.
Only with a human decision
- Publishing new claims about the sequence.
May
- Compute and check narcissistic numbers and explain the definition.
- Cite the full list from recognised integer sequence references.
Moral aspects Filled
- Recreational maths builds interest, and errors erode trust.
- Using a clinical-sounding name for a number should not trivialise the personality disorder.
Who is affected
- Learners
- Puzzle and maths readers
- Researchers
Owners Filled
Steward
Nobody owns a number; it is held in common.
Links to other meta-models Filled
parent
- Q85792806 - registry parent class
related
- perfect digital invariant - in registry terms
- integer - a special class
- happy number - another digit-based class
- recreational mathematics - the field
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.narcissistic-number
- Wikidata: Q777616 (https://www.wikidata.org/wiki/Q777616)
- OEIS: A005188 narcissistic numbers in base 10
Direct properties not applicable Not applicable
- three-digit examples: 153, 370, 371, 407 set
- count in base 10: 88 count - including single digits
Plane XCT: no invented physical properties.
Recognition optional Filled
- Sum of digits to the power of digit count equals the number
- 88 in base 10, largest 39 digits
- Perfect digital invariants use a fixed power; happy numbers use iteration
- Not a visible object; integers such as 153, 370, 371 and 407.
Capabilities and actions required Filled
- define and list examples
- explain finiteness and base dependence
- help test or generate numbers
- distinguish related digit invariants
Hazards and failure modes required Filled
- Treating the property as mathematically deep
- Confusing with other digit invariants
- Overflow in naive computation of large cases
Standards and interfaces required Filled
- No regulation; the OEIS is the reference database
Context of use required Filled
- Recreational number theory and programming exercises.
- narcissistic numbers in base 10
- narcissistic numbers in other bases
- perfect digital invariants with fixed power
- related curiosities such as Dudeney and Kaprekar numbers
Sources Filled
- Wikidata item Q777616: narcissistic number - identity and sense of the item
- Wikipedia: Narcissistic number - general description of the item
Open questions
- Should perfect digital invariant be the primary entry?
- How should the OEIS be linked?
- How should base-dependent sets be recorded?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q777616/spec.json