← Back to catalogue
Published

integer sequence

vr.tr.integer-sequence · thing-q2297602

Let an agent explain integer sequences and how they are defined, relay notable examples and the OEIS from mathematical references, describe their uses across mathematics, and route to entries for specific sequences.

Thing Registry Cross-cutting context XCT.QLT
Bundle → Layer → Finding → QuestionsClassifiersWhat it isWhy it existsDistinguishing featuresWhat robots and AI may and may not doMoral aspectsOwnersLinks to other meta-modelsIdentity and identifiersDirect propertiesRecognitionCapabilities and actionsHazards and failure modesStandards and interfacesContext of useSources

Bundle → Layer → Finding → Questions Filled

4 bundles · 8 layers · 8 findings · 16 questions

Understand What an integer sequence is.

Definition

Definition.

Definition

Definition.

  1. What is an integer sequence, and how are sequences defined by formulas, recurrences and properties? definition
  2. Is the question about integer sequences in general or a specific sequence? boundary

Examples

Notable examples.

Examples

Examples.

  1. What are Goodstein, Hofstadter, Piatetski-Shapiro and Sindel sequences and degree sequences? definition
  2. Which entry fits the specific sequence? action
Explore Exploring sequences.

OEIS

The OEIS.

OEIS

OEIS.

  1. How does the OEIS work, and how can a sequence be looked up or submitted? action
  2. Which references are standard? provenance

Analysis

Analysing sequences.

Analysis

Analysis.

  1. How are growth rates, generating functions and recurrences used to analyse sequences? provenance
  2. Which entry fits generating function? action
Apply Applications.

Mathematics

In mathematics.

Mathematics

Mathematics.

  1. How do integer sequences appear in number theory, combinatorics, logic and graph theory? provenance
  2. Which sources are cited? provenance

Applications

Beyond mathematics.

Applications

Applications.

  1. How are integer sequences used in computing, physics and devices such as the Prague astronomical clock? provenance
  2. Which entry fits the specific application? action
Context History and culture.

History

History.

History

History.

  1. How have integer sequences been studied from antiquity to the OEIS? provenance
  2. Which entry fits the history of number theory? action

Culture

Puzzles and culture.

Culture

Culture.

  1. How do integer sequences appear in puzzles, tests and popular mathematics? provenance
  2. Which entry fits recreational mathematics? action

Classifiers Filled

Family
Thing Registry
Category
Cross-cutting context
Entry kind
thing
Plane
XCT
Domain
XCT.QLT
Other names and narrower kinds
triangular–factorial equation, Šindel sequence, Goodstein sequence, Piatetski-Shapiro sequences, degree sequence, Hofstadter sequence, aliquot sequence, Irrationality sequence, Lucas sequence, k-regular sequence, juggler sequence, Ban number

What it is Filled

An ordered list of integers, finite or infinite, defined by a formula, a recurrence, a property of its members or a construction, such as the primes, the Fibonacci numbers, degree sequences of graphs, Goodstein sequences that eventually reach zero despite explosive growth, Hofstadter sequences defined by nested recurrences, Piatetski-Shapiro sequences of floor functions of powers, and the Sindel sequence of the Prague astronomical clock; integer sequences are catalogued in the On-Line Encyclopedia of Integer Sequences.

Why it exists Filled

Let an agent explain integer sequences and how they are defined, relay notable examples and the OEIS from mathematical references, describe their uses across mathematics, and route to entries for specific sequences.

Distinguishing features Filled

  • Ordered integers
  • Definition by rule
  • Catalogued in OEIS
  • Cross-mathematical role

What robots and AI may and may not do Filled

Must not

  • Claim a pattern holds for all terms on the evidence of a few computed ones.
  • Present a conjectured formula as proved.
  • Fabricate terms, references or catalogue entries for a sequence.
  • Confuse two sequences that share initial terms.

Only with a human decision

  • Publishing a new sequence or a correction to a shared reference catalogue.

May

  • Compute, list and check terms of an integer sequence from its definition.
  • Cite a sequence with its standard reference and give its first terms.

Moral aspects Filled

  • Reference catalogues of sequences are relied on by researchers; errors spread widely.
  • Credit for discovering sequences and results belongs to those who found them.

Who is affected

  • Mathematicians and students
  • Maintainers of reference catalogues

Owners Filled

Steward

Nobody owns the concept; editors of reference catalogues answer for their entries.

Links to other meta-models Filled

parent

  • Q4516355 - registry parent class

related

  • number sequence - in registry terms
  • OEIS - the On-Line Encyclopedia of Integer Sequences
  • Fibonacci sequence - as a classic example
  • number theory - and combinatorics

What else AI and robots need to interact with it Filled

Identity and identifiers required Filled

  • Vercy registry: vr.tr.integer-sequence
  • Wikidata: Q2297602 (https://www.wikidata.org/wiki/Q2297602)

Direct properties not applicable Not applicable

  • OEIS entries: over 380000 count - 2025
  • OEIS founded: 1964 as a card file, online 1996 year - Neil Sloane

Plane XCT: no invented physical properties.

Recognition optional Filled

  • Ordered lists of integers
  • Primes, Fibonacci, Goodstein, Hofstadter, Piatetski-Shapiro, Sindel and degree sequences
  • Real sequences and series are broader; a set of integers is unordered
  • Not a visible object; lists of integers.

Capabilities and actions required Filled

  • explain definitions
  • relay notable examples
  • describe the OEIS
  • route to specific sequences

Hazards and failure modes required Filled

  • Guessing rules from few terms
  • Confusing sequences with sets or series
  • Mislabelled sequences

Standards and interfaces required Filled

  • No regulation; OEIS editorial standards for entries

Context of use required Filled

  • Not applicable; a mathematical concept.
  • sequences defined by formulas
  • recurrence sequences such as Fibonacci and Hofstadter sequences
  • sequences defined by properties such as primes and perfect numbers
  • combinatorial sequences such as degree sequences
  • sequences from logic such as Goodstein sequences
  • number-theoretic sequences such as Piatetski-Shapiro sequences
  • sequences from applications such as the Sindel sequence

Sources Filled

  1. Wikidata item Q2297602: integer sequence - identity and sense of the item
  2. Wikipedia: Integer sequence - general description of the item

Open questions

  • Should notable sequences be separate entries?
  • How should the OEIS be linked?
  • The registry entry has merged aliases naming specific sequences; should they be split off?

Machine files

Card as JSON Specification Card backlog vercy.card/1

Provenance

thing registry research (pass 2) · unreviewed

Built from: models/things/publications/thing-q2297602/spec.json