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The On-Line Encyclopedia of Integer Sequences (OEIS)

The largest online integer sequences database, searchable. It provides a searchable interface to identify sequences by numerical terms, keywords, or internal identifiers. Each entry includes technical data such as recurrence relations, generating functions, asymptotic behavior, and cross-references to peer-reviewed literature.

The platform also hosts computational scripts in multiple programming languages, enabling the numerical verification and algorithmic extension of sequence data for research and development.

Iniziata nel 1967 da NJA Sloane e poi pubblicata in due libri, ora è disponibile la versione online, che comprende più di un quarto di milione di sequenze.

You also have a video illustration of 1000 of these, illustrated by a sequence converted into notes: https://www.youtube.com/watch?v=LCWglXljevY

I professionisti nel campo della scienza e dell'ingegneria utilizzano l'OEIS per identificare le strutture matematiche che governano i set di dati sperimentali e per ottimizzare la complessità degli algoritmi ricorsivi. crittografia e la teoria dell'informazione, il database viene utilizzato per valutare le proprietà di sequenza richieste per la sicurezza crittografia e protocolli di correzione degli errori per:

  • Modeling spatial packing efficiency and lattice configurations in materials science.
  • Solving combinatorial optimization problems in logistics and automated assembly line balancing.
  • Validating statistical sampling models and reliability distributions in quality control.
Discipline: Matematica, informatica, crittografia, combinatoria, istruzione.
Free alternative to Wolfram Alpha, Mathematica, SageMath.
OEIS compared with Wolfram Alpha, Mathematica and SageMath
OEISWolfram AlphaMathematicaSageMath
Core function: OEIS is a curated database of integer sequences. Its home page reported 400438 sequences on 18 October 2026, searchable by terms, words or A-number.Core function: Wolfram Alpha is a computation service, not a catalogue. From a list of terms it computes a possible formula and continues the sequence, and it also accepts an OEIS number as input.Core function: Mathematica is a technical computing environment built on the Wolfram Language. Looking up OEIS entries goes through the OEISLookup function from the Wolfram Function Repository, which needs Wolfram Language 13.0 or later.Core function: SageMath is a Python-based mathematics system. Its OEIS interface searches by list of integers, by text description or by entry text, and fetches a sequence by A-number.
Outputs and data access: Each entry offers views named list, graph, refs, listen (MIDI), table, text, internal format and history. Two gzipped files, sequences and names, are refreshed daily for bulk download.Outputs and data access: Wolfram Alpha can return the generating function of a sequence given by OEIS number, for example the generating function of A000108.Outputs and data access: OEISLookup queries the OEIS JSON API and returns the matching sequences, so results depend on the online database.Outputs and data access: A fetched sequence exposes terms, name, formulas, comments, examples, cross-references and programs. Some sequences convert into Sage objects such as continued fractions or real numbers from decimal expansions.
Licence and cost: Content is provided under the OEIS End-User License Agreement. The database is run by the OEIS Foundation Inc., a nonprofit set up in 2009.Licence and cost: Mathematica is proprietary software with licensing and trial options on a separate pricing page.Licence and cost: SageMath is free and open source under the GPL.
Platform and offline use: OEIS runs in any browser. For automated or offline work the daily files can be mirrored locally.Platform and offline use: Mathematica is available on Windows, macOS, Linux and Cloud. The OEIS lookup requires an internet connection.Platform and offline use: Binaries are listed for Linux and macOS through conda-forge, and Windows is supported through the Windows Subsystem for Linux. Most OEIS calls need internet, and a local partial copy called SloaneEncyclopedia exists for heavy searching.

Argomenti trattati: sequenze di interi, database ricercabile, relazioni di ricorrenza, funzioni generatrici, comportamento asintotico, riferimenti incrociati, script computazionali, verifica numerica, estensione algoritmica, strutture matematiche, algoritmi ricorsivi, crittografia, teoria dell'informazione, efficienza di impacchettamento spaziale, ottimizzazione combinatoria, modelli di campionamento statistico, controllo qualità, ISO 9001, ISO/IEC 27001, ISO 26262, ISO/IEC 25010 e ISO 31000.

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