The On-Line Encyclopedia of Integer Sequences (OEIS)

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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.

Started in 1967 by N.J.A. Sloane, then edited as two books, now is the online version, now featuring more than a quarter of a million sequences.

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

Professionals in science and engineering utilize the OEIS to identify governing mathematical structures in experimental datasets and to optimize the complexity of recursive algorithms. In cryptography and information theory, the database is used to evaluate sequence properties required for secure encryption and error-correction protocols for:

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.

Disciplines: Mathematics, Computer science, Cryptography, Combinatorics, Education.

Free alternative to Wolfram Alpha, Mathematica, SageMath.

OEIS compared with Wolfram Alpha, Mathematica and SageMath
OEIS	Wolfram Alpha	Mathematica	SageMath
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.

Topics covered: integer sequences, searchable database, recurrence relations, generating functions, asymptotic behavior, cross-references, computational scripts, numerical verification, algorithmic extension, mathematical structures, recursive algorithms, cryptography, information theory, spatial packing efficiency, combinatorial optimization, statistical sampling models, quality control, ISO 9001, ISO/IEC 27001, ISO 26262, ISO/IEC 25010, and ISO 31000..