在线整数序列百科全书（OEIS）

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最大的在线整数序列数据库，可搜索。它提供了一个可搜索的界面，可以通过数值、关键词或内部标识符来识别序列。每个条目都包含技术数据，例如递推关系、生成函数、渐近行为以及与同行评审文献的交叉引用。

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

始于 1967 年，由 NJA Sloane 编辑成两本书，现在是在线版本，目前收录了超过 25 万个序列。

你还可以观看一段视频演示，其中展示了 1000 个这样的示例，这些示例是通过一系列转换成音符的序列来演示的： https://www.youtube.com/watch?v=LCWglXljevY

科学和工程领域的专业人士利用 OEIS 来识别实验数据集中的主导数学结构，并优化递归算法的复杂度。密码学结合信息论，该数据库用于评估安全所需的序列属性。加密以及以下方面的纠错协议：

材料科学中的空间堆积效率和晶格构型建模。
解决物流和自动化装配线平衡中的组合优化问题。
验证质量控制中的统计抽样模型和可靠性分布。

学科： 数学、计算机科学、密码学、组合数学、教育学。

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.
许可证和费用： 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.		许可证和费用： Mathematica is proprietary software with licensing and trial options on a separate pricing page.	许可证和费用： 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.

涵盖的主题： 整数序列、可搜索数据库、递归关系、生成函数、渐近行为、交叉引用、计算脚本、数值验证、算法扩展、数学结构、递归算法、密码学、信息论、空间打包效率、组合优化、统计抽样模型、质量控制、ISO 9001、ISO/IEC 27001、ISO 26262、ISO/IEC 25010 和 ISO 31000。