The On-Line Encyclopedia of Integer Sequences (OEIS) is a comprehensive, free online database of integer sequences, serving as a vital reference for researchers and enthusiasts in mathematics and related fields. It allows users to search for sequences by terms, keywords, or sequence ID, and provides formulas, references, and cross-references for each entry.
Background
- The OEIS (On-Line Encyclopedia of Integer Sequences) is a vast, searchable database of integer sequences — ordered lists of numbers with mathematical patterns, like the Fibonacci sequence (0, 1, 1, 2, 3, 5, 8…) or the primes (2, 3, 5, 7, 11…). Each sequence has its own "A-number" (e.g. A000045 for Fibonacci) and includes formulas, references, and cross-links.
- Founded by mathematician Neil Sloane in the 1960s as a card file, it went online in the mid-1990s and is now a curated, community-driven resource with over 370,000 sequences. It is widely used by mathematicians, computer scientists, puzzle-solvers, and hobbyists.
- If you encounter an unfamiliar sequence — whether from a math problem, a graph of data, or a programming challenge — searching the OEIS can instantly tell you if it has been studied before, what its properties are, and where it appears in the literature.
- Reading the OEIS typically requires familiarity with basic math notation, but many entries also include English explanations, code snippets (in languages like Maple, Mathematica, Python), and references to Wikipedia or academic papers.