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OEIS

Research & AcademiaMisc References

Look up integer sequences in the OEIS, the On-Line Encyclopedia of Integer Sequences, which has catalogued nearly 400,000 of them since 1964. Hand it the numbers falling out of a calculation and find out what they are, search by subject, read a sequence's whole entry with its formulas, citations and code, pull thousands of exact terms into a spreadsheet or a chart, or follow the sequences related to one you already have. Free and public: no account, no API key, no sign-up.

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Steps your workflow can run in OEIS.

Identify a sequenceGive the OEIS a run of whole numbers and find out what it is. This is what the encyclopedia is for: the counts falling out of a calculation go in, and the sequences that begin that way come back, named and explained. Signs are matched as given, so the Moebius function is not confused with its absolute value. The answer also says plainly whether anything matched, so a workflow can branch on it.
Search sequencesSearch by words rather than by numbers, and narrow the matches by the tags the OEIS puts on every sequence or by who contributed it. The tags are the most useful filter the OEIS has and the least readable, so all thirty are offered in plain English rather than as codes like cofr and tabf. Order by relevance, by how often a sequence is referred to elsewhere, or by what was added or updated most recently.
Get a sequenceRead one sequence's entry: its definition, its first terms, who contributed it and when it last changed. A well-studied sequence also carries hundreds of comments, formulas, citations and programs in Maple, Mathematica and a dozen other languages, which run to hundreds of kilobytes, so each of those is returned only when it is asked for.
Get more termsRead terms from a sequence's full table, which runs far past the handful an entry displays: the Fibonacci numbers are listed to the 2000th, the Moebius function to the 100000th. Start anywhere in the sequence and take as many terms as are wanted. Terms come back as exact text rather than as numbers, because an OEIS term routinely runs to hundreds of digits and a number that long would quietly round.
Find related sequencesList the sequences whose entries mention a given one, which is how the OEIS records that two sequences have something to do with each other. Order by how often a sequence is referred to elsewhere to surface the important relatives first: the Fibonacci numbers lead to the Catalan numbers, Pascal's triangle, the golden ratio and the Lucas numbers.

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