# famous mathematical sequences

Arithmetic sequences are sequences of numbers where any pair of adjacent numbers has the same difference, e.g. If the database helped Professional mathematicians use highly complex algorithms to find and analyse all these patterns, but we are going to start with something a bit more basic. Trigonometric, inverse trigonometric, hyperbolic, and inverse hyperbolic functions relationship, Calculate the Fourier expansion of the function, Series (mathematics) § Examples of numerical series, On-Line Encyclopedia of Integer Sequences, "Theoretical computer science cheat sheet", "Bernoulli polynomials: Series representations (subsection 06/02)", "A simple proof of 1+1/2^2+1/3^2+...=PI^2/6 and related identities", Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, https://en.wikipedia.org/w/index.php?title=List_of_mathematical_series&oldid=990757742, Short description is different from Wikidata, Creative Commons Attribution-ShareAlike License, This page was last edited on 26 November 2020, at 09:42. Baum–Sweet sequence {1, 1, 0, 1, 1, 0, 0, 1, 0, 1, ...} a(n) = 1 if the binary representation of n … he launched Here, however, we ran into a very serious problem. it was that no one had published such a collection before. (The sequences mentioned are A000027, A000217, A000292, A000332, A000389, A000579, A000110, A007318, A000058, A000215, A000289, A000324, A234953 (= A001854(n)/n), A000435, A000169, A000142, A000272, A000312, A000111.) For information about the format of replies received from the database, click here. Again, once the book appeared, many further sequences and updates were In fact, the name was developed hundreds of years ago, when mathematicians thought about multiplication and square roots in a much more geometric way.. He had encountered a sequence of numbers while working (See harmonic numbers, themselves defined j Following the publication of She can be reached through her user page on this wiki. Born into a humble family, the celebrated mathematician struggled with poverty but still managed to publish first of his papers in the Journal of the Indian Mathematical Society. During this period, from 1996 to 2009, the database grew ) Starting in 2002, NJAS added a group of associate editors to help This facility is essential in a scientific database, in order that questions involving definitions, possible errors, etc., can be discussed. ( The main table in the OEIS is a collection of over a quarter-million number sequences. H After 46 years of running the database, this came as a great relief to him. n This book contained 2372 sequences. ; is an Euler number. n Find out about their fascinating properties and take your time to think these through. ), Contributing a New Sequence, Comment or More Terms, Email Addresses, Getting in Touch With Authors, Timeline of Systematic Data and the Development of Computable Knowledge, https://oeis.org/w/index.php?title=Welcome&oldid=1639529, License Agreements, Terms of Use, Privacy Policy, If your favorite sequence isn't in the database, and if it is interesting, please submit it using the web page for, If you have stumped the database, you can try, Also worth visiting are the pages dealing with. NJAS waited a year, until the people remarked how useful they found the book, and how surprising In both math and English, a “sequence” refers to a group of things arranged in some particular order. NJAS's colleague David Applegate has also been of enormous help in getting the new system working. contain much useful information about analyzing an unknown sequence and many other topics. A. Sloane and S. Plouffe's Encyclopedia of Integer Sequences (1995) Click on any of the following to see examples of famous sequences in the On-Line Encyclopedia of Integer Sequences (the OEIS), then hit "Back" in your browser to return here: . n Thus with a value like 62, you multiply 6 x 2 and get 12. by at least 10000 entries per year (18000 new sequences were added in 2009 alone). (click here) Click on any of the following to see examples of famous sequences in the On-Line Encyclopedia of Integer Sequences (the OEIS), then hit "Back" in your browser to return here: For some other fascinating sequences see Pictures from the OEIS: The (Free) OEIS Store. The most famous property of this sequence is that $f_{n} = \frac{a_{n}}{a_{n+1}}$ generates all reduced positive rational numbers (in the same order as the … process submissions. A group of about 130 editors has been formed, whose job it is to review submissions before they become a permanent part of the OEIS. He noticed that although several books in the Cornell library contained sequences somewhat similar to this, this particular sequence was not mentioned. This is wrong, they were always called "punched cards". your work and you wish to reference it, the usual citation is something like this: The On-Line Encyclopedia of Integer Sequences, published electronically at https://oeis.org, [date], N. J. Mathematical equations, from the formulas of special and general relativity, to the Pythagorean theorem, are both powerful and pleasing in their beauty to many scientists. In the end, Russ Cox completely rewrote all the programs needed to maintain the database and answer queries - a huge task! Sums of sines and cosines arise in Fourier series. Mathematical Journeys: Carl Gauss and the Sum of an Arithmetic Series There's a famous (and probably apocryphal) story about the mathematician Carl Friedrich Gauss that goes something like this: Gauss was 9 years old, and sitting in his math class.

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