On-Line Encyclopedia of Integer Sequences

The On- Line Encyclopedia of Integer Sequences ( OEIS; German Online Encyclopedia of Integer Sequences ) is an English-language database of integer sequences (integer sequences) that can be searched on the Internet. It is a tool frequently used and important source in mathematical research.

The database

Content

The Encyclopedia is a database that collects information on integer sequences that are in the mathematics of interest. The database contained the end of June 2013, 226,000 sequences. Each entry contains the first followers and a motivation for this episode, keywords, references, hyperlinks, programs for Mathematica, Maple, Pari and other evidence to produce a result, references to related sequences and much more.

The database can be searched both by keywords and by the subsequences.

Internal format

The consequences are described in the database in a pure ASCII line format. Each line begins with a percent sign, a letter code for the type of part information, the number of the sequence and the respective partial information. Sequence A004002 is stored like this:

% I A004002 M3010 % S A004002 1,3,15,3814279 % N A004002 Benford numbers: a (n ) = e ^ e ^ ... ^ e (n times) rounded to nearest integer. % C A004002 The next term, a ( 4) ~ 2.3315 * 10 ^ 1.65652 million, 1,656,521 decimal digits Has and is THEREFORE too large to be included. [ Rephrased by _M. F. Hasler_, May 01 2013 ] % D NJA Sloane and Simon Plouffe A004002, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). % D A004002 PR Turner, Will the "real " real arithmetic please stand up?, Notices Amer. Math Soc., 38 (1991 ), 298-304. % Y A004002 Cf. A056072, A225053. Nonn % K A004002 % O A004002 0.2 % A A004002 _N. J. A. Sloane_. importance

The On- Line Encyclopedia of Integer Sequences is regarded by many as the most important reference in the field of integer sequences. Most of the work in which the numbers like this occur, contain references to the database.

The database is the world's largest of its kind and has thousands of requests every day. Your success is partly due to the fact that the data can be accessed for free.

History

Neil Sloane began in the 1960s in order to collect integer sequences to facilitate his work in combinatorics. He published two parts of the database in book form:

These books were enthusiastically received, and after the second publication of other mathematicians began to provide him with additional sequences. The collection was too large to be published once as a book, and when the database contained 16,000 entries, Sloane decided to make the data available online, at first as an e -mail service (1995) and soon thereafter as a web service ( 1996). The database is growing since then to about 10,000 entries per year.

After Neil Sloane had its database managed for almost 40 years, a group of editors in 2002 took over much of the maintenance work. Supreme authority for acceptance or rejection of an entry remains Neil Sloane as before, and since the beginning of 2006, the common acceptance of new episodes changed in a relatively restrictive policy.

As an offshoot of his database work founded Sloane, 1998, the Journal of Integer Sequences. In October 2009, the intellectual property and the operation of the server went to, which was established to OEIS Foundation.

Sloane 's Gap

You Represents a chart in as many all listed in the database sequences is a natural number n appears each, followed by the dot plot for this frequency Nn approximate the curve Nn = 253 million / n1, 33 A curiosity in this cloud / curve represents a gap ( engl. gap) in this, which is particularly noticeable for the numbers 300-10000. This gap divides seemingly mathematically interesting, present in very many episodes of the numbers uninteresting. Thus, there are, for example, almost all ( 99.7 %) of the emerging 300-10000 prime numbers in the upper part of the curve. Also, approximately 95 % of all square numbers 300-10000 can be found there. While the curve itself corresponds to the expected value, the gap has so far been unable to explain in a purely mathematical way. Therefore, it is possibly also due to the popularity of certain sequences of numbers and thus to social factors.