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The Encyclopedia of Integer Sequences
"... This article gives a brief introduction to the OnLine Encyclopedia of Integer Sequences (or OEIS). The OEIS is a database of nearly 90,000 sequences of integers, arranged lexicographically. The entry for a sequence lists the initial terms (50 to 100, if available), a description, formulae, programs ..."
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This article gives a brief introduction to the OnLine Encyclopedia of Integer Sequences (or OEIS). The OEIS is a database of nearly 90,000 sequences of integers, arranged lexicographically. The entry for a sequence lists the initial terms (50 to 100, if available), a description, formulae, programs to generate the sequence, references, links to relevant web pages, and other
Sloane’s Gap: Do Mathematical and Social Factors Explain the Distribution of Numbers in the OEIS?
"... The Online Encyclopedia of Integer Sequences (OEIS) is a catalog of integer sequences. We are particularly interested in the number of occurrences of N(n) of an integer n in the database. This number N(n) marks the importance of n and it varies noticeably from one number to another, and from one num ..."
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The Online Encyclopedia of Integer Sequences (OEIS) is a catalog of integer sequences. We are particularly interested in the number of occurrences of N(n) of an integer n in the database. This number N(n) marks the importance of n and it varies noticeably from one number to another, and from one number to the next in a series. “Importance ” can be mathematically objective (2 10 is an example of an “important ” number in this sense) or as the result of a shared mathematical culture (10 9 is more important than 9 10 because we use a decimal notation). The concept of algorithmic complexity [6, 2, 7] (also known as Kolmogorov or KolmogorovChaitin complexity) will be used to explain the curve shape as an “objective ” measure. However, the observed curve does not conform to the curve predicted by an analysis based on algorithmic complexity because of a clear gap separating the distribution into two clouds of points. We shall call this phenomenon “Sloane’s gap”.