Abstract / Synopsis

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 (also known as Kolmogorov or Kolmogorov-Chaitin 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”.



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© Nicolas J.-P. Gauvrit, Jean-Paul Delahaye and Hector Zenil

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