Sloane's Gap. Mathematical and Social Factors Explain the Distribution of Numbers in the OEIS

TL;DR

This paper investigates the distribution of numbers in the OEIS, revealing a distinct gap in the frequency distribution and exploring the mathematical and social factors behind this pattern.

Contribution

It introduces the concept of 'Sloane's Gap' in the distribution of OEIS numbers and analyzes the factors contributing to this phenomenon.

Findings

The frequency distribution decreases rapidly with increasing n.

A clear gap, 'Sloane's Gap', separates two regions in the distribution.

Mathematical explanations account for the overall decrease, but social factors influence the gap.

Abstract

The Online Encyclopedia of Integer Sequences (OEIS) is made up of thousands of numerical sequences considered particularly interesting by some mathematicians. The graphic representation of the frequency with which a number n as a function of n appears in that database shows that the underlying function decreases fast, and that the points are distributed in a cloud, seemingly split into two by a clear zone that will be referred to here as "Sloane's Gap". The decrease and general form are explained by mathematics, but an explanation of the gap requires further considerations.