Figure 1. The number of entries into the OEIS for each number between 1-10,000. |

The Online Encyclopaedia of Integer Sequences (OEIS) is a
database that lists the first few numbers in various whole number sequences.
For example, multiples of 3 or square numbers. Each number has a value for the
frequency that it occurs in the database e.g. the number 1729 occurs in the
database 653 times.

Figure 1 displays a distribution of the number of occurrences
that a number has in the database. There are two clear groups: group 0 and
group 1. Group 0 consists of numbers with fewer entries in the database than
group 1. Group 1 has some interesting properties. It consists mostly of prime
numbers and squares. In fact, 70% of the numbers in group 1 being either a
square or prime. This interested mathematicians, could this effect be explained
mathematically?

Gauvrit, Delahaye and Zenil (2011) were interested in
explaining this gap, with a particularly emphasis on mathematical complexity
being the driving force. The reasoning behind this is that simple sequences can
be broken up in multiple ways. For example, square numbers form a simple
sequence and can be broken into more sequences very simply, e.g. squared odd
numbers or squared even numbers. However, this explanation proves inadequate as
it can explain some variation in the numbers but does not predict a gap.

The researchers instead concluded that there was some
interaction between the simplicity of numbers and the mathematicians recording
sequences into the OEIS. The driving force for this effect may be the
availability heuristic, which states that the ease of recall is used as an
indicator of importance (Tversky & Kahneman, 1973). This may suggest that
when mathematicians are creating new sequences, their starting point may be the
square numbers or primes and that leads to these numbers having a higher number
of entries in the OEIS.

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