OEIS Sequences

Recreating plots from the sequences of the Online Encyclopedia of Integer Sequences. Stems off of a current project to create as many OEIS sequences on Python as I can.

A133058

This sequence came to my attention via a Numberphile video. It was coined as the “Fly straight, dammit” sequence by N. J. A. Sloane. The sequence is described by:

a_0 = a_1 = 1

a_n = a_{n-1}+n+1 if gcd(a_{n-1}, n) = 1

a_n = \frac{a_{n-1}}{gcd(a_{n-1}, n)} otherwise.

This sequence is interesting, because at n = 638, the sequence becomes quasi-periodic, meaning that it cycles between four similar but changing values.

A000188

This sequence is generated by calculating the largest square number d that divides a number n, and value a_n = \sqrt{d}. The sequence can also be generated as:

\sum_{d^2|n} \phi(d). d^2|n means that the sum runs over all numbers d^2 that divides n, and \phi is the Euler totient function

A274086

This is what I call an arcsinh-arithmic plot of A274086. The reason for the arcsinh function instead of a logarithm is because many of the values of A274086 are negative, undefined for the \log function. A274086 is described as:

a_n = [n*\tan{n}], where [n] is the nearest integer function.