1 citations · 3 across the 8 of their papers we have counts for
8 papers
The appearance function for paper-folding words
Rob Burns
We provide a complete characterisation of the appearance function for paper-folding sequences for factors of any length. We make use of the software package {\tt Walnut} to establi…
Factorials and Legendre's three-square theorem: II
Rob Burns
Let denote the set of integers such that cannot be written as a sum of three squares. Let denote . We establish an exact formul…
Factorials and Legendre's three-square theorem
Rob Burns
We provide a necessary and sufficient condition for to be a sum of three squares. The condition is based on the binary representation of and can be expressed by the operat…
Extremely symmetric primes
Rob Burns
We introduce extremely symmetric primes and provide some elementary properties of these.
Counting birthday collisions using partitions
Rob Burns, Jen McKenzie
We use partitions to provide some formulae for counting s-collisions and other events in various forms of the Birthday Problem.
Representing numbers as the sum of squares and powers in the ring
Rob Burns
We examine the representation of numbers as the sum of two squares in for a general positive integer . Using this information we make some comments about the dens…