3 papers
math.NT2024
On the structure of the complement $\overline{\Mfib}$ of the set $\Mfib$ of fibbinary numbers in the set of positive natural numbers
A. J. Macfarlane
The set $\Mfib$ of fibbinary numbers is defined via a bijection between the set $\BB{N}$ of natural numbers and $\Mfib$. Since the elements of $\Mfib$ do not exhaust $\BB{N}$, the…
math.CO2024
On the fibbinary numbers and the Wythoffarray
A. J. Macfarlane
This paper defines the set fib of fibbinary numbers and displays its structure in the form of a table of a specialised type, and in array form. It uses the Zeckendorf representatio…
math.NT2024
Pi Formulas: some smooth stones on the beach of rough numbers
A. J. Macfarlane
This article is about Pi Formulas, infinite series of fractions which sum to multiples of Pi. Each such one can be associated with a unique set of rough numbers, where is…