O. Cain

collaborators

5 papers

math.NT2020

Inventory Loops (i.e. Counting Sequences) have Pre-period $2 max S_{1} + 60$

Onno M. Cain, Sela T. Enin

An Inventory Sequence $(S_{0}, S_{1}, S_{2}, ...)$ is the iteration of the map $f$ defined roughly by taking an integer to its numericized description (e.g. $f (1381) = 211318$ since "$1381…

math.HO2019

Prime-bounded subwords

Onno M. Cain

In the number $373$ all subwords ( $3$ , $7$ , $37$ , $73$ , and $373$ ) are prime. Similarly, in $9719$ all subwords are divisible by at most one prime. And similarly again in $73197979…

math.HO2019

The Exceptional Selfcondensability of Powers of Five

O. M. Cain

We show any power of five may be expressed arithmetically with the digits of its decimal representation. We also show powers of five (in decimal) contain any amount of zeros in a r…

math.RA2019

Gaussian Integers, Rings, Finite Fields, and the Magic Square of Squares

Onno Cain

We show the 3 by 3 magic square of squares problem equivalent to solving quartic polynomials with certain factorization constraints over an abelian extension of the rationals. We a…