John Rhodes, Math Teacher at Senioritis.io

John Rhodes
August 16, 2023
Computational Mathematics

Numbers with a Given Prime Factor Sum

Consider the numbers $15$, $16$ and $18$: $15=3\times 5$ and $3+5=8$. $16 = 2\times 2\times 2\times 2$ and $2+2+2+2=8$. $18 = 2\times 3\times 3$ and $2+3+3=8$. $15$,...

John Rhodes
August 16, 2023
Computational Mathematics

Mirror Power Sequence

For two integers $n,e \gt 1$, we define an $(n,e)$-MPS (Mirror Power Sequence) to be an infinite sequence of integers $(a_i)_{i\ge 0}$ such that for all $i\ge...

John Rhodes
August 16, 2023
Computational Mathematics

Creative Numbers

Alice plays the following game, she starts with a list of integers $L$ and on each step she can either: remove two elements $a$ and $b$ from...

John Rhodes
August 16, 2023
Computational Mathematics

The Millionth Number with at Least One Million Prime Factors

Consider the natural numbers having at least $5$ prime factors, which don’t have to be distinct. Sorting these numbers by size gives a list which starts with:...

John Rhodes
August 16, 2023
Computational Mathematics

Special Partitions 2

An integer partition of a number $n$ is a way of writing $n$ as a sum of positive integers. Partitions that differ only by the order of...

John Rhodes
August 16, 2023
Computational Mathematics

Pythagorean Ant

Dave is doing his homework on the balcony and, preparing a presentation about Pythagorean triangles, has just cut out a triangle with side lengths 30cm, 40cm and...

John Rhodes
August 16, 2023
Computational Mathematics

Friend Numbers

Let’s call two numbers friend numbers if their representation in base $10$ has at least one common digit. E.g. $1123$ and $3981$ are friend numbers. Let $f(n)$...

John Rhodes
August 16, 2023
Computational Mathematics

Hallway of Square Steps

Peter moves in a hallway with $N + 1$ doors consecutively numbered from $0$ through $N$. All doors are initially closed. Peter starts in front of door...