Computational Mathematics

John Rhodes
August 16, 2023
Computational Mathematics

Shortest Distance Among Points

We create an array of points $P_n$ in a two dimensional plane using the following random number generator: $s_0=290797$ $s_{n+1}={s_n}^2 \bmod 50515093$ $P_n=(s_{2n},s_{2n+1})$ Let $d(k)$ be the...

John Rhodes
August 16, 2023
Computational Mathematics

Group by Value

A pack of cards contains $4n$ cards with four identical cards of each value. The pack is shuffled and cards are dealt one at a time and...

John Rhodes
August 16, 2023
Computational Mathematics

Mezzo-forte

$4n$ people stand in a circle with their heads down. When the bell rings they all raise their heads and either look at the person immediately to...

John Rhodes
August 16, 2023
Computational Mathematics

XOR-Powers

We use $x\oplus y$ to be the bitwise XOR of $x$ and $y$. Define the XOR-product of $x$ and $y$, denoted by $x \otimes y$, similar to...

John Rhodes
August 16, 2023
Computational Mathematics

Bitwise Recursion

Let $b(n)$ be the largest power of 2 that divides $n$. For example $b(24) = 8$. Define the recursive function: \begin{align*} \begin{split} A(0) &= 1\\ A(2n) &=...

John Rhodes
August 16, 2023
Computational Mathematics

XOR-Primes

We use $x\oplus y$ for the bitwise XOR of $x$ and $y$. Define the XOR-product of $x$ and $y$, denoted by $x \otimes y$, similar to a...

John Rhodes
August 16, 2023
Computational Mathematics

Rational Recurrence Relation

The following is a function defined for all positive rational values of $x$. $$ f(x)=\begin{cases} x &x\text{ is integral}\\ f(\frac 1{1-x}) &x \lt 1\\ f\Big(\frac 1{\lceil x\rceil...

John Rhodes
August 16, 2023
Computational Mathematics

Reversible Prime Squares

Both $169$ and $961$ are the square of a prime. $169$ is the reverse of $961$. We call a number a reversible prime square if: It is...