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View article: A Note on the Ramanujan Machine
A Note on the Ramanujan Machine Open
The Ramanujan Machine project detects new expressions related to constants of interest, such as $ζ$ function values, $γ$ and algebraic numbers (to name a few). In particular the project lists a number of conjectures involving even and odd …
View article: The Multiplicative Persistence Conjecture Is True for Odd Targets
The Multiplicative Persistence Conjecture Is True for Odd Targets Open
In 1973, Neil Sloane published a very short paper introducing an intriguing problem: Pick a decimal integer $n$ and multiply all its digits by each other. Repeat the process until a single digit $Δ(n)$ is obtained. $Δ(n)$ is called the \te…
View article: Near-Optimal Pool Testing under Urgency Constraints
Near-Optimal Pool Testing under Urgency Constraints Open
Detection of rare traits or diseases in a large population is challenging. Pool testing allows covering larger swathes of population at a reduced cost, while simplifying logistics. However, testing precision decreases as it becomes unclear…
New number-theoretic cryptographic primitives Open
This paper introduces new prq-based one-way functions and companion signature schemes. The new signature schemes are interesting because they do not belong to the two common design blueprints, which are the inversion of a trapdoor permutat…
A Fractional $3n+1$ Conjecture Open
In this paper we introduce and discuss the sequence of \emph{real numbers} defined as $u_0 \in \mathbb R$ and $u_{n+1} = Δ(u_n)$ where \begin{equation*} Δ(x) = \begin{cases} \frac{x}{2} &\text{if } \operatorname{frac}(x)
The Look-and-Say The Biggest Sequence Eventually Cycles Open
In this paper we consider a variant of Conway's sequence (OEIS A005150, A006715) defined as follows: the next term in the sequence is obtained by considering contiguous runs of digits, and rewriting them as $ab$ where $b$ is the digit and …
Stuttering Conway Sequences Are Still Conway Sequences Open
A look-and-say sequence is obtained iteratively by reading off the digits of the current value, grouping identical digits together: starting with 1, the sequence reads: 1, 11, 21, 1211, 111221, 312211, etc. (OEIS A005150). Starting with an…
Optimal Covid-19 Pool Testing with a priori Information Open
As humanity struggles to contain the global Covid-19 infection, prophylactic actions are grandly slowed down by the shortage of testing kits. Governments have taken several measures to work around this shortage: the FDA has become more lib…
New number-theoretic cryptographic primitives Open
This paper introduces new p r q -based one-way functions and companion signature schemes. The new signature schemes are interesting because they do not belong to the two common design blueprints, which are the inversion of a trapdoor permu…