A note on OEIS sequence A111384
$A111384(n)$ is an upper bound for the number of primes that can be written as a sum of three distinct primes selected from a set of $n$ primes. Is this bound sharp?
math.CO↗
arXiv subjects
Markus Sigg
Publications and source records attributed to Markus Sigg.
On the cluster structures in Collatz level sets
The cluster structures that can be observed in the first few level sets of the Collatz tree are maintained through all its levels, provided that the orbit steadiness \[ \prod_{\substack{k \in R(n)\\ k \equiv 4\ (\mathrm{mod}\ 6)}} \frac{k-1}k \] of the elements $n$ of the Collatz tree is suitably bounded from below, where $R(n)$ denotes the Collatz orbit of $n$.
math.GM↗
Gasper's determinant theorem, revisited
Let $n \ge 2$ be a natural number, $M$ a real $n \times n$ matrix, $s$ the sum of the entries of $M$ and $q$ the sum of their squares. With $α:= s/n$ and $β:= q/n$, Gasper's determinant bound says that $ |\det M| \le β^{n/2}$, and in case of $α^2 \ge β$: $$|\det M| \le |α| \left(\frac{nβ-α^2}{n-1}\right)^{\frac{n-1}2}$$ This article gives a corrected proof of Gasper's theorem and lists some more applications.
math.CO↗
On a conjecture of John Hoffman regarding sums of palindromic numbers
We disprove the conjecture that every sufficiently large natural number $n$ is the sum of three palindromic natural numbers where one of them can be chosen to be the largest or second largest palindromic natural number smaller than or equal to $n$.
math.NT↗