Thomas Luckner

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20222026

most citedConsecutive primes which are widely digitally delicate and Brier numbers

1 citations · 1 across the 4 of their papers we have counts for

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math.NT2026

$d$ -Translated Unit Sensitive Primes

Thomas Luckner, R. James Philpott

A nonnegative integer $n$ is $d$ -translated unit sensitive when appending $d$ zeros to the right of the number and changing the unit digit to any possible unit digit (so long as th…

math.NT2023

On $n^{th}$ order Euler polynomials of degree $n$ that are Eisenstein

Michael Filaseta, Thomas Luckner

For $m$ an even positive integer and $p$ a prime, we show that the generalized Euler polynomial $E_{m p}^{(m p)} (x)$ is in Eisenstein form with respect to $p$ if and only if $p$ does…

math.NT2023

Generalized Sierpiński Numbers

Michael Filaseta, Robert Groth, Thomas Luckner

A Sierpiński number is a positive odd integer $k$ such that $k \cdot 2^{n} + 1$ is composite for all positive integers $n$ . Fix an integer $A$ with $2 \leq A$ . We show that there exis…

math.NT2022★ 1 cited

Consecutive primes which are widely digitally delicate and Brier numbers

Michael Filaseta, Jacob Juillerat, Thomas Luckner

Making use of covering systems and a theorem of D. Shiu, the first and second authors showed that for every positive integer $k$ , there exist $k$ consecutive widely digitally delic…

d-Translated Unit Sensitive Primes

On nth order Euler polynomials of degree n that are Eisenstein

Generalized Sierpiński Numbers

Consecutive primes which are widely digitally delicate and Brier numbers

$d$ -Translated Unit Sensitive Primes

On $n^{th}$ order Euler polynomials of degree $n$ that are Eisenstein