Building off the ideas of Erdós, Sierpiński, Riesel, and more

Abstract: In 1950, Erd\H{o}s proved there are infinitely many odd integers that are not of the form $2^k + p$, where $p$ is a prime. In 1956, using similar methods, Riesel proved there are infinitely many odd integers $k$ such that $k\cdot 2^n - 1$ is composite for all positive integers~$n$. Then, in 1960, Sierpi\'{n}ski proved that there are infinitely many odd integers $\ell$ such that $\ell\cdot 2^n + 1$ is composite for all positive integers $n$. We will discuss various other related results such as how some classical sequences like Fibonacci, triangular, and more intersect the set of all possible Reisel and/or Sierpiński numbers.

number theory

Audience: researchers in the topic

Combinatorial and additive number theory seminar (CANT 2026)