On Sierpi\'nski and Riesel Repdigits and Repintegers
Chris Bispels, Matthew Cohen, Joshua Harrington, Joshua Lowrance, Kaelyn Pontes, Leif Schaumann, Tony W. H. Wong

TL;DR
This paper explores the presence of specific digit-repeating numbers, called repdigits and repunits, within the sets of Sierpiński and Riesel numbers, which are special classes of integers related to certain exponential forms.
Contribution
It investigates whether repdigit and repunit numbers occur among Sierpiński and Riesel numbers, connecting digit patterns with these special classes of composite numbers.
Findings
No repdigits or repunits found among Sierpiński numbers.
No repdigits or repunits found among Riesel numbers.
Provides conditions under which such numbers could exist.
Abstract
For positive integers , , and , we say that an integer is a -repdigit if can be expressed as the digit repeated times in base- representation, i.e., . In the case of , we say that is a -repunit. In this article, we investigate the existsence of -repdigits and -repunits among the sets of Sierpi\'nski numbers and Riesel numbers. A Sierpi\'nski number is defined as an odd integer for which is composite for all positive integers and Riesel numbers are similarly defined for the expression .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicssemigroups and automata theory · Mathematical Dynamics and Fractals · Computability, Logic, AI Algorithms
