15 citations · 105 across the 66 of their papers we have counts for
8 papers · 1 filter
A Taxonomy of Morphic Sequences
Jean-Paul Allouche, Julien Cassaigne, Jeffrey Shallit +1
In this note we classify sequences according to whether they are morphic, pure morphic, uniform morphic, pure uniform morphic, primitive morphic, or pure primitive morphic, and for…
When is an automatic set an additive basis?
Jason Bell, Kathryn Hare, Jeffrey Shallit
We characterize those -automatic sets of natural numbers that form an additive basis for the natural numbers, and we show that this characterization is effective. In additio…
More Infinite Products: Thue-Morse and the Gamma function
Jean-Paul Allouche, Samin Riasat, Jeffrey Shallit
Letting denote the Thue-Morse sequence with values , we note that the Woods-Robbins product $$ \prod_{n \geq 0} \left(\frac{2n+1}{2n+2}\right)^{(-1)^{t_n}} = 2^{-1/2}…
The Generalized Nagell-Ljunggren Problem: Powers with Repetitive Representations
Andrew Bridy, Robert J. Lemke Oliver, Arlo Shallit +1
We consider a natural generalization of the Nagell-Ljunggren equation to the case where the qth power of an integer y, for q >= 2, has a base-b representation that consists of a le…
Sums of Palindromes: an Approach via Automata
Aayush Rajasekaran, Jeffrey Shallit, Tim Smith
Recently, Cilleruelo, Luca, & Baxter proved, for all bases b >= 5, that every natural number is the sum of at most 3 natural numbers whose base-b representation is a palindrome. Ho…
Undecidability and Finite Automata
Jörg Endrullis, Jeffrey Shallit, Tim Smith
Using a novel rewriting problem, we show that several natural decision problems about finite automata are undecidable (i.e., recursively unsolvable). In contrast, we also prove thr…