2022/09/07 by Sajed Haque, Haque, Sajed
Computer Science · Mathematics · #Analytic Number Theory Research #Coding theory and cryptography #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2209.03265
openalex publication_date 2022/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The discriminator of an integer sequence s = (s(i))i ≥ 0, introduced by Arnold, Benkoski, and McCabe in 1985, is the function Ds (n) that sends n to the least integer m such that the numbers s(0), s(1), …, s(n - 1) are pairwise incongruent modulo m. In this note, we try to determine all quadratic sequences whose discriminator is given by p\lceil logp n \rceil for prime p, i.e., the smallest power of p which is ≥ n. We determine all such sequences for p = 2, show that there are none for p ≥ 5, and provide some partial results for p = 3.