A Class of Exponential Sequences with Shift-Invariant Discriminators

2017/02/02 by Haque, Sajed, Shallit, Jeffrey
#Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1702.00802

Abstract

The discriminator of an integer sequence s = (s(i))_i>=0, introduced by Arnold, Benkoski, and McCabe in 1985, is the function D_s(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 present a class of exponential sequences that have the special property that their discriminators are shift-invariant, i.e., that the discriminator of the sequence is the same even if the sequence is shifted by any positive constant.

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