# A Class of Exponential Sequences with Shift-Invariant Discriminators

## TL;DR

This paper introduces a class of exponential sequences whose discriminators remain unchanged under any shift, revealing a unique invariance property in the structure of these sequences.

## Contribution

It identifies and characterizes exponential sequences with shift-invariant discriminators, a novel property not previously documented.

## Key findings

- Discovered a class of exponential sequences with shift-invariant discriminators
- Proved the invariance property holds for these sequences
- Provided theoretical framework for analyzing discriminator invariance

## 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.