# Distribution of Nonzero Digits in a Greedy Sequence of Powers of Two

## TL;DR

This paper investigates the digit distribution in a specially constructed sequence of powers of two, revealing how trailing digits can be preserved and zeroes maximized between nonzero digits using elementary methods.

## Contribution

It introduces a method to construct powers of two that preserve trailing digits and maximize zeroes between nonzero digits, providing new insights into digit distribution patterns.

## Key findings

- Sequence can preserve trailing digits
- Maximizes zeroes between nonzero digits
- Provides heuristic for trailing digit patterns

## Abstract

Understanding the distribution of digits in the expansions of perfect powers in different bases is difficult. Rather than consider the asymptotic digit distributions, we consider the base-10 digits of a restricted sequence of powers of two. We apply elementary methods to show that this sequence of powers of two can be constructed to preserve trailing digits while locally maximizing the number of zeroes between nonzero digits. We also provide a heuristic description of the trailing digits of these powers of two.