On a conjecture of John Hoffman regarding sums of palindromic numbers

TL;DR

This paper disproves a conjecture by John Hoffman that every large natural number can be expressed as the sum of three palindromic numbers with specific size constraints.

Contribution

It provides a counterexample to Hoffman's conjecture, showing that the proposed representation does not hold universally for large numbers.

Findings

Counterexamples to Hoffman's conjecture.

The conjecture does not hold for all sufficiently large numbers.

Abstract

We disprove the conjecture that every sufficiently large natural number $n$ is the sum of three palindromic natural numbers where one of them can be chosen to be the largest or second largest palindromic natural number smaller than or equal to $n$.