Porous Numbers

TL;DR

This paper introduces the concept of porous numbers, characterizes them, and identifies all such numbers less than 1000, revealing their specific properties and limitations.

Contribution

It defines porous numbers and proves that only five such numbers less than 1000 exist, providing a complete classification within this range.

Findings

11, 37, 74, 101, and 121 are the only porous numbers below 1000

Porous numbers are characterized by digit and divisor properties

The paper establishes criteria for identifying porous numbers

Abstract

The concept of porous numbers is presented. A number $k$ which is not a multiple of 10 is called {\it porous} if every number $m$ with sum of digits = $k$ and $k$ a divisor of both $m$ and digit reversal of $m$ has a zero in its digits. It is proved that 11, 37, 74, 101 and 121 are the only porous numbers smaller than 1000.