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.

9 pages