A recurring pattern in natural numbers of a certain property

Abstract

Natural numbers satisfying an unusual property are mentioned by the author in [5], in which their infinitude is also proved. In this paper, we start with an arbitrary natural number which is not a multiple of 10 and non-palindromic, form numbers by concatenating its decimal digits, and investigate which of them have the unusual property. In particular, the pattern of which of them have the unusual property recurs.