On the Construction of Some Lychrel Numbers

Abstract

For decades now, Lychrel numbers have been a passionate topic for many researchers. Their construction leads to the construction of palindromes which are important in biotechnology, notably in DNA and RNA sequences, as they help to stabilize these types of molecules (5). In some basis, the existence of these numbers has been proven. It is the case in base 2. In others, just candidates are known. It is the case in base 10 where a list of Lychrel candidates (smaller than 10000) has been computed. The question answered in this piece of paper is presented as follow: is there a non trivial relation between Lychrel numbers or Lychrel candidates such that some of them can be obtained from others via these relations? We answer this question by proposing in bases between 3 and 10 some mathematical approaches of extracting new Lychrel numbers or new Lychrel candidates from others, and by applying these approaches on some cases, notably in base 4 and base 10