Arnold's Digitized Summation Technique and Generalized Notion of the Collatz Conjecture

Abstract

Many mathematicians have studied Collatz conjecture and its applications; however, it remains an open problem in the field of number theory and is interesting to study. In the present paper, we give a generalized notion of Collatz conjecture as per the new notion of Arnold's Digitized Summation Technique which involves adding digits of a number until we are left with only one single digit. Moreover, a detailed description of the first twenty positive integers is given.