Absolutely symmetric trees and complexity of natural number

Abstract

We consider the rooted trees which not have isomorphic representation and introduce a conception of complexity a natural number also. The connection between quantity such trees with $n$ edges and a complexity of natural number $n$ is established. The recurrent ratio for complexity of a natural number is founded. An expression for calculation of difference complexities of two adjacent natural numbers is constructed. It is proved that this difference equal 1 if and only if a natural number is simple. From proved theorems it follows corollaries.