Calculation of Position for Odd Numbers to Change Length in Valuated Binary Tree

The paper first investigates the node in tree on how the length of digits changes when the node is in decimal expression and presents a method to calculate the position where the number of digits is changed. Several formulas are proved with detailed mathematical reasoning. The paper then demonstrates application of the method in analyzing big integers such as the RSA numbers. An example to analyze RSA-155 is exhibited to make readers have a more concrete understanding of the method. Experiments show the method is helpful to reduce searching time when searching for a data set of numbers with equal length.