On the Black-Hole Numbers of the Iteration of Digital Biquadratic Sum in the Quanternary, Octonary or Hexadecimal System

Abstract

There are different periodic and fixed points under the iteration of biquadratic sum of digits of positive integer in different carry systems. There are three fixed points and one 2-circle in quanternary, seven fixed points in octonary, two fixed points, one 2-circle and one 6-circle in hexadecimal system.