On Black-Hole Numbers of Iteration of Digital Biquadratic Power Sum in the Ternary, Quinary or Quindenary 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 one fixed point and two 2-circles in ternary; four fixed points and three 4-circles in quinary; seven fixed points, two 2-circles, one 3-circle, one 9-circle and one 63-circle in quindenary.