On Black-Hole Numbers of Iteration of Digital Sextic Power Sum

For iteration of six power sum of digits there are two fixed points, one 2-circle, one 3-circle, one 4-circle, one 10-circles and one 30-circle. The probabilities for natural numers falling into each fixed point or circle by several times iterating of six power sum are unbalanced. In it about 48.7% fall into 30-circle, about 39.3% into 10-circle, about 11.4% into 3-circle, the probability of falling into other circles and two fixed points is...