Abstract:Abstract. There are different periodic and fixed points under iteration of sum of squares or cubes of digits of positive integer in different positional systems. On the iteration of sum of squares of digits, in binary and quaternary these points all converge to fixed point 1. There are three fixed points and one 2-circle in ternary, three fixed points and one 3-circle in quinary, one fixed points and one 8-scircle in senary, five fixed points and two 4-circles in septenary, three fixed points and two 2-circles… Show more
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