Proceedings of the 3rd International Conference on Material, Mechanical and Manufacturing Engineering 2015
DOI: 10.2991/ic3me-15.2015.327
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Periodic Points Under Iteration of Sum of Squares or Cubes of Digits in Some Positional Systems

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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