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|Two happy ends (Posted on 2011-03-07)
Consider a series of numbers, defined as follows:
Starting with any natural number, each member is a sum of the squares of the previous member`s digits.
Prove : The series always reaches either a stuck-on-one sequence: 1,1,1… or a closed loop of the following 8 numbers: 145,42,20,4,16,37,58,89, ...
Ex1: 12345,55,50,25,29,85,89,145….. etc
re(7): NOT enough by Gamer
Comment 11 of 11 |
(In reply to re(6): NOT enough by Gamer
Even 3*81=243 allows that a 3-digit number could produce another 3-digit number and there might be a cycle wholly within the 100-243 range.
Please see my post, showing a one way trend(descending function).
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