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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(6): NOT enough by Gamer
| Comment 8 of 11 |
(In reply to re(5): NOT enough by Gamer
by Ady TZIDON)
"Jer understood that only 99 (and not 999 ) numbers have to be examined (need I explain WHY?) "
I have realized that 999 was overkill, but I don't see that 99 would suffice. 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. Certainly a proof would have to spell out what may seem obvious to you.
Posted by Charlie
on 2011-03-09 15:20:18
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