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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
Ex2: 66,72,53,34,25,29,85,89,145…
Ex3: 91,10,1,1,1…..

 See The Solution Submitted by Ady TZIDON No Rating

 Subject Author Date re(7): NOT enough by Gamer Ady TZIDON 2011-03-09 19:46:55 re: How the numbers get there- I EXPLAIN Ady TZIDON 2011-03-09 19:43:15 How the numbers get there Charlie 2011-03-09 15:39:48 re(6): NOT enough by Gamer Charlie 2011-03-09 15:20:18 re(5): NOT enough by Gamer Ady TZIDON 2011-03-09 07:17:33 re(4): solution NOT enough Gamer 2011-03-09 04:46:40 re(3): solution NOT enough Jer 2011-03-08 10:08:47 re(2): solution NOT enough Gamer 2011-03-08 05:17:54 re: solution NOT enough Ady TZIDON 2011-03-07 17:57:23 solution Charlie 2011-03-07 15:15:40 solution enough Jer 2011-03-07 14:32:20

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