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Sequence with only 3 numbers (Posted on 2009-03-07) Difficulty: 2 of 5
Trying to define a way to generate the terms of a sequence, and starting with the number 5, I found, surprisingly, that the way I used generated this sequence:

5, 8, 11, 5, 8, 11, 5, 8, 11, ...

And these 3 numbers repeat in this order indefinitely.

Define a simple way to generate this sequence.

  Submitted by pcbouhid    
Rating: 2.0000 (1 votes)
Solution: (Hide)
My simple way was:
square the previous one, add the digits, plus 1.

Watch this:

2, 5, 8, 11,...
3, 10, 2, 5, 8, 11,...
4, 8, 11, 5, 8, 11,...
6, 10, 2, 5, 8, 11,...
7, 14, 17, 20, 5, 8, 11,...
22, 17, 20, 5, 8, 11,...
etc...

That is, no matter the "seed", I always get the periodic 5, 8, 11!!!!!

This can be proved? I didnīt find (yet) a counterproof!!

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: to the question posed in the official solution (spoiler)pcbouhid2009-03-11 18:11:41
Solutionto the question posed in the official solution (spoiler)Charlie2009-03-11 10:55:45
SolutionAnother simple way...Dej Mar2009-03-10 10:44:37
Hints/TipsMy solutionRobby Goetschalckx2009-03-10 05:24:31
re(2): How to solve it recursively? 10 excessGamer2009-03-10 02:03:31
Hints/Tipsre: How to solve it recursively? 10 excessAdy TZIDON2009-03-09 08:19:31
How to solve it recursively?Gamer2009-03-08 00:36:18
general solutionDaniel2009-03-07 22:59:00
RecurrenceHarry2009-03-07 19:22:16
SolutionWITHOUT MODAdy TZIDON2009-03-07 16:50:19
my solutionDaniel2009-03-07 14:09:34
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