All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Sequence with only 3 numbers (Posted on 2009-03-07)
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.

 See The Solution Submitted by pcbouhid Rating: 2.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 My solution | Comment 8 of 11 |
Using the function SOD (sum of digits in base 10), we can express it recursively as:
f(n) = SOD(f(n-1)² + 1); f(0) = 5
We get: 5, SOD(26) = 2+6 = 8; SOD(65) = 6+5 = 11; SOD(122) = 1+2+2 = 5
Sequences for other f(0):
* 0, 1, 2, 5, 8, 11, ...
* 3, 10, 2, 5, 8, 11, ...
* 4, 8, 11, 5, ...
* 6, 10, 2, 5, 8, 11, ...
* 7, 5, 8, 11, ...
It seems that every sequence ends up in the given sequence, which supports the claim that this might have been the generating function pcbouhid is looking for.

 Posted by Robby Goetschalckx on 2009-03-10 05:24:31

 Search: Search body:
Forums (0)