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.

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