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.