[pdurrant]

Originally Posted by obs20

Maybe this is it?

Spoiler:

8,4,2,1 after that it repeats 2,1,.....The rule if the number is odd x=x+(x+1)/2 if the number is even the next element is x/2

Yes, spot on. The interesting thing about the rules for this sequence is that it always seems to end up the same way no matter what number you start with. But — no-one has managed to prove that it works for all positive integers.

Although not quite the same, the rules for my sequence are effectively the same as for the sequence in the Collatz Conjecture, just missing out some terms.

http://en.wikipedia.org/wiki/Collatz_conjecture

But do see if you can work out the sequence yourself before 'cheating'.