[seqfan] Add (to me) my even biggest digit

[Eric Angelini]

Hello SeqFans,
I'm playing around with integers to 
which one would add their biggest
even digit.

The rule:
> To get a(n+1), add to a(n) its biggest 
even digit. Iterate.

Is there an infinite such sequence?
If yes, it might start with a(1)=2:

E=2,4,8,16,22,24,28,36,42,46,52,54,
58,66,72,74,78,86,94,98,106,...

But I'm not sure E won't stop at some 
point.

This is because the sequence starting 
for instance with a(1)=804 indeed 
stops:

804,812,820,... ,884,892, 900 END.

Best,
É.