A093094

[Klaus Brockhaus]

http://www.research.att.com/~njas/sequences/A093094

A093094: "Products into digits": start with a(1)=2, a(2)=2; repeatedly adjoin digits of product of previous two terms. 
2,2,4,8,3,2,2,4,6,4,8,2,4,2,4,3,2,1,6,8,8,8,1,2,6,2,6,4,8,...

A comment says that the sequence is not periodic. Perhaps this is obvious, but not to me.
Is there a simple proof? Does it follow from a well-known theorem?

Can someone help?

Klaus