a(1)=1, a(2)=2; thereafter successive products of pairs of digits make further digits.
1, 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, 6, 4, 6, 4
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Mon Aug 8 12:14:12 CEST 2011 [seqfan] Summer sequence boot camp : adding digits to the right... and more