[seqfan] Cumulative multiplication

[Eric Angelini]

Hello SeqFans, 
take an integer N like 2188;
create this (repeated) pattern:
2 1 8 8 2 1 8 8 2 1 8 8 2 1 8 8 ...
Insert the "multiply sign" everywhere:
2*1*8*8*2*1*8*8*2*1*8*8*2*1*8*8*...
Look at the partial cumulative 
multiplications -- if N reappears, 
you have a hit:

2*1=2
2*1*8=16
2*1*8*8=128
2*1*8*8*2=256
2*1*8*8*2*1=256
2*1*8*8*2*1*8=2048
2*1*8*8*2*1*8*8=16384
...
We have obviously a miss here.
What would be the first hit for N > 10?

Best,
É.