I have some kind of idea...

I'm coming over to CANADA next winter for holidays. Let me know which words, I European, shouldn't use

I thought the "&" operator would keep (isolate) only bits 0-3 of "Value" but I was wrong. For the fours LSB, I should have written $0F.

What is then this "& $03" for?

As you suggested, I modified my code as (I've added the "Value = R_V0" in le loop):
Code:
Value Var WORD
Store_MEM:
FOR Counter = 0 to 20
   RANDOM Value
   R_V0 = (value & $03)
   IF Mem_L > 3 THEN READ Mem_L - 3, R_V1 'Do not allow more than 3 same # in a row
   IF R_V1 = R_V0 THEN STORE_MEM
   WRITE Mem_L, R_V0
   Mem_L = Mem_L + 1
   Value = R_V0
NEXT
Nevertheless, I always get the same number sequence over again.