Jud McCranie :

Doesn't rule 4 violate rule 3?

...

3) When adding a new integer to the sequence, put always the smallest unused so far

4) Always have in mind that the final sequence must be as long as possible -- this explains why the above 8th integer is "1122" and not "1111", for instance: "1111" would block the sequence very fast:

... yes, strictly speaking, you are right... well... you know what I had in mind... Let's merge the two rules together: 3) When adding a new integer to the sequence, put always the smallest unused so far which allows the final se- quence to be as long as possible. Does it fix the pb ? Best, É.