A certain thing can be done with the list 2, 2, 1, 1, 0 to obtain the sequence
2, 2, 2, 2, 1, 1, 1, 1, 0, 2, 2, 1, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 0, 2, 2, 2, 1, 1, 1, 1, 0, 0, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 0, 2, 2, 0, 0, 2, 2, 2, 1, 1, 1, 0, 0, 2, 2, 2, 2, 1, 1, 0, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 0, 2, 1, 1, 0, 0, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 0, 0, 2, 2, 2, 2, 1, 1, 1, 0, 2, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 2, 2, 2, 1, 1, 1, 0, 0, 2, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 0, 0, 2, 2, 1, 0, 0, 2, 2, 1, 0, 2, 2, 1, 2, 2, 2, 2, 1, 1, 1, 0, 2, 1, 1, 0, 0, 2, 2, 2, 2, 1, 1, 0, 0, 2, 2, 2, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 2, 2, 1, 1, 1, 0, 0, 2, 2, 2, 2, 1, 1, 1, 0, 2, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 2, 2, 2, 1, 2, 2, 2, 2, 1, 1, 1, 0, 2, 1, 1, 0, 2, 1, 1, 0, 2, 2, 1, 1, 1, 0, 2, 1, 1, 0, 0, 2, 2, 2, 2, 1, 1, 0, 2, 2, 1, 1, 0, 2, 1, 1, 0, 1, 1, 1, 1, 0, 0, 2, 2, 2, 1, 1, 1, 1, 0, 0, 2, 2, 1, 0, 0, 2, 2, 1, 1, 0, 2, 1, 1, 1, 1, 0, 2, 2, 1, 1, 0, 2, 1, 1, 0, 0, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2, 1, 0, 2, 2, 1, 2, 2, 2, 2, 1, 1, 1, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 1, 0, 0, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 1, 1, 1, 0, 2, 2, 2, 1, 1, 1, 1, 0, 0, 2, 2, 1, 1, 1, 1, 0, 0, 2, 1, 1, 1, 1, 0, 2, 2, 2, 2, 1, 1, 1, 1, 0, 2, 2, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 2, 1, 1, 0, 0, 2, 2, 1, 1, 1, 1, 0, 0, 2, 2, 2, 1, 1, 1, 0, 0, 2, 2, 2, 1, 1, 1, 1, 0, 0, 2, 2, 2, 1, 1, 0, 2, 2, 1, 1, 1, 1, 0, 2, 2, 1, 2, 2, 2, 2, 1, 1, 0, 2, 1, 1, 0, 2, 2, 1, 0, 0, 2, 2, 2, 2, 1, 1, 1, 0, 2, 2, 1, 1, 0, 0, 2, 2, 0, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 0, 2, 2, 0, 0, 2, 2, 2, 2, 1, 1, 0, 1, 1, 1, 1, 0, 0, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 0, 2, 2, 1, 0, 0, 2, 2, 2, 1, 1, 1, 1, 0, 0, 2, 2, 2, 1, 0, 0, 2, 2, 1, 1, 0, 0, 2, 1, 1, 0, 0, 2, 2, 2, 2, 1, 1, 0, 2, 2, 1, 1, 1, 0, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 0, 0, 2, 2, 1, 1, 1, 1, 0, 2, 2, 2, 1, 1, 1, 0, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 0, 0, 2, 2, 1, 0, 2, 2, 0, 0, 2, 2, 2, 1, 1, 1, 0, 0, 2, 2, 1, 1, 2, 2, 2, 1, 1, 0, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 0, 2, 2, 1, 2, 2, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 2, 2, 2, 1, 0, 0, 2, 2, 2, 1, 1, 2, 2, 1, 1, 0, 0, 2, 2, 2, 2, 1, 1, 1, 0, 2, 1, 1, 0, 0, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 0, 2, 1, 1, 1, 0, 2, 2, 1, 1, 1, 1, 0, 2, 2, 1, 2, 2, 2, 2, 1, 0, 0, 2, 2, 1, 1, 0, 0, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 0, 2, 2, 2, 2, 1, 1, 1, 0, 2, 2, 1, 1, 1, 0, 2, 2, 2, 1, 1, 1, 0, 2, 2, 1, 1, 0, 0, 2, 2, 2, 1, 1, 1, 1, 0, 0, 2, 2, 1, 1, 1, 0, 0, 2, 2, 1, 0, 2, 2, 1, 0, 2, 2, 0, 0, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 1, 1, 0, 2, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 0, 0, 2, 2, 1, 0, 0, 2, 2, 0, 0, 2, 2, 2, 1, 1, 1, 0, 0, 2, 2, 2, 2, 1, 1, 0, 2, 2, 1, 1, 0, 2, 2, 1, 1, 1, 0, 2, 2, 1, 1, 0, 0, 2, 2, 2, 1, 1, 1, 1, 0, 0, 2, 1, 1, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 1, 1, 0, 0, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 0, 2, 2, 1, 1, 0, 0, 2, 2, 1, 0, 0, 2, 2, 2, 2, 1, 1, 0, 2, 2, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 2, 2, 1, 1, 2, 2, 1, 1, 1, 0, 2, 1, 1, 0, 0, 2, 1, … (It is higly likely that this sequence continues endlessly)

The same thing, when done with the list 3, 1, 2, 0, 0, yields the sequence
3, 3, 3, 1, 1, 1, 2, 2, 2, 0, 0, 3, 1, 1, 2, 2, 0, 0, 1, 1, 1, 2, 0, 0, 0, 3, 3, 0, 0, 3, 1, 1, 3, 3, 3, 1, 1, 1, 0, 0, 0, 3, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 3, 1, 2, 1, 1, 1, 2, 0, 0, 0, 0, 3, 3, 2, 2, 2, 0, 0, 0, 3, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 1, 1, 2, 2, 1, 1, 1, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 3, 1, 1, 2, 2, 0, 0, 3, 1, 1, 0, 0, 3, 3, 1, 1, 1, 1, 1, 2, 0, 0, 0, 3, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 1, 2, 0, 0, 3, 3, 0, 0, 0, 3, 3, 3, 3, 3, 3, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 3, 3, 3, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 3, 3, 0, 0, 3, 3, 1, 1, 3, 3, 1, 1, 2, 2, 0, 0, 0, 3, 3, 3, 1, 1, 1, 2, 0, 0, 3, 3, 1, 1, 2, 2, 2, 2, 2, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 0, 3, 3, 3, 1, 1, 1, 2, 0, 0, 0, 3, 3, 0, 0, 0, 3, 3, 3, 1, 1, 1, 2, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 3, 1, 2, 2, 0, 0, 0, 0, 3, 3, 1, 1, 3, 1, 2, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 3, 3, 3, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 1, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 3, 3, 3, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 3, 3, 3, 2, 2, 2, 0, 0, 0, 0, 0, 0, 3, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 3, 1, 1, 3, 3, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 3, 3, 1, 1, 3, 3, 3, 1, 2, 2, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 3, 3, 1, 1, 0, 0, 0, 0, 3, 1, 1, 2, 2, 0, 0, 3, 3, 3, 1, 2, 0, 0, 0, 0, 0, 0, 3, 1, 2, 2, 0, 0, 0, 3, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 1, 2, 0, 0, 0, 0, 0, 0, 3, 3, 3, 1, 2, 2, 0, 0, 0, 0, 3, 1, 1, 2, 2, 0, 0, 0, 0, 0, 3, 3, 3, 1, 2, 2, 2, 2, 0, 0, 3, 3, 1, 1, 0, 0, 0, 3, 3, 3, 1, 1, 1, 2, 0, 0, 3, 3, 3, 1, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 3, 3, 3, 1, 2, 2, 0, 0, 0, 3, 3, 3, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 3, 1, 2, 2, 0, 0, 0, 0, 0, 3, 3, 3, 1, 1, 1, 2, 0, 0, 0, 0, 3, 3, 1, 1, 0, 0, 0, 3, 3, 3, 1, 2, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 3, 1, 2, 2, 3, 3, 3, 1, 1, 1, 2, 2, 2, 0, 0, 0, 3, 3, 0, 0, 0, 0, 3, 3, 0, 0, 0, 3, 3, 3, 2, 2, 2, 0, 0, 0, 0, 0, 0, 3, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 3, 1, 2, 2, 3, 3, 3, 1, 2, 2, 0, 0, 0, 0, 0, 3, 3, 3, 1, 1, 1, 2, 0, 0, 3, 3, 3, 3, 3, 1, 1, 1, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 3, 1, 1, 2, 0, 0, 3, 3, 1, 1, 2, 2, 2, 2, 2, 0, 0, 0, 3, 3, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 3, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 3, 3, 3, 1, 1, 1, 2, 2, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 0, 3, 3, 1, 2, 0, 0, 0, 3, 3, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 3, 3, 3, 1, 1, 1, 2, 2, 2, 0, 0, 0, 3, 3, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 3, 1, 2, 2, 3, 3, 3, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 3, 1, 2, 0, 0, 3, 3, 1, 1, 2, 2, 0, 0, 0, 3, 1, 2, 2, 3, 3, 3, 1, 1, 1, 2, 0, 0, 0, 3, 3, 1, 1, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 3, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 3, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 3, 1, 2, 0, 0, 0, 0, 0, 3, 1, 2, 2, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, 2, 0, 0, 3, 3, 3, 3, 3, 1, 1, 1, 2, 2, 2, 0, 0, 3, 1, 1, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 3, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 3, 1, 1, 2, 2, 0, 0, 0, 0, 0, 0, 3, 3, 3, 1, …

What is the rule for forming these long sequences from the short lists? Can you continue the sequences?

Hints:

Share:  E-Mail Twitter Facebook LinkedIn Reddit
Contact and legal info | © 2019-03-22 siquod.org

Discussion

No entries yet
Comments have been disabled for this page.