The sequence that describes its own runs

Question

A sequence uses only the digits 1 and 2:

2, 2, 1, 1, 2, 1, 2, 2, 1, ?, ?

Find the rule and the next two terms. As a clue, write down the lengths of the runs of equal digits in the sequence and compare with the sequence itself.

Accepted Answer

The run lengths of the sequence are the sequence itself. The next two terms are 2, 2. The rule. Split the sequence into maximal runs of equal digits: (2, 2), (1, 1), (2), (1), (2, 2), (1). Their lengths are 2, 2, 1, 1, 2, 1, which are exactly the first six terms of the sequence. Each term tells you how long the corresponding run is: the first term, 2, says the first run has length 2; the second term, 2, says the second run has length 2; the third term, 1, says the third run has length 1; and so on. Runs alternate between 2s and 1s. Extending it. The seventh term is 2, so the seventh run has l…

The sequence that describes its own runs

Your answer

Discussion

Learn the concepts

Related questions