# Grow in a slow-growing sequence [duplicate]

### Background

There is an interesting question on MathSE about some conjectures that are disproven by extremely large counter-examples. This delightful answer tells the story of a sequence of numbers called Gijswijt's sequence, which is now registered as A090822. The sequence is defined as follows

Let $$\a_1 = 1\$$ and for $$\n>1\$$, set $$\a_n\$$ as the largest integer $$\k\$$, such that the word $$\a_1 a_2 \cdots a_{n-1}\$$ is of the form $$\x y^k\$$ for words $$\x\$$ and $$\y\$$ (where $$\y\$$ has positive length), i.e., the maximal number of repeating blocks at the end of the sequence so far.

I hope it's OK here to copy the demonstration given by Yuriy S: At first it was thought that no number in this sequence exceeds 4, which appears for the first time in $$\n=220\$$. But later, it was proved that we will have a 5 after a very very long time, and the sequence is actually unbounded!

### Challenge

Given the input $$\n\$$ which is a positive integer, print the sequence $$\a_1 a_2\cdots a_n\$$. If you are more comfortable with separating the $$\a_i\$$s by an arbitrary separator, do as you wish.

Standard rules apply. Please let me know if any more clarifications (or maybe test cases) are needed.

• Should I delete my question? – polfosol ఠ_ఠ Sep 23 '20 at 12:53
• I don’t think there’s any need to delete your question, you were just unlucky that it had already been asked before. I’d recommend using the Sandbox next time though – caird coinheringaahing Sep 23 '20 at 12:59