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