It is also possible to create the sequence directly from itself. To do this, the first 3 values of the sequence are selected: 1, 2, 2. The last 2 in this start sequence mean that a block of running length 2 should now follow; So you should continue with 1, 1. These two new numbers in the sequence in turn specify that there should now be two blocks of one running length each. So you append 2 and 1 to the sequence, which results in the sequence 1, 2, 2, 1, 1, 2, 1. Then there should be a block with a run length of 2, followed by a block with a run length of 1: 1, 2, 2, 1, 1, 1, 2, 1, 2, 2, 1. This can go on indefinitely.

### Is the Kolakowski sequence periodic?

It’s easy to miss all the letters A and B, but it’s really easy to write down the odd sequence. American mathematician Rufus Oldenburger did this for the first time in 1939, albeit in a very specific context of symbolic dynamics that was not likely to attract the attention of a large number of mathematicians. In turn, the artist William Kolakowski succeeded. Although he was very interested in mathematics and philosophy, he preferred to study art. However, in 1965 he sent a brief note to the Monthly American Mathematics Journal. In it he noted the existence of a series of numbers one and two – which he discovered independently of Oldenburger – and asked for a simple method to be able to describe how this sequence is calculated and whether it is periodic, which entries eventually begin to repeat.

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Whether the Kolakoski sequence, as it is now commonly called, is in fact cyclic or not showing any pattern is still unknown today. It is also unknown, in the finite case of an infinitely long sequence, whether a greater number or two exist in the sum, or whether both are present equally often.

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