[js8]

Is there, for a given k, an easy to remember sequence (easy to remember algorithm with little state) that has all the k-grams with the same frequency?

For k=1: 01 repeating

For k=2: 0011 repeating

For k=3: 00010111 repeating

[justinpombrio]

They're called De Bruijn sequences[1], and there's an algorithm for constructing them. I'm not sure how easy it is to run in your head, though.

[1] https://en.wikipedia.org/wiki/De_Bruijn_sequence#Algorithm

[WillKirkby]

probably relevant: https://en.wikipedia.org/wiki/De_Bruijn_sequence

edit: dangit, beaten to the punch.