de Bruijn cycles might be a better starting point --- see OEIS A080679, and https://en.wikipedia.org/wiki/De_Bruijn_sequence WFL On 3/29/18, Henry Baker <hbaker1@pipeline.com> wrote:
Most of the applications in the Wikipedia article on Gray codes consider *fixed length* codes for some length n.
One of the properties of binary gray codes is that substrings of them contain all of the n-bit binary integers, but far more efficiently than simply concatenating all 2^n of them.
I'm interested in a slightly different *infinite* sequence of bits, which contain these n-bit substrings as early as possible, s.t., for any n, there is a function f(n) that tells my how large of an initial substring of this infinite sequence I have to generate in order to make sure that all 2^n binary integers appear at least once.
Furthermore, I may want to "tune" this infinite sequence in order to change the statistics of how frequently all of the different k-bit integers appear, how frequently all of the (k+1)-bit integers appear, etc.
Has anyone studied such sequences?
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