Activity: Talk or presentation › Oral presentation
Description
The Thue--Morse sequence t=01101001⋯ is an automatic sequence over the alphabet {0,1}. It can be defined as the binary sum-of-digits function s:N→N, reduced modulo 2, or by using the substitution 0↦01, 1↦10. We prove that the asymptotic density of the set of natural numbers n satisfying t(n^3)=0 equals 1/2.