Equations of the form $t(x+a)=t(x)$ and $t(x+a)=1-t(x)$ for Thue-Morse sequence

Details Equations of the form $t(x+a)=t(x)$ and $t(x+a)=1-t(x)$ for Thue-Morse sequence Equations of the form $t(x+a)=t(x)$ and $t(x+a)=1-t(x)$ for Thue-Morse sequence

2009-07-05

arxiv.org/abs/0907.0880v6

Mathematics

Number Theory

13 pages. Adding a theorem and some references

Scientific paper

For every $a\geq1$ we give a recursion algorithm of building of set of
solutions of equations of the form $t(x+a)=t(x)$ and $t(x+a)=1-t(x),$ where
$\{t(n)\}$ is Thue-Morse sequence. We pose an open problem and two conjectures.

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