On A Family Of 2-Automatic Sequences Derived From Ultimately Periodic Sequences And Generating Algebraic Continued Fractions In F2((1/T))

By replacing the letters to polynomials in F_2[t], an infinite word, over a finite alphabet, can be seen as the sequence of partial quotients of a continued fraction in F_2((1/t)). Here is described a family of such infinite words, corresponding to continued fractions which are algebraic over F_2(t). This family includes a classical example already studied in different previous works by Y. Hu, G-N. Han, Y. Bugeaud and the author of this note.