Automaticity of the Hankel determinants of difference sequences of the Thue–Morse sequence

Envelope Words and Return Words Sequences in the Period-doubling Sequence

“…(2) The A m locates at [4], [5] followed by A m = B m , so they can't extend to a A m+1 = A m B m . This means, A m+1 occurs exactly twice in A m+1 A m+1 (resp.…”

“…In 1998, Allouche-Peyrière-Wen-Wen [1] proved that all the Hankel determinants of the period-doubling sequence are odd integers. In 2014, Guo-Wen [5] determined the automaticity of the Hankel determinants of difference sequences of the Thue-Morse sequence, including D. In 2015, Parreau-Rigo-Rowland-Vandomme [11] proved that D have 2-abelian complexity sequences that are 2-regular. Fu-Han [4] considered t-extensions of the Hankel determinants of some certain automatic sequences, such as D.…”

On the regularity of {⌊logb⁡(αn+β)⌋

“…Automatic sequence is studied by many authors both in formula language theory and number theory. It has many descriptions [3,8,9,11]. One of them is that its k-kernel is finite.…”

On the rational approximations to the real numbers corresponding to the differences of the Fibonacci sequence

“…We prove that the irrationality exponent is invariant under direct product with a shift of the original Sturmian sequence. Recently, Guo and Wen proved in [16] that all the irrationality exponents of the differences are equal to 2. Recall that the difference of an binary sequence…”