We introduce and study two analogs of Thue-Morse sequence. The first analog is concerned with the parity of number of runs of 1's in the representation of nonnegative integers in binary (or in base $2).$ The second one is connected with the parity of number of 1's in the representation of nonnegative integers in so-called negabinary (or in base $-2).$ We give for them some recurrent and structure formulas and consider several interesting difficult problems.
Families Of Elliptic Curves With The Same Mod 8 Representations
Partitions of the set of nonnegative integers with the same representation functions
Representation of Unity by Binary Forms
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