The paper defines a nowhere nonmonotonic function, the argument of which is represented in the \\ Cantorian number system with a sequence of natural bases $(s_k)$, where $s_k=2k+1$:
x=α1s1+α2s1⋅s2+...+αks1⋅s2⋅...⋅sk+...≡Δ(sk)α1α2…αk…,x=α1s1+α2s1⋅s2+...+αks1⋅s2⋅...⋅sk+...≡Δα1α2…αk…(sk),
where $\alpha_k(x) \in A_k \equiv \{0,1,...,s_k-1\}$, $s_k=2k+1$. The value of the function is determined by the chain dependence of the digits of the $Q_s$-image of the number on the digits of the image of the argument and has the following form:
g(x)=g(Δ(sk)α1(x)α2(x)…αk(x)…)=ΔQ3β1β2…βk…,βk∈A3≡{0,1,2},g(x)=g(Δα1(x)α2(x)…αk(x)…(sk))=Δβ1β2…βk…Q3,βk∈A3≡{0,1,2},where $\beta_1=\gamma(\alpha_1)$ and $\beta_k= \gamma(\alpha_k),\:\:\text{if } c_k=0 $ or $\beta_k= 2-\gamma(\alpha_k), \:\:\text{if } c_k\ne 0.$
Also $c_1=c_2=0$, $c_k= c_{k-1},\:\:\text{if }\:\: \alpha_{k-1}\ne \frac{s_{k-1}-1}{2}$ or $ c_k=1-c_{k-1}, \:\:\text{if } \:\:\alpha_{k-1}=\frac{s_{k-1}-1}{2} $ and
$\gamma(\alpha) \in A_3$.
The properties of its levels, differential and fractal properties are described.

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