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This is a discrete time process on $\\mathbb{Z}$ defined by parameters $(p_1,\\dots p_M) \\in [0,1]^M$ for some positive integer $M$, where the walker upon the $i$-th visit to $z \\in \\mathbb{Z}$ moves to $z+1$ with probability $p_{i\\pmod M}$, and moves to $z-1$ with probability $1-p_{i \\pmod M}$. We give an explicit formula in terms of the parameters $(p_1,\\dots,p_M)$ which determines whether the walk is recurrent, transient to the left, or transient to the right. 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