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Im looking for a real-entire function* $f(z)$ such that for any (finite) complex $z$ we have both properties at once :
Property 1)
$$ \lim_{t \to +\infty} |f(z+t)| = \infty $$
$$ \lim_{t \to +\infty} f(z-t) = 0 $$
where $t$ is real and
Property 2)
$-1$ is not in the range of $f$:
$$f(z) \ne -1$$
...
