f(x)=0 works.
f(x)=e^(x-floor(x)) also works except f' is undefined at the integers.
You can replace floor(x) with ceil(x) or with round(x). The latter shifts the f' problem to the half-integers.
This only works because with f(x)=e^x we have f'(x)=f(x).
For an explanation, refer to the solution submitted by Jer in this location.
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