Will that be a small triangle?

Let the three sides of a triangle be integers a,b,ca,b,c respectively, satisfying a>b>ca > b > c and f(3a104)=f(3b104)=f(3c104) f\left (\frac{3^a}{10^4}\right)=f\left (\frac{3^b}{10^4}\right)=f\left(\frac{3^c}{10^4}\right) where f(x)=xxf(x)=x-\lfloor x \rfloor. Find the minimum perimeter of such a triangle.

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