# Logarithmic Fibonacci ? Sounds Crazy !

Fibonacci sequence is defined as $F_0=0,F_1=1$ and for $n\geq 2$, $F_n=F_{n-1}+F_{n-2}$

Thus, the fibonacci sequence is $0,1,1,2,3,5,8,13,...$

Find the sum of all the Fibonacci numbers $F_n$ less than $\textbf{1 billion}$ which follow that $\log_{10}(F_n) \in \mathbb{Z}$

Details and assumptions:-

$\bullet \quad F_n$ denotes $n^{th}$ number in the Fibonacci sequence.

$\bullet\quad \log_{10}( F_n) \in \mathbb{Z}$ means that $F_n$ is of the form $10^k$ for integer value of $k$.

This problem is a part of the set Crazy Fibonacci

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