Logarithmic Fibonacci ? Sounds Crazy !

Fibonacci sequence is defined as F0=0,F1=1F_0=0,F_1=1 and for n2n\geq 2, Fn=Fn1+Fn2F_n=F_{n-1}+F_{n-2}

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

Find the sum of all the Fibonacci numbers FnF_n less than 1 billion\textbf{1 billion} which follow that log10(Fn)Z\log_{10}(F_n) \in \mathbb{Z}

Details and assumptions:-

Fn\bullet \quad F_n denotes nthn^{th} number in the Fibonacci sequence.

log10(Fn)Z\bullet\quad \log_{10}( F_n) \in \mathbb{Z} means that FnF_n is of the form 10k10^k for integer value of kk.


This problem is a part of the set Crazy Fibonacci

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