Logarithmic Fibonacci ? Sounds Crazy !

Computer Science Level 3

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

The answer is 2.

2 solutions

David Holcer
Apr 4, 2015

from math import *
fib=[0,1]
n=10**9
while fib[-1]<n:
    test=fib[-1]+fib[-2]
    if test<n:
        fib.append(test)
    else:
        break
summ=0
for i in fib:
    try:
        if (log(i)/float(log(10))).is_integer():
            summ+=i
    except(ValueError):
        pass
print summ

Just adding a C++ solution here for the sake of variety ( here ).

Prasun Biswas - 5 years, 10 months ago

Kenny Lau
Aug 29, 2014

Java code:

public class brilliant{
    public static void main(String args[]){
        long previous=-1, current=1, next; //these are the -2th and the -1th term
        long sum=0;
        while(current<1000000000){
            next = previous + current;
            previous = current;
            current = next;
            if(Math.log(current)-((int)(Math.log(current)))==0) sum += current;
        }
        System.out.println(sum);
    }
}

Logarithmic Fibonacci ? Sounds Crazy !

The answer is 2.

2 solutions

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