Fibonacci Sequence [1]

Computer Science Level 1

The $n$ th term of sequence can be written as following $F_n = F_{n-1} +F_{n-2}$ , with $F_{1}=1$ and $F_{2}=1$ .

For the question part: $F_{9}=34$ and sum of its digits is 7.

Find the sum of digits of $F_{99}$

Bonus: Can you find the digit sum of $F_{9999}$ ?

The answer is 101.

2 solutions

Amal Hari
Feb 18, 2019

This was part of my assignment but i decided to extend it a bit (You can find $F_{9999}$ using this )

import java.util. ; import java.math. ; public class Fibonacci {

public static void main(String[] args) {
    Scanner in=new Scanner(System.in);
    String dec="Y";
    System.out.println("Enter number of terms in fibonacci sequence:");
    int size=in.nextInt();
    in.nextLine();
    int stop1=0;
    int stopm=0;
    while(stopm==0) {

        while(size>0 && stop1==0) {

            BigInteger[] fibs =new BigInteger[size];
            if (size==1) {
                fibs[0]=BigInteger.valueOf(1);
            }
            else if(size==2) {
                fibs[0]=BigInteger.valueOf(1);
                fibs[1]=BigInteger.valueOf(1);
            }
            else {
                fibs[0]=BigInteger.valueOf(1);
                fibs[1]=BigInteger.valueOf(1);
                int r=2;
                while(r<size) {

                    fibs[r]=fibs[r-1].add(fibs[r-2]);
                    r++;
                }
            }

            System.out.println("The last number of the sequence is "+ fibs[size-1]);
            String g=new String(fibs[size-1].toString());
            int lengthg=g.length();
            int sum=0;
            int start=0;
            while(start<lengthg) {

                sum+= g.charAt(start)-'0' ;
                start++;
            }
            System.out.println("Sum of digits of the number is: "+sum);
            System.out.println("Would you like to continue?(Y/N)");
            dec=in.nextLine();
            if (dec.equals("Y")) {
                System.out.println("Enter size of fibonacci sequence:");
                size=in.nextInt();
                in.nextLine();
            }
            else {
                System.out.println("Bye!");
                stop1=100;
                stopm=1;
            }

        }

    }
    in.close();
}

}

I believe that $F_{9999} = 9385$ . This made me curious about the numbers $n$ which are equal to the digit sum of $F_{n}$ . The list is given here . It's unknown if the list is infinite or not, but the largest known value for $n$ is $2222$ .

Brian Charlesworth - 2 years, 3 months ago

I tried to find one higher than 2222 it seems like a far stretch.

What i found is here

Here is link to the code i used code

Amal Hari - 2 years, 3 months ago

Great! Thanks for working on my follow-up question. :)

Brian Charlesworth - 2 years, 3 months ago

Kyle T
Feb 22, 2019

sum of digits fibonacci 99 equals 101
sum of digits fibonacci 9999 equals 9385

Fibonacci Sequence [1]

The answer is 101.

2 solutions

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