Using biginteger to find the sequence of sum of powers

Question

Sum(N) =1^1+2^2+3^3+...+N^N

Using Java, How would I use BigInteger to find the smallest integer N such that the value of Sum(N) is larger than 10^20? I'm really stuck,please give me some advice

This is what I have so far:

import java.math.BigInteger;
public class PROJECTV1 {
    public static void main(String [] args) {
        BigInteger bResult= bigFunctionExample_2();
        System.out.println(" => result_got:"+ bResult);
        System.out.println(); //newline
    }// end_main 

    public static BigInteger bigFunctionExample_2() {
        BigInteger bSum = BigInteger.ZERO;
        BigInteger bTmp;
        String sSum;
        // BigInteger bResult =0;
        for (int i=1; ; i++) {
            bTmp = BigInteger.valueOf(i);
            bTmp = bTmp.pow(i); // i^i
            bSum = bSum.add(bTmp); // sum = i^i+ (i-1)^(i-1)+ ....
            sSum = bSum.toString();
            if ( sSum.length() >21) {
                System.out.println("i="+i +" bSum ="+bSum);
                break;
            }//
        }//end_for
        return bSum; // result
    } // end_bigFunctionExample_2
}

Answer 1

Looking at your code, you have a line bTmp.pow(2). That squares the numbers in your series, but you need to raise bTmp to the bTmp power. Java doesn’t seem to want to take a BigInteger as an argument to pow, but you could replace pow with another for loop.

Also, sSum.length() >30 looks like it will only occur if your sum is greater than or equal to 10²⁹. Is there a reason you convert the number to a string each time through the loop, rather than comparing the number to 10²⁰? Perhaps you could put something like bSum > bMax as the test condition in your for loop, rather than leaving it blank and exiting with a break. Then you could make a new BigInteger bMax and set it to 10²⁰ at the start of your code.

For testing, you could set bMax to something small, like 100, and see if your program gives the correct result. You can calculate the first few steps of the series by hand to check your program.