Question

How to find the first power of 2 whose leading digits are 12 in Java

Answer 1

import java.lang.Math;

public class LeadingDigits {

    // return true if 2^n starts with prefix, else false
    static boolean startsWithPrefix(long n, int prefix) {
        final double log2v = Math.log10(2.0);

        double x = n * log2v;
        double frac = x - Math.floor(x);

        // count digits in prefix
        String buf = Integer.toString(prefix);
        int digits = buf.length();

        // compute leading digits 
        int leading = (int) Math.pow(10, frac + digits - 1);

        return leading == prefix;
    }

    public static void main(String[] args) {
        int prefix = 12;

        for (long n = 1; n < Long.MAX_VALUE; n++) {
            if (startsWithPrefix(n, prefix)) {
                System.out.println("First n = " + n);
                System.out.println("2 ^ " + n + " = " + (int) Math.pow(2, n));  
                break;
            }
        }
    }
}


/*
run:

First n = 7
2 ^ 7 = 128

*/

 

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