Question

How to find the first 3 integers equal to the sum of their digits raised to some power in C#

Answer 1

using System;
using System.Collections.Generic;

class DigitPower
{
    // compute sum of digits
    static long digitSum(long n)
    {
        long s = 0;

        while (n > 0) {
            s += n % 10;
            n /= 10;
        }

        return s;
    }

    static void Main()
    {
        List<long> results = new List<long>();

        for (long n = 2; results.Count < 3; n++) {
            long s = digitSum(n);

            // Try powers k = 2..10 (enough for reasonable ranges)
            long p = s * s;
            for (int k = 2; k <= 10; k++) {
                if (p == n) {
                    Console.WriteLine($"Found: {n} = ({s})^{k}");
                    results.Add(n);
                    break; // stop checking powers for this n
                }
                p *= s; // next power
            }
        }

        Console.WriteLine("\nFirst 3 numbers:");
        foreach (long x in results) {
            Console.WriteLine(x);
        }
    }
}



/*
run:

Found: 81 = (9)^2
Found: 512 = (8)^3
Found: 2401 = (7)^4

First 3 numbers:
81
512
2401

*/

 

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