MC: Ping-Pong Cubes

[ijabbott]

To clarify my previous point, I really meant it is not mathematically interesting to me, or just searching for numbers that have some arbitrary property is not interesting to me. I understand some people are interested in finding out the fastest or most efficient ways to search for those numbers on their particular devices. I didn't mean to come across as confrontational.

I suppose the only interesting part to me is whether there are any ping-pong cubes beyond 725^3. Intuitively, they should be less common for larger numbers because there are more digits in the cube that need to alternate their decimal digit even parity. Anyway, I wrote a small C++ program with the GNU MP library for bignum support, and left it running overnight. The first 10 results popped up in a fraction of a second, but it didn't find an 11th result.

Code:

#include <iostream>
#include <gmpxx.h>

using namespace std;

static mpz_class nextpp(mpz_class n)
{
    mpz_class a;
    mpz_class pow = 1;
    mpz_class d;

    n += 2;
    a = n;
    while ((d = (a % 10)) < 2)
    {
        pow *= 10;
        a /= 10;
        if (a >= 10)
        {
            n += pow;
            a += 1;
        }
        else
        {
            break;
        }
    }
    if (a < 10)
    {
        n = a * pow;
        if ((a % 2) == 0)
        {
            pow /= 10;
        }
        else
        {
            pow /= 100;
        }
        while (pow)
        {
            n += pow;
            pow /= 100;
        }
    }
    return n;
}

static bool ispp(mpz_class a)
{
    mpz_class parity = (a % 2);
    
    while (a /= 10)
    {
        if ((a % 2) == parity)
            return false;
        parity = 1 - parity;
    }
    return true;
}

int main()
{
    mpz_class i, cube;
    
    for (i = 10; ; i = nextpp(i))
    {
        cube = i * i * i;
        if (ispp(cube))
            cout << i << " " << cube << "\n";    
    }
    return 0;
}