public static long Problem49()
{
/*
* The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.
* There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property, but there is one other 4-digit increasing sequence.
* What 12-digit number do you form by concatenating the three terms in this sequence?
*/
List <long> primes = Formulas.PrimeSieve(10000);
List <long> numbers = new List <long>();
List <string> results = new List <string>();
int limit = 10000;
foreach (long n in primes)
{
if (n > 1000)
{
numbers.Add(n);
}
}
for (int i = 0; i < numbers.Count(); i++)
{
for (int j = i + 1; j < numbers.Count; j++)
{
long k = numbers[j] + (numbers[j] - numbers[i]);
if (k < limit && numbers.Contains(k))
{
if (Formulas.IsPermutation((int)numbers[i], (int)numbers[j]) && Formulas.IsPermutation((int)numbers[i], (int)k))
{
if (numbers[i] != 1487)
{
results.Add(String.Concat(numbers[i], numbers[j], k));
}
}
}
}
}
return(Int64.Parse(results[0]));
}
public static long Problem52()
{
/*
* It can be seen that the number, 125874, and its double, 251748, contain exactly the same digits, but in a different order.
* Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits
*/
int x = 0;
bool ok = true;
do
{
x++;
ok = true;
for (int i = 2; i < 7; i++)
{
if (!Formulas.IsPermutation(x * i, x))
{
ok = false;
}
}
} while (!ok);
return(x);
}