Project Euler(49)

Posted on Saturday, May 23rd, 2009 at 5:19 am by Universe Queen

Problem 49:

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?

Answer: 296962999629

Implementation in Java:

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import java.util.*;
 
public class Euler49 
{
	public static boolean isPrime( int number )
	{
		if( number < 2 )
		{
			return false;
		}
		else if ( number == 2 )
		{
			return true;
		}
		else
		{
			for( long i=2; i<=Math.sqrt(number); i++ )
			{
				if( number%i == 0 )
				{
					return false;
				}
			}
		}
 
		return true;
	}
 
	public static boolean isPermutation( int n1, int n2 )
	{
		boolean result = true;
		String s1 = String.valueOf( n1 );
		String s2 = String.valueOf( n2 );
 
		for( int i=0; i<s1.length(); i++ )
		{
			if( !s2.contains( String.valueOf( s1.charAt(i) ) ) )
			{
				result = false;
			}
		}
 
		for( int i=0; i<s2.length(); i++ )
		{
			if( !s1.contains( String.valueOf( s2.charAt(i) ) ) )
			{
				result = false;
			}
		}
 
		return result;
	}
 
	public static void main(String[] args)
	{
		String result = null;
		Set smallerPrimers = new TreeSet();
		boolean find = false;
 
		for( int i=1000; i<10000; i++ )
		{
			if( isPrime(i) )
			{
				Iterator it = smallerPrimers.iterator();
 
				while( it.hasNext() )
				{
					int pre = (Integer)(it.next());
 
					if( isPermutation( pre, i ) )
					{
						int next = i + ( i - pre );
 
						if( isPrime( next ) && isPermutation( i, next ) && next < 10000 )
						{
							result = String.valueOf( pre ) + String.valueOf( i ) + String.valueOf( next );
							find = true;
							break;
						}
					}
				}
 
				if( find && i != 4817 )
				{
					break;
				}
				else
				{
					find = false;
				}
 
				smallerPrimers.add( i );
			}
		}
 
		System.out.println( result );
	}
}

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