1. 

/** * FWP, Ausgewählte Probleme aus dem ACM Programming Contest, SS10  
 * * Problem: 11703 - sqrt log sin
 * * Link: http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&category=117&problem=2750&mosmsg=Submission+received+with+ID+7883709
 * *  
 * * @author Barny Porcio  
 * * @version 1.0, 04/08/2010 
 * *  
 * * Method : Ad-Hoc 
 * * Status : Accepted 
 * * Runtime: 0.776
 * */

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
public class Main {
	public static void main(String[] args) throws Exception, IOException {

		 int[] array = new int[1000001];
			array[0] = 1;
			for(int i = 1;i < array.length; ++i){
				array[i] = (array[(int)(i - Math.sqrt(i))]
				          + array[(int) Math.log(i)]
				          + array[(int)(i* Math.pow(Math.sin(i), 2.0))]) %1000000;
			}	
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		for (int t = Integer.parseInt(br.readLine()); t !=-1 ; t = Integer.parseInt(br.readLine()))
			System.out.println(array[t]);
	}
}


2.

/**
 * FWP, Ausgewählte Probleme aus dem ACM Programming Contest, SS10 
 * Problem: 11703 sqrtlogsin
 * Link: http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&category=117&problem=2750&mosmsg=Submission+received+with+ID+7883453
 * 
 * @author Barny Porcio
 * @version 1.0, 04/08/2010
 * 
 * Method : -
 * Status : Accepted
 * Runtime: 0.9400
 */

import java.util.Scanner;


public class sqrtlogsin11703 {
	//leeres array für die lösung
	static int[] ans;
	
	//das array für die lösung wird gefüllt mit der gegebenen formel
	static void initial(){
		ans[0] = 1;
		for (int i = 1; i <ans.length; ++i){
			ans[i] = (ans[(int) (i-Math.sqrt(i))] + ans[(int) Math.log(i)]+ ans[(int)(i*Math.pow(Math.sin(i), 2))])%1000000 ;
		}
	}
	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		ans =  new int[1000001];
		initial();
		Scanner sc = new Scanner(System.in);
		
		for(int i = sc.nextInt(); i != -1; i = sc.nextInt()){
			System.out.println(ans[i]);
		}

	}

}

3.

/**
 * FWP, Ausgewählte Probleme aus dem ACM Programming Contest, SS10 
 * Problem: 11703 sqrtlogsin
 * Link: http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&category=117&problem=2750&mosmsg=Submission+received+with+ID+7883453
 * 
 * @author Siegfried Ippisch
 * @version 1.0, 06/08/2010
 * 
 * Method : -
 * Status : Accepted
 * Runtime: 0.916
 */

import java.io.*;

public class Main {
	
	private static int[] x = new int[1000001];
	
	private static int x(int i){
		if(x[i] > 0)
			return x[i];
		
		int result = (	x( (int)(i-Math.sqrt(i)) ) +
						x( (int)(Math.log(i)) ) +
						x( (int)(i*Math.sin(i)*Math.sin(i)) )	) %1000000;
		
		x[i] = result;
		
		return result;
	}
	
	public static void main(String[] args) throws IOException{
		BufferedReader input = new BufferedReader(new InputStreamReader(System.in));
		x[0]=1;
					
		int next = Integer.parseInt(input.readLine());
		while(next >= 0){
			System.out.println(x(next));
			next = Integer.parseInt(input.readLine());
		}
		
		input.close();
	}
	
}