Édouard Lucas (1842 – 1891) is known for improving and expanding the Fibonacci series. Lucas worked in the Paris observatory and later became a professor of mathematics in Paris. Similar to the Fibonacci, the ratio between two consecutive Lucas numbers converges to the golden ratio. Lucas numbers appear in nature often enough to prove that they reflect some naturally occurring patterns.

public class Lucas {
public static void main(String args[]) {
int x,y,z,max; //Declare four integers
x=2;
y=1;
max=10000;
while( max > x ) {
System.out.print(x+", ");
z=x+y;
x=y;
y=z;
}
}
}

Lucas numbers (beginning at 2): L(n) = L(n-1) + L(n-2).