clear
a = input('start with any number:  ')
b = input('and another number:  ')
N = input('the maximum number of sequence:  ')
x(1) = a;
x(2) = b;
phi(1) = 0;
phi(2) = 1;
I(1) = 1;
I(2) = 2;
for k = 3:N;
    I(k) = k;
    x(k) = x(k-1) + x(k-2);
    phi(k)= x(k)/x(k-1);
end
subplot(211), plot(I,x), grid on, ylabel('x(k)')
subplot(212), plot(I,phi), grid on, xlabel('sequence k'), ylabel('phi')
'and the natural beauty of PHI is' 
format long
PHI = phi(N)