What your describing is something completely different altogether and it isn't the Pollard rho factoring algorithm;
This is the Pollardrho factoring algorithm;
rho(n)=
{
local(x,y);
x=2; y=5;
while(gcd(yx,n)==1,
x=(x^2+1)%n;
y=(y^2+1)%n; y=(y^2+1)%n
);
gcd(n,yx)
}
