PHI=(1+ Sqrt[5])/2;


f[x_]:=(
a1=-Log[x]/Log[PHI];
a1=Floor[a1];
y=x Power[PHI,a1])


g1[x_]:= -PHI x + PHI

g[x_]:=ss[f[g1[f[x]]]]


ss[w_]:=(
x=Simplify[w];
x1=Expand[Numerator[x]];
x2=Expand[Denominator[x]];
test=x2-Floor[x2];
If[test==0,Simplify[w],s0[w]])

s0[w_]:=(
x=Simplify[w];
x1=Expand[Numerator[x]];
x2=Expand[Denominator[x]];
a1=Coefficient[x2,Sqrt[5],0];
a2=Coefficient[x2,Sqrt[5],1];
x3=a1 - a2 Sqrt[5];
y1=Simplify[x1 x3];
y2=Simplify[x2 x3];
y=Simplify[y1/y2])



PREP[n_]:=(
start=f[n];
start=N[start,400];
X1=Table[Nest[g,start,h],{h,1,80}];
X1=Table[X1[[40+j]],{j,1,40}];
X2=N[X1,20];
X3=Rationalize[X2,.0000001];
d=Length[Union[X3]]
)



RAN0[]:=(
a0=1000 Random[];
a1=Floor[a0];
2 a1)

RAN1[]:=(
a0=1000 Random[];
a1=Floor[a0];
2 a1 + 1)

x=RAN0[] + RAN0[] PHI