Generalized Fibonacci sequences

Any linear recurrence relation yields sequences with many properties in common with the Fibonacci numbers—though with GoldenRatio replaced by other algebraic numbers. The Perrin sequence f[n_]:=f[n-2]+f[n-3]; f[0]=3; f[1]=0; f[2]=2 has the peculiar property that Mod[f[n], n]==0 mostly but not always only for n prime. (For more on recurrence relations see page 128.)