I tried to code John Conway's Subprime Fibs into Mathematica. This is a sequence where each number is the sum of the two previous number, divided by the smallest factor when this sum isn't prime. In the code below everything works correctly except for the recurrence table. The third entry should be 5. Is it me? You can tell me if it is :-)

In[25]:= SD[x_] :=(*smallest divisor not equal to x*)
 If[Or[x == 1, PrimeQ[x]], 1, Divisors[x][[2]]]

SS[x_] := (* x if prime, otherwise x/ smallest prime factor of x *)
   x/SD[x]

In[27]:= S[x_, y_] := 
 SS[x + y] (* x+y devided by it's smallest factor, or itself if prime*)


RecurrenceTable[{a[n + 2] == S[a[n + 1], a[n]], a[1] == 2, 
  a[2] == 3}, a, {n, 10}]

Out[28]= {2, 3, 1, 2, 1, 1, 1, 1, 1, 1}

In[29]:= SD[5]

Out[29]= 1

In[30]:= SS[5]

Out[30]= 5

In[31]:= S[3, 2]

Out[31]= 5