Playing with c = (a*b) mod (a+b)

[Eric Angelini]

Hello MathFun & SeqFans,

  Start S = 2, 9,...

Next term is (2*9)mod(2+9)
               18 mod 11 = 7
  S = 2, 9, 7,...

Next term is (9*7)mod(9+7)
               63 mod 16 = 15
  S = 2, 9, 7, 15,...

Next term is (7*15)mod(7+15)
               105 mod 22 = 17
  S = 2, 9, 7, 15, 17,...

Next term is (15*17)mod(15+17)
               255 mod 32 = 31
  S = 2, 9, 7, 15, 17, 31,...

Next term is (17*31)mod(17+31)
               527 mod 48 = 47
 S = 2, 9, 7, 15, 17, 31, 47,...

Does this end in a loop?
If yes, is there another start
which doesn't?

Best,
É.