Kochanski approximates to sqrt(2) starting with R_0=3, S_0=2.

Terms

a(0) =2a(1) =4a(2) =4a(3) =15a(4) =17a(5) =77a(6) =101a(7) =119a(8) =143a(9) =250a(10) =362a(11) =1401a(12) =31168a(13) =88629a(14) =184654a(15) =259251a(16) =298769a(17) =4196069a(18) =38538873a(19) =616984562a(20) =1975413034a(21) =5345718056a(22) =27843871196a(23) =54516286512a(24) =334398528973a(25) =445879679625a(26) =495957494385