Sum of terms in period of continued fraction for sqrt(a(n)) increases.

Terms

a(0) =2a(1) =3a(2) =5a(3) =6a(4) =7a(5) =11a(6) =13a(7) =18a(8) =19a(9) =22a(10) =31a(11) =43a(12) =46a(13) =61a(14) =67a(15) =94a(16) =109a(17) =127a(18) =139a(19) =151a(20) =166a(21) =199a(22) =211a(23) =214a(24) =271a(25) =301a(26) =331a(27) =379a(28) =454a(29) =526